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A Randomized Algorithm for Sparse Recovery

Huiyuan Yu, Maggie Cheng, Yingdong Lu

Auto-TLDR; A Constrained Graph Optimization Algorithm for Sparse Signal Recovery

Abstract Poster

This paper considers the problem of sparse signal recovery where there is a structure in the signal. Efficient recovery schemes can be designed to leverage the signal structure. Following the model-based compressive sensing framework, we have developed an efficient algorithm for both head and tail approximations for the model-projection problem. The problem is modeled as a constrained graph optimization problem, which is an NP-hard optimization problem. Solving the NP-hard optimization program is then transformed to solving a linear program and finding a randomized algorithm to find an integral solution. The integral solution is optimal-in-expectation. The algorithm is proved to have the same geometric convergence as previous work. The algorithm has been tested on various compressing matrices. It worked well with the matrices with the Restricted Isometry Property (RIP), also worked well with some matrices that have not been shown to have RIP. The proposed algorithm demonstrated improved recoverability and used fewer number of iterations to recover the signal.

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Classification and Feature Selection Using a Primal-Dual Method and Projections on Structured Constraints

Michel Barlaud, Antonin Chambolle, Jean_Baptiste Caillau

Auto-TLDR; A Constrained Primal-dual Method for Structured Feature Selection on High Dimensional Data

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This paper deals with feature selection using supervised classification on high dimensional datasets. A classical approach is to project data on a low dimensional space and classify by minimizing an appropriate quadratic cost. Our first contribution is to introduce a matrix of centers in the definition of this cost. Moreover, as quadratic costs are not robust to outliers, we propose to use an $\ell_1$ cost instead (or Huber loss to mitigate overfitting issues). While control on sparsity is commonly obtained by adding an $\ell_1$ constraint on the vectorized matrix of weights used for projecting the data, our second contribution is to enforce structured sparsity. To this end we propose constraints that take into account the matrix structure of the data, based either on the nuclear norm, on the $\ell_{2,1}$ norm, or on the $\ell_{1,2}$ norm for which we provide a new projection algorithm. We optimize simultaneously the projection matrix and the matrix of centers thanks to a new tailored constrained primal-dual method. The primal-dual framework is general enough to encompass the various robust losses and structured constraints we use, and allows a convergence analysis. We demonstrate the effectiveness of the approach on three biological datasets. Our primal-dual method with robust losses, adaptive centers and structured constraints does significantly better than classical methods, both in terms of accuracy and computational time.

Cluster-Size Constrained Network Partitioning

Maksim Mironov, Konstantin Avrachenkov

Auto-TLDR; Unsupervised Graph Clustering with Stochastic Block Model

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In this paper we consider a graph clustering problem with a given number of clusters and approximate desired sizes of the clusters. One possible motivation for such task could be the problem of databases or servers allocation within several given large computational clusters, where we want related objects to share the same cluster in order to minimize latency and transaction costs. This task differs from the original community detection problem, though we adopt some ideas from Glauber Dynamics and Label Propagation Algorithm. At the same time we consider no additional information about node labels, so the task has nature of unsupervised learning. We propose an algorithm for the problem, show that it works well for a large set of parameters of Stochastic Block Model (SBM) and theoretically show its running time complexity for achieving almost exact recovery is of $O(n\cdot\deg_{av} \cdot \omega )$ for the mean-field SBM with $\omega$ tending to infinity arbitrary slow. Other significant advantage of the proposed approach is its local nature, which means it can be efficiently distributed with no scheduling or synchronization.

Learning Sign-Constrained Support Vector Machines

Kenya Tajima, Kouhei Tsuchida, Esmeraldo Ronnie Rey Zara, Naoya Ohta, Tsuyoshi Kato

Auto-TLDR; Constrained Sign Constraints for Learning Linear Support Vector Machine

Abstract Poster Similar

Domain knowledge is useful to improve the generalization performance of learning machines. Sign constraints are a handy representation to combine domain knowledge with learning machine. In this paper, we consider constraining the signs of the weight coefficients in learning the linear support vector machine, and develop two optimization algorithms for minimizing the empirical risk under the sign constraints. One of the two algorithms is based on the projected gradient method, in which each iteration of the projected gradient method takes O(nd) computational cost and the sublinear convergence of the objective error is guaranteed. The second algorithm is based on the Frank-Wolfe method that also converges sublinearly and possesses a clear termination criterion. We show that each iteration of the Frank-Wolfe also requires O(nd) cost. Furthermore, we derive the explicit expression for the minimal iteration number to ensure an epsilon-accurate solution by analyzing the curvature of the objective function. Finally, we empirically demonstrate that the sign constraints are a promising technique when similarities to the training examples compose the feature vector.

2D Discrete Mirror Transform for Image Non-Linear Approximation

Alessandro Gnutti, Fabrizio Guerrini, Riccardo Leonardi

Auto-TLDR; Discrete Mirror Transform (DMT)

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In this paper, a new 2D transform named Discrete Mirror Transform (DMT) is presented. The DMT is computed by decomposing a signal into its even and odd parts around an optimal location in a given direction so that the signal energy is maximally split between the two components. After minimizing the information required to regenerate the original signal by removing redundant structures, the process is iterated leading the signal energy to distribute into a continuously smaller set of coefficients. The DMT can be displayed as a binary tree, where each node represents the single (even or odd) signal derived from the decomposition in the previous level. An optimized version of the DMT (ODMT) is also introduced, by exploiting the possibility to choose different directions at which performing the decomposition. Experimental simulations have been carried out in order to test the sparsity properties of the DMT and ODMT when applied on images: referring to both transforms, the results show a superior performance with respect to the popular Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) in terms of non-linear approximation.

Scalable Direction-Search-Based Approach to Subspace Clustering

Yicong He, George Atia

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.

Wasserstein k-Means with Sparse Simplex Projection

Takumi Fukunaga, Hiroyuki Kasai

Auto-TLDR; SSPW $k$-means: Sparse Simplex Projection-based Wasserstein $ k$-Means Algorithm

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This paper presents a proposal of a faster Wasserstein $k$-means algorithm for histogram data by reducing Wasserstein distance computations exploiting sparse simplex projection. We shrink data samples, centroids and ground cost matrix, which enables significant reduction of the computations to solve optimal transport problems without loss of clustering quality. Furthermore, we dynamically reduce computational complexity by removing lower-valued data samples harnessing sparse simplex projection while keeping degradation of clustering quality lower. We designate this proposed algorithm as sparse simplex projection-based Wasserstein $k$-means, for short, SSPW $k$-means. Numerical evaluations against Wasserstein $k$-means algorithm demonstrate the effectiveness of the proposed SSPW $k$-means on real-world datasets.

Budgeted Batch Mode Active Learning with Generalized Cost and Utility Functions

Arvind Agarwal, Shashank Mujumdar, Nitin Gupta, Sameep Mehta

Auto-TLDR; Active Learning Based on Utility and Cost Functions

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Active learning reduces the labeling cost by actively querying labels for the most valuable data points. Typical active learning methods select the most informative examples one-at-a-time, their batch variants exist where a set of most informative points are selected. These points are selected in such a way that when added to the training data along with their labels, they provide maximum benefit to the underlying model. In this paper, we present a learning framework that actively selects optimal set of examples (in a batch) within a given budget, based on given utility and cost functions. The framework is generic enough to incorporate any utility and any cost function defined on a set of examples. Furthermore, we propose a novel utility function based on the Facility Location problem that considers three important characteristics of utility i.e., diversity, density and point utility. We also propose a novel cost function, by formulating the cost computation problