Directionally Paired Principal Component Analysis for Bivariate Estimation Problems

Navdeep Dahiya, Yifei Fan, Samuel Bignardi, Tony Yezzi, Romeil Sandhu

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Auto-TLDR; Asymmetrically-Paired Principal Component Analysis for Linear Dimension-Reduction

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We propose Asymmetrically-Paired Principal Component Analysis (APPCA), a novel linear dimension-reduction model for estimating coupled yet partially available variable sets. Unlike partial least square methods (e.g., partial least square regression and canonical correlation analysis) which maximize correlation/covariance between the two datasets, our APPCA directly minimizes, either conditionally or unconditionally, the reconstruction and prediction errors for the observable and unobservable part, respectively. We demonstrate the optimality of the proposed APPCA approach, we compare and evaluate relevant linear cross-decomposition methods with data reconstruction and prediction experiments on synthetic Gaussian data, multi-target regression datasets and single-channel image datasets. Results show that when only a single pair of bases is allowed, the conditional APPCA achieves lowest reconstruction error on the observable part and the total variable sets as a whole, meanwhile the unconditional APPCA reaches lowest prediction errors on the unobservable part. When extra budget is allowed for the PCA basis of the observable part, one can reach optimal solution using a combine method: standard PCA for the observable part and unconditional APPCA for the unobservable part.

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Dependently Coupled Principal Component Analysis for Bivariate Inversion Problems

Navdeep Dahiya, Yifei Fan, Samuel Bignardi, Tony Yezzi, Romeil Sandhu

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Auto-TLDR; Asymmetric Principal Component Analysis between Paired Data in an Asymmetric manner

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Principal Component Analysis (PCA) is a widely used technique for dimensionality reduction in various problem domains including data compression, image processing, visualization, exploratory data analysis, pattern recognition, time series prediction and machine learning. Often, data is presented in a correlated paired manner such there exists observable and correlated unobservable measurements. Unfortunately, traditional PCA techniques generally fail to optimally capture the leverageable correlations between such paired data as it does not yield a maximally correlated basis between the observable and unobservable counterparts. This instead is the objective of Canonical Correlation Analysis (and the more general Partial Least Squares methods); however, such techniques are still symmetric in maximizing correlation (covariance for PLSR) over all choices of basis for both datasets without differentiating between observable and unobservable variables (except for the regression phase of PLSR). Further, these methods deviate from PCA's formulation objective to minimize approximation error, seeking instead to maximize correlation or covariance. While these are sensible optimization objectives, they are not equivalent to error minimization. We therefore introduce a new method of leveraging PCA between paired datasets in an asymmetric manner which is optimal with respect to approximation error during training. We generate an asymmetrically paired basis for which we relax orthogonality constraints on the orthogonality in decomposing unreliable unobservable measurements. In doing so, this allows us to optimally capture the variations of the observable data while conditionally minimizing the expected prediction error for the unobservable component. We show preliminary results that demonstrate improved learning of our proposed method compared to that of traditional techniques.

Embedding Shared Low-Rank and Feature Correlation for Multi-View Data Analysis

Zhan Wang, Lizhi Wang, Hua Huang

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Auto-TLDR; embedding shared low-rank and feature correlation for multi-view data analysis

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The diversity of multimedia data in the real-world usually forms multi-view features. How to explore the structure information and correlations among multi-view features is still an open problem. In this paper, we propose a novel multi-view subspace learning method, named embedding shared low-rank and feature correlation (ESLRFC), for multi-view data analysis. First, in the embedding subspace, we propose a robust low-rank model on each feature set and enforce a shared low-rank constraint to characterize the common structure information of multiple feature data. Second, we develop an enhanced correlation analysis in the embedding subspace for simultaneously removing the redundancy of each feature set and exploring the correlations of multiple feature data. Finally, we incorporate the low-rank model and the correlation analysis into a unified framework. The shared low-rank constraint not only depicts the data distribution consistency among multiple feature data, but also assists robust subspace learning. Experimental results on recognition tasks demonstrate the superior performance and noise robustness of the proposed method.

Feature Extraction by Joint Robust Discriminant Analysis and Inter-Class Sparsity

Fadi Dornaika, Ahmad Khoder

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Auto-TLDR; Robust Discriminant Analysis with Feature Selection and Inter-class Sparsity (RDA_FSIS)

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Feature extraction methods have been successfully applied to many real-world applications. The classical Linear Discriminant Analysis (LDA) and its variants are widely used as feature extraction methods. Although they have been used for different classification tasks, these methods have some shortcomings. The main one is that the projection axes obtained are not informative about the relevance of original features. In this paper, we propose a linear embedding method that merges two interesting properties: Robust LDA and inter-class sparsity. Furthermore, the targeted projection transformation focuses on the most discriminant original features. The proposed method is called Robust Discriminant Analysis with Feature Selection and Inter-class Sparsity (RDA_FSIS). Two kinds of sparsity are explicitly included in the proposed model. The first kind is obtained by imposing the $\ell_{2,1}$ constraint on the projection matrix in order to perform feature ranking. The second kind is obtained by imposing the inter-class sparsity constraint used for getting a common sparsity structure in each class. Comprehensive experiments on five real-world image datasets demonstrate the effectiveness and advantages of our framework over existing linear methods.

A Globally Optimal Method for the PnP Problem with MRP Rotation Parameterization

Manolis Lourakis, George Terzakis

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Auto-TLDR; A Direct least squares, algebraic PnP solver with modified Rodrigues parameters

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The perspective-n-point (PnP) problem is of fundamental importance in computer vision. A global optimality condition for PnP that is independent of a particular rotation parameterization was recently developed by Nakano. This paper puts forward a direct least squares, algebraic PnP solution that extends Nakano's work by combining his optimality condition with the modified Rodrigues parameters (MRPs) for parameterizing rotation. The result is a system of polynomials that is solved using the Groebner basis approach. An MRP vector has twice the rotational range of the classical Rodrigues (i.e., Cayley) vector used by Nakano to represent rotation. The proposed solver provides strong guarantees that the full rotation singularity associated with MRPs is avoided. Furthermore, detailed experiments provide evidence that our solver attains accuracy that is indistinguishable from Nakano's Cayley-based solution with a moderate increase in computational cost.

Modeling the Distribution of Normal Data in Pre-Trained Deep Features for Anomaly Detection

Oliver Rippel, Patrick Mertens, Dorit Merhof

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Auto-TLDR; Deep Feature Representations for Anomaly Detection in Images

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Anomaly Detection (AD) in images is a fundamental computer vision problem and refers to identifying images and/or image substructures that deviate significantly from the norm. Popular AD algorithms commonly try to learn a model of normality from scratch using task specific datasets, but are limited to semi-supervised approaches employing mostly normal data due to the inaccessibility of anomalies on a large scale combined with the ambiguous nature of anomaly appearance. We follow an alternative approach and demonstrate that deep feature representations learned by discriminative models on large natural image datasets are well suited to describe normality and detect even subtle anomalies. Our model of normality is established by fitting a multivariate Gaussian to deep feature representations of classification networks trained on ImageNet using normal data only in a transfer learning setting. By subsequently applying the Mahalanobis distance as the anomaly score we outperform the current state of the art on the public MVTec AD dataset, achieving an Area Under the Receiver Operating Characteristic curve of 95.8 +- 1.2 % (mean +- SEM) over all 15 classes. We further investigate why the learned representations are discriminative to the AD task using Principal Component Analysis. We find that the principal components containing little variance in normal data are the ones crucial for discriminating between normal and anomalous instances. This gives a possible explanation to the often sub-par performance of AD approaches trained from scratch using normal data only. By selectively fitting a multivariate Gaussian to these most relevant components only, we are able to further reduce model complexity while retaining AD performance. We also investigate setting the working point by selecting acceptable False Positive Rate thresholds based on the multivariate Gaussian assumption.

A Novel Random Forest Dissimilarity Measure for Multi-View Learning

Hongliu Cao, Simon Bernard, Robert Sabourin, Laurent Heutte

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Auto-TLDR; Multi-view Learning with Random Forest Relation Measure and Instance Hardness

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Multi-view learning is a learning task in which data is described by several concurrent representations. Its main challenge is most often to exploit the complementarities between these representations to help solve a classification/regression task. This is a challenge that can be met nowadays if there is a large amount of data available for learning. However, this is not necessarily true for all real-world problems, where data are sometimes scarce (e.g. problems related to the medical environment). In these situations, an effective strategy is to use intermediate representations based on the dissimilarities between instances. This work presents new ways of constructing these dissimilarity representations, learning them from data with Random Forest classifiers. More precisely, two methods are proposed, which modify the Random Forest proximity measure, to adapt it to the context of High Dimension Low Sample Size (HDLSS) multi-view classification problems. The second method, based on an Instance Hardness measurement, is significantly more accurate than other state-of-the-art measurements including the original RF Proximity measurement and the Large Margin Nearest Neighbor (LMNN) metric learning measurement.

Phase Retrieval Using Conditional Generative Adversarial Networks

Tobias Uelwer, Alexander Oberstraß, Stefan Harmeling

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Auto-TLDR; Conditional Generative Adversarial Networks for Phase Retrieval

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In this paper, we propose the application of conditional generative adversarial networks to solve various phase retrieval problems. We show that including knowledge of the measurement process at training time leads to an optimization at test time that is more robust to initialization than existing approaches involving generative models. In addition, conditioning the generator network on the measurements enables us to achieve much more detailed results. We empirically demonstrate that these advantages provide meaningful solutions to the Fourier and the compressive phase retrieval problem and that our method outperforms well-established projection-based methods as well as existing methods that are based on neural networks. Like other deep learning methods, our approach is very robust to noise and can therefore be very useful for real-world applications.

AdaFilter: Adaptive Filter Design with Local Image Basis Decomposition for Optimizing Image Recognition Preprocessing

Aiga Suzuki, Keiichi Ito, Takahide Ibe, Nobuyuki Otsu

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Auto-TLDR; Optimal Preprocessing Filtering for Pattern Recognition Using Higher-Order Local Auto-Correlation

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Image preprocessing is an important process during pattern recognition which increases the recognition performance. Linear convolution filtering is a primary preprocessing method used to enhance particular local patterns of the image which are essential for recognizing the images. However, because of the vast search space of the preprocessing filter, almost no earlier studies have tackled the problem of identifying an optimal preprocessing filter that yields effective features for input images. This paper proposes a novel design method for the optimal preprocessing filter corresponding to a given task. Our method calculates local image bases of the training dataset and represents the optimal filter as a linear combination of these local image bases with the optimized coefficients to maximize the expected generalization performance. Thereby, the optimization problem of the preprocessing filter is converted to a lower-dimensional optimization problem. Our proposed method combined with a higher-order local auto-correlation (HLAC) feature extraction exhibited the best performance both in the anomaly detection task with the conventional pattern recognition algorithm and in the classification task using the deep convolutional neural network compared with typical preprocessing filters.

Verifying the Causes of Adversarial Examples

Honglin Li, Yifei Fan, Frieder Ganz, Tony Yezzi, Payam Barnaghi

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Auto-TLDR; Exploring the Causes of Adversarial Examples in Neural Networks

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The robustness of neural networks is challenged by adversarial examples that contain almost imperceptible perturbations to inputs which mislead a classifier to incorrect outputs in high confidence. Limited by the extreme difficulty in examining a high-dimensional image space thoroughly, research on explaining and justifying the causes of adversarial examples falls behind studies on attacks and defenses. In this paper, we present a collection of potential causes of adversarial examples and verify (or partially verify) them through carefully-designed controlled experiments. The major causes of adversarial examples include model linearity, one-sum constraint, and geometry of the categories. To control the effect of those causes, multiple techniques are applied such as $L_2$ normalization, replacement of loss functions, construction of reference datasets, and novel models using multi-layer perceptron probabilistic neural networks (MLP-PNN) and density estimation (DE). Our experiment results show that geometric factors tend to be more direct causes and statistical factors magnify the phenomenon, especially for assigning high prediction confidence. We hope this paper will inspire more studies to rigorously investigate the root causes of adversarial examples, which in turn provide useful guidance on designing more robust models.

How to Define a Rejection Class Based on Model Learning?

Sarah Laroui, Xavier Descombes, Aurelia Vernay, Florent Villiers, Francois Villalba, Eric Debreuve

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Auto-TLDR; An innovative learning strategy for supervised classification that is able, by design, to reject a sample as not belonging to any of the known classes

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In supervised classification, the learning process typically trains a classifier to optimize the accuracy of classifying data into the classes that appear in the learning set, and only them. While this framework fits many use cases, there are situations where the learning process is knowingly performed using a learning set that only represents the data that have been observed so far among a virtually unconstrained variety of possible samples. It is then crucial to define a classifier which has the ability to reject a sample, i.e., to classify it into a rejection class that has not been yet defined. Although obvious solutions can add this ability a posteriori to a classifier that has been learned classically, a better approach seems to directly account for this requirement in the classifier design. In this paper, we propose an innovative learning strategy for supervised classification that is able, by design, to reject a sample as not belonging to any of the known classes. For that, we rely on modeling each class as the combination of a probability density function (PDF) and a threshold that is computed with respect to the other classes. Several alternatives are proposed and compared in this framework. A comparison with straightforward approaches is also provided.

Soft Label and Discriminant Embedding Estimation for Semi-Supervised Classification

Fadi Dornaika, Abdullah Baradaaji, Youssof El Traboulsi

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Auto-TLDR; Semi-supervised Semi-Supervised Learning for Linear Feature Extraction and Label Propagation

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In recent times, graph-based semi-supervised learning proved to be a powerful paradigm for processing and mining large datasets. The main advantage relies on the fact that these methods can be useful in propagating a small set of known labels to a large set of unlabeled data. The scarcity of labeled data may affect the performance of the semi-learning. This paper introduces a new semi-supervised framework for simultaneous linear feature extraction and label propagation. The proposed method simultaneously estimates a discriminant transformation and the unknown label by exploiting both labeled and unlabeled data. In addition, the unknowns of the learning model are estimated by integrating two types of graph-based smoothness constraints. The resulting semi-supervised model is expected to learn more discriminative information. Experiments are conducted on six public image datasets. These experimental results show that the performance of the proposed method can be better than that of many state-of-the-art graph-based semi-supervised algorithms.

Unveiling Groups of Related Tasks in Multi-Task Learning

Jordan Frecon, Saverio Salzo, Massimiliano Pontil

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Auto-TLDR; Continuous Bilevel Optimization for Multi-Task Learning

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A common approach in multi-task learning is to encourage the tasks to share a low dimensional representation. This has led to the popular method of trace norm regularization, which has proved effective in many applications. In this paper, we extend this approach by allowing the tasks to partition into different groups, within which trace norm regularization is separately applied. We propose a continuous bilevel optimization framework to simultaneously identify groups of related tasks and learn a low dimensional representation within each group. Hinging on recent results on the derivative of generalized matrix functions, we devise a smooth approximation of the upper-level objective via a dual forward-backward algorithm with Bregman distances. This allows us to solve the bilevel problem by a gradient-based scheme. Numerical experiments on synthetic and benchmark datasets support the effectiveness of the proposed method.

Bayesian Active Learning for Maximal Information Gain on Model Parameters

Kasra Arnavaz, Aasa Feragen, Oswin Krause, Marco Loog

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Auto-TLDR; Bayesian assumptions for Bayesian classification

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The fact that machine learning models, despite their advancements, are still trained on randomly gathered data is proof that a lasting solution to the problem of optimal data gathering has not yet been found. In this paper, we investigate whether a Bayesian approach to the classification problem can provide assumptions under which one is guaranteed to perform at least as good as random sampling. For a logistic regression model, we show that maximal expected information gain on model parameters is a promising criterion for selecting samples, assuming that our classification model is well-matched to the data. Our derived criterion is closely related to the maximum model change. We experiment with data sets which satisfy this assumption to varying degrees to see how sensitive our performance is to the violation of our assumption in practice.

Tensorized Feature Spaces for Feature Explosion

Ravdeep Pasricha, Pravallika Devineni, Evangelos Papalexakis, Ramakrishnan Kannan

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Auto-TLDR; Tensor Rank Decomposition for Hyperspectral Image Classification

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In this paper, we present a novel framework that uses tensor factorization to generate richer feature spaces for pixel classification in hyperspectral images. In particular, we assess the performance of different tensor rank decomposition methods as compared to the traditional kernel-based approaches for the hyperspectral image classification problem. We propose ORION, which takes as input a hyperspectral image tensor and a rank and outputs an enhanced feature space from the factor matrices of the decomposed tensor. Our method is a feature explosion technique that inherently maps low dimensional input space in R^K to high dimensional space in R^R, where R >> K, say in the order of 1000x, like a kernel. We show how the proposed method exploits the multi-linear structure of hyperspectral three-dimensional tensor. We demonstrate the effectiveness of our method with experiments on three publicly available hyperspectral datasets with labeled pixels and compare their classification performance against traditional linear and non-linear supervised learning methods such as SVM with Linear, Polynomial, RBF kernels, and the Multi-Layer Perceptron model. Finally, we explore the relationship between the rank of the tensor decomposition and the classification accuracy using several hyperspectral datasets with ground truth.

Feature Extraction and Selection Via Robust Discriminant Analysis and Class Sparsity

Ahmad Khoder, Fadi Dornaika

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Auto-TLDR; Hybrid Linear Discriminant Embedding for supervised multi-class classification

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The main goal of discriminant embedding is to extract features that can be compact and informative representations of the original set of features. This paper introduces a hybrid scheme for linear feature extraction for supervised multi-class classification. We introduce a unifying criterion that is able to retain the advantages of robust sparse LDA and Inter-class sparsity. Thus, the estimated transformation includes two types of discrimination which are the inter-class sparsity and robust Linear Discriminant Analysis with feature selection. In order to optimize the proposed objective function, we deploy an iterative alternating minimization scheme for estimating the linear transformation and the orthogonal matrix. The introduced scheme is generic in the sense that it can be used for combining and tuning many other linear embedding methods. In the lights of the experiments conducted on six image datasets including faces, objects, and digits, the proposed scheme was able to outperform competing methods in most of the cases.

Supervised Domain Adaptation Using Graph Embedding

Lukas Hedegaard, Omar Ali Sheikh-Omar, Alexandros Iosifidis

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Auto-TLDR; Domain Adaptation from the Perspective of Multi-view Graph Embedding and Dimensionality Reduction

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Getting deep convolutional neural networks to perform well requires a large amount of training data. When the available labelled data is small, it is often beneficial to use transfer learning to leverage a related larger dataset (source) in order to improve the performance on the small dataset (target). Among the transfer learning approaches, domain adaptation methods assume that distributions between the two domains are shifted and attempt to realign them. In this paper, we consider the domain adaptation problem from the perspective of multi-view graph embedding and dimensionality reduction. Instead of solving the generalised eigenvalue problem to perform the embedding, we formulate the graph-preserving criterion as loss in the neural network and learn a domain-invariant feature transformation in an end-to-end fashion. We show that the proposed approach leads to a powerful Domain Adaptation framework which generalises the prior methods CCSA and d-SNE, and enables simple and effective loss designs; an LDA-inspired instantiation of the framework leads to performance on par with the state-of-the-art on the most widely used Domain Adaptation benchmarks, Office31 and MNIST to USPS datasets.

MedZip: 3D Medical Images Lossless Compressor Using Recurrent Neural Network (LSTM)

Omniah Nagoor, Joss Whittle, Jingjing Deng, Benjamin Mora, Mark W. Jones

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Auto-TLDR; Recurrent Neural Network for Lossless Medical Image Compression using Long Short-Term Memory

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As scanners produce higher-resolution and more densely sampled images, this raises the challenge of data storage, transmission and communication within healthcare systems. Since the quality of medical images plays a crucial role in diagnosis accuracy, medical imaging compression techniques are desired to reduce scan bitrate while guaranteeing lossless reconstruction. This paper presents a lossless compression method that integrates a Recurrent Neural Network (RNN) as a 3D sequence prediction model. The aim is to learn the long dependencies of the voxel's neighbourhood in 3D using Long Short-Term Memory (LSTM) network then compress the residual error using arithmetic coding. Experiential results reveal that our method obtains a higher compression ratio achieving 15% saving compared to the state-of-the-art lossless compression standards, including JPEG-LS, JPEG2000, JP3D, HEVC, and PPMd. Our evaluation demonstrates that the proposed method generalizes well to unseen modalities CT and MRI for the lossless compression scheme. To the best of our knowledge, this is the first lossless compression method that uses LSTM neural network for 16-bit volumetric medical image compression.

Randomized Transferable Machine

Pengfei Wei, Tze Yun Leong

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Auto-TLDR; Randomized Transferable Machine for Suboptimal Feature-based Transfer Learning

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Feature-based transfer method is one of the most effective methodologies for transfer learning. Existing works usually claim the learned new feature representation is truly \emph{domain-invariant}, and thus directly train a transfer model $\mathcal{M}$ on source domain. In this paper, we work on a more realistic scenario where the new feature representation is suboptimal where small divergence still exists across domains. We propose a new learning strategy and name the transfer model following the learning strategy as Randomized Transferable Machine (RTM). More specifically, we work on source data with the new feature representation learned from existing feature-based transfer methods. Our key idea is to enlarge source training data populations by randomly corrupting source data using some noises, and then train a transfer model $\widetilde{\mathcal{M}}$ performing well on all these corrupted source data populations. In principle, the more corruptions are made, the higher probability of the target data can be covered by the constructed source populations and thus a better transfer performance can be achieved by $\widetilde{\mathcal{M}}$. An ideal case is with infinite corruptions, which however is infeasible in reality. We instead develop a marginalized solution. With a marginalization trick, we can train an RTM that is equivalently trained using infinite source noisy populations without truly conducting any corruption. More importantly, such an RTM has a closed-form solution, which enables a super fast and efficient training. Extensive experiments on various real-world transfer tasks show that RTM is a very promising transfer model.

Computing Stable Resultant-Based Minimal Solvers by Hiding a Variable

Snehal Bhayani, Zuzana Kukelova, Janne Heikkilä

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Auto-TLDR; Sparse Permian-Based Method for Solving Minimal Systems of Polynomial Equations

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Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e., solving minimal problems, in a RANSAC-style framework. Minimal problems often result in complex systems of polynomial equations. The existing state-of-the-art methods for solving such systems are either based on Groebner Basis and the action matrix method, which have been extensively studied and optimized in the recent years or recently proposed approach based on a resultant computation using an extra variable. In this paper, we study an interesting alternative resultant-based method for solving sparse systems of polynomial equations by hiding one variable. This approach results in a larger eigenvalue problem than the action matrix and extra variable resultant-based methods; however, it does not need to compute an inverse or elimination of large matrices that may be numerically unstable. The proposed approach includes several improvements to the standard sparse resultant algorithms, which significantly improves the efficiency and stability of the hidden variable resultant-based solvers as we demonstrate on several interesting computer vision problems. We show that for the studied problems, our sparse resultant based approach leads to more stable solvers than the state-of-the-art Groebner Basis as well as existing resultant-based solvers, especially in close to critical configurations. Our new method can be fully automated and incorporated into existing tools for the automatic generation of efficient minimal solvers.

Automatically Mining Relevant Variable Interactions Via Sparse Bayesian Learning

Ryoichiro Yafune, Daisuke Sakuma, Yasuo Tabei, Noritaka Saito, Hiroto Saigo

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Auto-TLDR; Sparse Bayes for Interpretable Non-linear Prediction

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With the rapid increase in the availability of large amount of data, prediction is becoming increasingly popular, and has widespread through our daily life. However, powerful non- linear prediction methods such as deep learning and SVM suffer from interpretability problem, making it hard to use in domains where the reason for decision making is required. In this paper, we develop an interpretable non-linear model called itemset Sparse Bayes (iSB), which builds a Bayesian probabilistic model, while simultaneously considering variable interactions. In order to suppress the resulting large number of variables, sparsity is imposed on regression weights by a sparsity inducing prior. As a subroutine to search for variable interactions, itemset enumeration algorithm is employed with a novel bounding condition. In computational experiments using real-world dataset, the proposed method performed better than decision tree by 10% in terms of r-squared . We also demonstrated the advantage of our method in Bayesian optimization setting, in which the proposed approach could successfully find the maximum of an unknown function faster than Gaussian process. The interpretability of iSB is naturally inherited to Bayesian optimization, thereby gives us a clue to understand which variables interactions are important in optimizing an unknown function.

Partial Monotone Dependence

Denis Khryashchev, Huy Vo, Robert Haralick

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Auto-TLDR; Partially Monotone Autoregressive Correlation for Time Series Forecasting

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We present a new measure of dependence suitable for time series forecasting: Partially Monotone Correlation (PMC) that generalizes Monotone Correlation. Unlike Monotone Correlation, the new measure of dependence uses piece-wise strictly monotone transformations that increase the value of the correlation coefficient. We explore its properties, its relationship with Monotone and Maximal Correlation, and present an algorithm that calculates it based on the Simultaneous Perturbation Stochastic Approximation method. We also demonstrate how to apply Partially Monotone Correlation for time series analysis and forecasting introducing Partially Monotone Autoregressive model (PMAR) of order 1. Its performance is then evaluated against the baseline of linear and non-linear autoregressive models (AR, LSTAR) on 150 time series produced from 3 datasets: Yellow Taxi pickups, Citi Bike pickups, and Cellular Network hits. Overall, PMAR model outperforms the baseline with the average sMAPE of about 1.7-4% lower.

RSAC: Regularized Subspace Approximation Classifier for Lightweight Continuous Learning

Chih-Hsing Ho, Shang-Ho Tsai

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Auto-TLDR; Regularized Subspace Approximation Classifier for Lightweight Continuous Learning

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Continuous learning seeks to perform the learning on the data that arrives from time to time. While prior works have demonstrated several possible solutions, these approaches require excessive training time as well as memory usage. This is impractical for applications where time and storage are constrained, such as edge computing. In this work, a novel training algorithm, regularized subspace approximation classifier (RSAC), is proposed to achieve lightweight continuous learning. RSAC contains a feature reduction module and classifier module with regularization. Extensive experiments show that RSAC is more efficient than prior continuous learning works and outperforms these works on various experimental settings.

Active Sampling for Pairwise Comparisons via Approximate Message Passing and Information Gain Maximization

Aliaksei Mikhailiuk, Clifford Wilmot, Maria Perez-Ortiz, Dingcheng Yue, Rafal Mantiuk

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Auto-TLDR; ASAP: An Active Sampling Algorithm for Pairwise Comparison Data

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Pairwise comparison data arise in many domains with subjective assessment experiments, for example in image and video quality assessment. In these experiments observers are asked to express a preference between two conditions. However, many pairwise comparison protocols require a large number of comparisons to infer accurate scores, which may be unfeasible when each comparison is time-consuming (e.g. videos) or expensive (e.g. medical imaging). This motivates the use of an active sampling algorithm that chooses only the most informative pairs for comparison. In this paper we propose ASAP, an active sampling algorithm based on approximate message passing and expected information gain maximization. Unlike most existing methods, which rely on partial updates of the posterior distribution, we are able to perform full updates and therefore much improve the accuracy of the inferred scores. The algorithm relies on three techniques for reducing computational cost: inference based on approximate message passing, selective evaluations of the information gain, and selecting pairs in a batch that forms a minimum spanning tree of the inverse of information gain. We demonstrate, with real and synthetic data, that ASAP offers the highest accuracy of inferred scores compared to the existing methods. We also provide an open-source GPU implementation of ASAP for large-scale experiments.

Object Detection on Monocular Images with Two-Dimensional Canonical Correlation Analysis

Zifan Yu, Suya You

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Auto-TLDR; Multi-Task Object Detection from Monocular Images Using Multimodal RGB and Depth Data

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Accurate and robust detection objects from monocular images is a fundamental vision task. This paper describes a novel approach of holistic scene understanding that can simultaneously achieve multiple tasks of scene reconstruction and object detection from a single monocular camera. Rather than pursuing an independent solution for each individual task as most existing work does, we seek a globally optimal solution that holistically resolves the multiple perception and reasoning tasks in an effective manner. The approach explores the complementary properties of multimodal RGB imagery and depth data to improve scene perception tasks. It uniquely combines the techniques of canonical correlation analysis and deep learning to learn the most correlated features to maximize the modal cross-correlation for improving the performance and robustness of object detection in complex environments. Extensive experiments have been conducted to evaluate and demonstrate the performances of the proposed approach.

Temporal Pattern Detection in Time-Varying Graphical Models

Federico Tomasi, Veronica Tozzo, Annalisa Barla

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Auto-TLDR; A dynamical network inference model that leverages on kernels to consider general temporal patterns

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Graphical models allow to describe the interplay among variables of a system through a compact representation, suitable when relations evolve over time. For example, in a biological setting, genes interact differently depending on external environmental or metabolic factors. To incorporate this dynamics a viable strategy is to estimate a sequence of temporally related graphs assuming similarity among samples in different time points. While adjacent time points may direct the analysis towards a robust estimate of the underlying graph, the resulting model will not incorporate long-term or recurrent temporal relationships. In this work we propose a dynamical network inference model that leverages on kernels to consider general temporal patterns (such as circadian rhythms or seasonality). We show how our approach may also be exploited when the recurrent patterns are unknown, by coupling the network inference with a clustering procedure that detects possibly non-consecutive similar networks. Such clusters are then used to build similarity kernels. The convexity of the functional is determined by whether we impose or infer the kernel. In the first case, the optimisation algorithm exploits efficiently proximity operators with closed-form solutions. In the other case, we resort to an alternating minimisation procedure which jointly learns the temporal kernel and the underlying network. Extensive analysis on synthetic data shows the efficacy of our models compared to state-of-the-art methods. Finally, we applied our approach on two real-world applications to show how considering long-term patterns is fundamental to have insights on the behaviour of a complex system.

Minimal Solvers for Indoor UAV Positioning

Marcus Valtonen Örnhag, Patrik Persson, Mårten Wadenbäck, Kalle Åström, Anders Heyden

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Auto-TLDR; Relative Pose Solvers for Visual Indoor UAV Navigation

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In this paper we consider a collection of relative pose problems which arise naturally in applications for visual indoor UAV navigation. We focus on cases where additional information from an onboard IMU is available and thus provides a partial extrinsic calibration through the gravitational vector. The solvers are designed for a partially calibrated camera, for a variety of realistic indoor scenarios, which makes it possible to navigate using images of the ground floor. Current state-of-the-art solvers use more general assumptions, such as using arbitrary planar structures; however, these solvers do not yield adequate reconstructions for real scenes, nor do they perform fast enough to be incorporated in real-time systems. We show that the proposed solvers enjoy better numerical stability, are faster, and require fewer point correspondences, compared to state-of-the-art solvers. These properties are vital components for robust navigation in real-time systems, and we demonstrate on both synthetic and real data that our method outperforms other methods, and yields superior motion estimation.

A Multilinear Sampling Algorithm to Estimate Shapley Values

Ramin Okhrati, Aldo Lipani

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Auto-TLDR; A sampling method for Shapley values for multilayer Perceptrons

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Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data science and machine learning. However, the time complexity to compute Shapley values based on the original formula is exponential, and as the number of features increases, this becomes infeasible. Castro et al. [1] developed a sampling algorithm, to estimate Shapley values. In this work, we propose a new sampling method based on a multilinear extension technique as applied in game theory. The aim is to provide a more efficient (sampling) method for estimating Shapley values. Our method is applicable to any machine learning model, in particular for either multiclass classifications or regression problems. We apply the method to estimate Shapley values for multilayer Perceptrons (MLPs) and through experimentation on two datasets, we demonstrate that our method provides more accurate estimations of the Shapley values by reducing the variance of the sampling statistics

Aggregating Dependent Gaussian Experts in Local Approximation

Hamed Jalali, Gjergji Kasneci

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Auto-TLDR; A novel approach for aggregating the Gaussian experts by detecting strong violations of conditional independence

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Distributed Gaussian processes (DGPs) are prominent local approximation methods to scale Gaussian processes (GPs) to large datasets. Instead of a global estimation, they train local experts by dividing the training set into subsets, thus reducing the time complexity. This strategy is based on the conditional independence assumption, which basically means that there is a perfect diversity between the local experts. In practice, however, this assumption is often violated, and the aggregation of experts leads to sub-optimal and inconsistent solutions. In this paper, we propose a novel approach for aggregating the Gaussian experts by detecting strong violations of conditional independence. The dependency between experts is determined by using a Gaussian graphical model, which yields the precision matrix. The precision matrix encodes conditional dependencies between experts and is used to detect strongly dependent experts and construct an improved aggregation. Using both synthetic and real datasets, our experimental evaluations illustrate that our new method outperforms other state-of-the-art (SOTA) DGP approaches while being substantially more time-efficient than SOTA approaches, which build on independent experts.

Inferring Functional Properties from Fluid Dynamics Features

Andrea Schillaci, Maurizio Quadrio, Carlotta Pipolo, Marcello Restelli, Giacomo Boracchi

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Auto-TLDR; Exploiting Convective Properties of Computational Fluid Dynamics for Medical Diagnosis

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In a wide range of applied problems involving fluid flows, Computational Fluid Dynamics (CFD) provides detailed quantitative information on the flow field, at various levels of fidelity and computational cost. However, CFD alone cannot predict high-level functional properties of the system that are not easily obtained from the equations of fluid motion. In this work, we present a data-driven framework to extract additional information, such as medical diagnostic output, from CFD solutions. The task is made difficult by the huge data dimensionality of CFD, together with the limited amount of training data implied by its high computational cost. By pursuing a traditional ML pipeline of pre-processing, feature extraction, and model training, we demonstrate that informative features can be extracted from CFD data. Two experiments, pertaining to different application domains, support the claim that the convective properties implicit into a CFD solution can be leveraged to retrieve functional information for which an analytical definition is missing. Despite the preliminary nature of our study and the relative simplicity of both the geometrical and CFD models, for the first time we demonstrate that the combination of ML and CFD can diagnose a complex system in terms of high-level functional information.

Total Estimation from RGB Video: On-Line Camera Self-Calibration, Non-Rigid Shape and Motion

Antonio Agudo

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Auto-TLDR; Joint Auto-Calibration, Pose and 3D Reconstruction of a Non-rigid Object from an uncalibrated RGB Image Sequence

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In this paper we present a sequential approach to jointly retrieve camera auto-calibration, camera pose and the 3D reconstruction of a non-rigid object from an uncalibrated RGB image sequence, without assuming any prior information about the shape structure, nor the need for a calibration pattern, nor the use of training data at all. To this end, we propose a Bayesian filtering approach based on a sum-of-Gaussians filter composed of a bank of extended Kalman filters (EKF). For every EKF, we make use of dynamic models to estimate its state vector, which later will be Gaussianly combined to achieve a global solution. To deal with deformable objects, we incorporate a mechanical model solved by using the finite element method. Thanks to these ingredients, the resulting method is both efficient and robust to several artifacts such as missing and noisy observations as well as sudden camera motions, while being available for a wide variety of objects and materials, including isometric and elastic shape deformations. Experimental validation is proposed in real experiments, showing its strengths with respect to competing approaches.

Subspace Clustering Via Joint Unsupervised Feature Selection

Wenhua Dong, Xiaojun Wu, Hui Li, Zhenhua Feng, Josef Kittler

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Auto-TLDR; Unsupervised Feature Selection for Subspace Clustering

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Any high-dimensional data arising from practical applications usually contains irrelevant features, which may impact on the performance of existing subspace clustering methods. This paper proposes a novel subspace clustering method, which reconstructs the feature matrix by the means of unsupervised feature selection (UFS) to achieve a better dictionary for subspace clustering (SC). Different from most existing clustering methods, the proposed approach uses a reconstructed feature matrix as the dictionary rather than the original data matrix. As the feature matrix reconstructed by representative features is more discriminative and closer to the ground-truth, it results in improved performance. The corresponding non-convex optimization problem is effectively solved using the half-quadratic and augmented Lagrange multiplier methods. Extensive experiments on four real datasets demonstrate the effectiveness of the proposed method.

End-To-End Multi-Task Learning of Missing Value Imputation and Forecasting in Time-Series Data

Jinhee Kim, Taesung Kim, Jang-Ho Choi, Jaegul Choo

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Auto-TLDR; Time-Series Prediction with Denoising and Imputation of Missing Data

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Multivariate time-series prediction is a common task, but it often becomes challenging due to missing values involved in data caused by unreliable sensors and other issues. In fact, inaccurate imputation of missing values can degrade the downstream prediction performance, so it may be better not to rely on the estimated values of missing data. Furthermore, observed data may contain noise, so denoising them can be helpful for the main task at hand. In response, we propose a novel approach that can automatically utilize the optimal combination of the observed and the estimated values to generate not only complete, but also noise-reduced data by our own gating mechanism. We evaluate our model on real-world time-series datasets and achieved state-of-the-art performance, demonstrating that our method successfully handle the incomplete datasets. Moreover, we present in-depth studies using a carefully designed, synthetic multivariate time-series dataset to verify the effectiveness of the proposed model. The ablation studies and the experimental analysis of the proposed gating mechanism show that the proposed method works as an effective denoising as well as imputation method for time-series classification tasks.

Adversarial Encoder-Multi-Task-Decoder for Multi-Stage Processes

Andre Mendes, Julian Togelius, Leandro Dos Santos Coelho

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Auto-TLDR; Multi-Task Learning and Semi-Supervised Learning for Multi-Stage Processes

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In multi-stage processes, decisions occur in an ordered sequence of stages. Early stages usually have more observations with general information (easier/cheaper to collect), while later stages have fewer observations but more specific data. This situation can be represented by a dual funnel structure, in which the sample size decreases from one stage to the other while the information increases. Training classifiers in this scenario is challenging since information in the early stages may not contain distinct patterns to learn (underfitting). In contrast, the small sample size in later stages can cause overfitting. We address both cases by introducing a framework that combines adversarial autoencoders (AAE), multi-task learning (MTL), and multi-label semi-supervised learning (MLSSL). We improve the decoder of the AAE with an MTL component so it can jointly reconstruct the original input and use feature nets to predict the features for the next stages. We also introduce a sequence constraint in the output of an MLSSL classifier to guarantee the sequential pattern in the predictions. Using real-world data from different domains (selection process, medical diagnosis), we show that our approach outperforms other state-of-the-art methods.

The Surprising Effectiveness of Linear Unsupervised Image-to-Image Translation

Eitan Richardson, Yair Weiss

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Auto-TLDR; linear encoder-decoder architectures for unsupervised image-to-image translation

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Unsupervised image-to-image translation is an inherently ill-posed problem. Recent methods based on deep encoder-decoder architectures have shown impressive results, but we show that they only succeed due to a strong locality bias, and they fail to learn very simple nonlocal transformations (e.g. mapping upside down faces to upright faces). When the locality bias is removed, the methods are too powerful and may fail to learn simple local transformations. In this paper we introduce linear encoder-decoder architectures for unsupervised image to image translation. We show that learning is much easier and faster with these architectures and yet the results are surprisingly effective. In particular, we show a number of local problems for which the results of the linear methods are comparable to those of state-of-the-art architectures but with a fraction of the training time, and a number of nonlocal problems for which the state-of-the-art fails while linear methods succeed.

Dimensionality Reduction for Data Visualization and Linear Classification, and the Trade-Off between Robustness and Classification Accuracy

Martin Becker, Jens Lippel, Thomas Zielke

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Auto-TLDR; Robustness Assessment of Deep Autoencoder for Data Visualization using Scatter Plots

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This paper has three intertwined goals. The first is to introduce a new similarity measure for scatter plots. It uses Delaunay triangulations to compare two scatter plots regarding their relative positioning of clusters. The second is to apply this measure for the robustness assessment of a recent deep neural network (DNN) approach to dimensionality reduction (DR) for data visualization. It uses a nonlinear generalization of Fisher's linear discriminant analysis (LDA) as the encoder network of a deep autoencoder (DAE). The DAE's decoder network acts as a regularizer. The third goal is to look at different variants of the DNN: ones that promise robustness and ones that promise high classification accuracies. This is to study the trade-off between these two objectives -- our results support the recent claim that robustness may be at odds with accuracy; however, results that are balanced regarding both objectives are achievable. We see a restricted Boltzmann machine (RBM) pretraining and the DAE based regularization as important building blocks for achieving balanced results. As a means of assessing the robustness of DR methods, we propose a measure that is based on our similarity measure for scatter plots. The robustness measure comes with a superimposition view of Delaunay triangulations, which allows a fast comparison of results from multiple DR methods.

Are Multiple Cross-Correlation Identities Better Than Just Two? Improving the Estimate of Time Differences-Of-Arrivals from Blind Audio Signals

Danilo Greco, Jacopo Cavazza, Alessio Del Bue

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Auto-TLDR; Improving Blind Channel Identification Using Cross-Correlation Identity for Time Differences-of-Arrivals Estimation

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Given an unknown audio source, the estimation of time differences-of-arrivals (TDOAs) can be efficiently and robustly solved using blind channel identification and exploiting the cross-correlation identity (CCI). Prior "blind" works have improved the estimate of TDOAs by means of different algorithmic solutions and optimization strategies, while always sticking to the case N = 2 microphones. But what if we can obtain a direct improvement in performance by just increasing N? In this paper we try to investigate this direction, showing that, despite the arguable simplicity, this is capable of (sharply) improving upon state-of-the-art blind channel identification methods based on CCI, without modifying the computational pipeline. Inspired by our results, we seek to warm up the community and the practitioners by paving the way (with two concrete, yet preliminary, examples) towards joint approaches in which advances in the optimization are combined with an increased number of microphones, in order to achieve further improvements.

Supervised Feature Embedding for Classification by Learning Rank-Based Neighborhoods

Ghazaal Sheikhi, Hakan Altincay

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Auto-TLDR; Supervised Feature Embedding with Representation Learning of Rank-based Neighborhoods

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In feature embedding, the recovery of associated discriminative information in the reduced subspace is critical for downstream classifiers. In this study, a supervised feature embedding method is proposed inspired by the well-known word embedding technique, word2vec. Proposed embedding method is implemented as representative learning of rank-based neighborhoods. The notion of context words in word2vec is extended into neighboring instances within a given window. Neighborship is defined using ranks of instances rather than their values so that regions with different densities are captured properly. Each sample is represented by a unique one-hot vector whereas its neighbors are encoded by several two-hot vectors. The two-hot vectors are identical for neighboring samples of the same class. A feed-forward neural network with a continuous projection layer, then learns the mapping from one-hot vectors to multiple two-hot vectors. The hidden layer determines the reduced subspace for the train samples. The obtained transformation is then applied on test data to find a lower-dimensional representation. Proposed method is tested in classification problems on 10 UCI data sets. Experimental results confirm that the proposed method is effective in finding a discriminative representation of the features and outperforms several supervised embedding approaches in terms of classification performance.

Scalable Direction-Search-Based Approach to Subspace Clustering

Yicong He, George Atia

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Auto-TLDR; Fast Direction-Search-Based Subspace Clustering

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Subspace clustering finds a multi-subspace representation that best fits a high-dimensional dataset. The computational and storage complexities of existing algorithms limit their usefulness for large scale data. In this paper, we develop a novel scalable approach to subspace clustering termed Fast Direction-Search-Based Subspace Clustering (Fast DiSC). In sharp contrast to existing scalable solutions which are mostly based on the self-expressiveness property of the data, Fast DiSC rests upon a new representation obtained from projections on computed data-dependent directions. These directions are derived from a convex formulation for optimal direction search to gauge hidden similarity relations. The computational complexity is significantly reduced by performing direction search in partitions of sampled data, followed by a retrieval step to cluster out-of-sample data using projections on the computed directions. A theoretical analysis underscores the ability of the proposed formulation to construct local similarity relations for the different data points. Experiments on both synthetic and real data demonstrate that the proposed algorithm can often outperform the state-of-the-art clustering methods.

Mean Decision Rules Method with Smart Sampling for Fast Large-Scale Binary SVM Classification

Alexandra Makarova, Mikhail Kurbakov, Valentina Sulimova

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Auto-TLDR; Improving Mean Decision Rule for Large-Scale Binary SVM Problems

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This paper relies on the Mean Decision Rule (MDR) method for solving large-scale binary SVM problems. It consists in taking small random samples of the full dataset and separate training for each of them with consecutive averaging the respective individual decision rules to obtain a final one. This paper proposes two new approaches to improve it. The first proposed approach is a new sampling technique that exploits SVM and MDR properties to fast form so called smart samples by selecting only the objects, that are candidates to be the support ones. The proposed technique essentially increases MDR convergence and allows to reach the highest quality in less time. In the case of kernel-based MDR (KMDR) the proposed sampling technique allows additionally to reduce the number of support objects in the final decision rule and, as a result, to decrease the recognition time. The second proposed approach is a new data strategy to accelerate random access to large datasets stored in the traditional libsvm format. The proposed strategy allows to quickly extract random subsets of objects from a file and load them into RAM, and is it also suitable for any sampling-based methods, including stochastic gradient methods. Joint using of the proposed approaches with (K)MDR allows to obtain the best (or near the best) decision of large-scale binary SVM problems faster, compared to the existing SVM solvers.

Naturally Constrained Online Expectation Maximization

Daniela Pamplona, Antoine Manzanera

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Auto-TLDR; Constrained Online Expectation-Maximization for Probabilistic Principal Components Analysis

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With the rise of big data sets, learning algorithms must be adapted to piece-wise mechanisms in order to tackle time and memory costs of large scale calculations. Furthermore, for most learning embedded systems the input data are fed in a sequential and contingent manner: one by one, and possibly class by class. Thus, learning algorithms should not only run online but cope with time-varying, non-independent, and non-balanced training data for the system's entire life. Online Expectation-Maximization is a well-known algorithm for learning probabilistic models in real-time, due to its simplicity and convergence properties. However, these properties are only valid in the case of large, independent and identically distributed (iid) samples. In this paper, we propose to constraint the online Expectation-Maximization on the Fisher distance between the parameters. After the presentation of the algorithm, we make a thorough study of its use in Probabilistic Principal Components Analysis. First, we derive the update rules, then we analyse the effect of the constraint on major problems of online and sequential learning: convergence, forgetting and interference. Furthermore we use several algorithmic protocols: iid {\em vs} sequential data, and constraint parameters updated step-wise {\em vs} class-wise. Our results show that this constraint increases the convergence rate of online Expectation-Maximization, decreases forgetting and slightly introduces transfer learning.

Relative Feature Importance

Gunnar König, Christoph Molnar, Bernd Bischl, Moritz Grosse-Wentrup

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Auto-TLDR; Relative Feature Importance for Interpretable Machine Learning

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Interpretable Machine Learning (IML) methods are used to gain insight into the relevance of a feature of interest for the performance of a model. Commonly used IML methods differ in whether they consider features of interest in isolation, e.g., Permutation Feature Importance (PFI), or in relation to all remaining feature variables, e.g., Conditional Feature Importance (CFI). As such, the perturbation mechanisms inherent to PFI and CFI represent extreme reference points. We introduce Relative Feature Importance (RFI), a generalization of PFI and CFI that allows for a more nuanced feature importance computation beyond the PFI versus CFI dichotomy. With RFI, the importance of a feature relative to any other subset of features can be assessed, including variables that were not available at training time. We derive general interpretation rules for RFI based on a detailed theoretical analysis of the implications of relative feature relevance, and demonstrate the method's usefulness on simulated examples.

3CS Algorithm for Efficient Gaussian Process Model Retrieval

Fabian Berns, Kjeld Schmidt, Ingolf Bracht, Christian Beecks

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Auto-TLDR; Efficient retrieval of Gaussian Process Models for large-scale data using divide-&-conquer-based approach

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Gaussian Process Models (GPMs) have been applied for various pattern recognition tasks due to their analytical tractability, ability to quantify uncertainty for their own results as well as to subsume prominent other regression techniques. Despite these promising prospects their super-quadratic computation time complexity for model selection and evaluation impedes its broader application for more than a few thousand data points. Although there have been many proposals towards Gaussian Processes for large-scale data, those only offer a linearly scaling improvement to a cubical scaling problem. In particular, solutions like the Nystrom approximation or sparse matrices are only taking fractions of the given data into account and subsequently lead to inaccurate models. In this paper, we thus propose a divide-&-conquer-based approach, that allows to efficiently retrieve GPMs for large-scale data. The resulting model is composed of independent pattern representations for non-overlapping segments of the given data and consequently reduces computation time significantly. Our performance analysis indicates that our proposal is able to outperform state-of-the-art algorithms for GPM retrieval with respect to the qualities of efficiency and accuracy.

Killing Four Birds with One Gaussian Process: The Relation between Different Test-Time Attacks

Kathrin Grosse, Michael Thomas Smith, Michael Backes

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Auto-TLDR; Security of Gaussian Process Classifiers against Attack Algorithms

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In machine learning (ML) security, attacks like evasion, model stealing or membership inference are generally studied in individually. Previous work has also shown a relationship between some attacks and decision function curvature of the targeted model. Consequently, we study an ML model allowing direct control over the decision surface curvature: Gaussian Process classifiers (GPCs). For evasion, we find that changing GPC's curvature to be robust against one attack algorithm boils down to enabling a different norm or attack algorithm to succeed. This is backed up by our formal analysis showing that static security guarantees are opposed to learning. Concerning intellectual property, we show formally that lazy learning does not necessarily leak all information when applied. In practice, often a seemingly secure curvature can be found. For example, we are able to secure GPC against empirical membership inference by proper configuration. In this configuration, however, the GPC's hyper-parameters are leaked, e.g. model reverse engineering succeeds. We conclude that attacks on classification should not be studied in isolation, but in relation to each other.

Camera Calibration Using Parallel Line Segments

Gaku Nakano

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Auto-TLDR; Closed-Form Calibration of Surveillance Cameras using Parallel 3D Line Segment Projections

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This paper proposes a camera calibration method suitable for surveillance cameras using the image projection of parallel 3D line segments of the same length. We assume that vertical line segments are perpendicular to the ground plane and their bottom end-points are on the ground plane. Under this assumption, the camera parameters can be directly solved by at least two line segments without estimating vanishing points. Extending the minimal solution, we derive a closed-form solution to the least squares case with more than two line segments. Lens distortion is jointly optimized in bundle adjustment. Synthetic data evaluation shows that the best depression angle of a camera is around 50 degrees. In real data evaluation, we use body joints of pedestrians as vertical line segments. The experimental results on publicly available datasets show that the proposed method with a human pose detector can correctly calibrate wide-angle cameras including radial distortion.

Trainable Spectrally Initializable Matrix Transformations in Convolutional Neural Networks

Michele Alberti, Angela Botros, Schuetz Narayan, Rolf Ingold, Marcus Liwicki, Mathias Seuret

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Auto-TLDR; Trainable and Spectrally Initializable Matrix Transformations for Neural Networks

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In this work, we introduce a new architectural component to Neural Networks (NN), i.e., trainable and spectrally initializable matrix transformations on feature maps. While previous literature has already demonstrated the possibility of adding static spectral transformations as feature processors, our focus is on more general trainable transforms. We study the transforms in various architectural configurations on four datasets of different nature: from medical (ColorectalHist, HAM10000) and natural (Flowers) images to historical documents (CB55). With rigorous experiments that control for the number of parameters and randomness, we show that networks utilizing the introduced matrix transformations outperform vanilla neural networks. The observed accuracy increases appreciably across all datasets. In addition, we show that the benefit of spectral initialization leads to significantly faster convergence, as opposed to randomly initialized matrix transformations. The transformations are implemented as auto-differentiable PyTorch modules that can be incorporated into any neural network architecture. The entire code base is open-source.

Sparse-Dense Subspace Clustering

Shuai Yang, Wenqi Zhu, Yuesheng Zhu

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Auto-TLDR; Sparse-Dense Subspace Clustering with Piecewise Correlation Estimation

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Subspace clustering refers to the problem of clustering high-dimensional data into a union of low-dimensional subspaces. Current subspace clustering approaches are usually based on a two-stage framework. In the first stage, an affinity matrix is generated from data. In the second one, spectral clustering is applied on the affinity matrix. However, the affinity matrix produced by two-stage methods cannot fully reveal the similarity between data points from the same subspace, resulting in inaccurate clustering. Besides, most approaches fail to solve large-scale clustering problems due to poor efficiency. In this paper, we first propose a new scalable sparse method called Iterative Maximum Correlation (IMC) to learn the affinity matrix from data. Then we develop Piecewise Correlation Estimation (PCE) to densify the intra-subspace similarity produced by IMC. Finally we extend our work into a Sparse-Dense Subspace Clustering (SDSC) framework with a dense stage to optimize the affinity matrix for two-stage methods. We show that IMC is efficient for large-scale tasks, and PCE ensures better performance for IMC. We show the universality of our SDSC framework for current two-stage methods as well. Experiments on benchmark data sets demonstrate the effectiveness of our approaches.

Q-SNE: Visualizing Data Using Q-Gaussian Distributed Stochastic Neighbor Embedding

Motoshi Abe, Junichi Miyao, Takio Kurita

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Auto-TLDR; Q-Gaussian distributed stochastic neighbor embedding for 2-dimensional mapping and classification

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The dimensionality reduction has been widely introduced to use the high-dimensional data for regression, classification, feature analysis, and visualization. As the one technique of dimensionality reduction, a stochastic neighbor embedding (SNE) was introduced. The SNE leads powerful results to visualize high-dimensional data by considering the similarity between the local Gaussian distributions of high and low-dimensional space. To improve the SNE, a t-distributed stochastic neighbor embedding (t-SNE) was also introduced. To visualize high-dimensional data, the t-SNE leads to more powerful and flexible visualization on 2 or 3-dimensional mapping than the SNE by using a t-distribution as the distribution of low-dimensional data. Recently, Uniform manifold approximation and projection (UMAP) is proposed as a dimensionality reduction technique. We present a novel technique called a q-Gaussian distributed stochastic neighbor embedding (q-SNE). The q-SNE leads to more powerful and flexible visualization on 2 or 3-dimensional mapping than the t-SNE and the SNE by using a q-Gaussian distribution as the distribution of low-dimensional data. The q-Gaussian distribution includes the Gaussian distribution and the t-distribution as the special cases with q=1.0 and q=2.0. Therefore, the q-SNE can also express the t-SNE and the SNE by changing the parameter q, and this makes it possible to find the best visualization by choosing the parameter q. We show the performance of q-SNE as visualization on 2-dimensional mapping and classification by k-Nearest Neighbors (k-NN) classifier in embedded space compared with SNE, t-SNE, and UMAP by using the datasets MNIST, COIL-20, OlivettiFaces, FashionMNIST, and Glove.

Watermelon: A Novel Feature Selection Method Based on Bayes Error Rate Estimation and a New Interpretation of Feature Relevance and Redundancy

Xiang Xie, Wilhelm Stork

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Auto-TLDR; Feature Selection Using Bayes Error Rate Estimation for Dynamic Feature Selection

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Feature selection has become a crucial part of many classification problems in which high-dimensional datasets may contain tens of thousands of features. In this paper, we propose a novel feature selection method scoring the features through estimating the Bayes error rate based on kernel density estimation. Additionally, we update the scores of features dynamically by quantitatively interpreting the effects of feature relevance and redundancy in a new way. Distinguishing from the common heuristic applied by many feature selection methods, which prefers choosing features that are not relevant to each other, our approach penalizes only monotonically correlated features and rewards any other kind of relevance among features based on Spearman’s rank correlation coefficient and normalized mutual information. We conduct extensive experiments on seventeen diverse classification benchmarks, the results show that our approach overperforms other seventeen popular state-of-the-art feature selection methods in most cases.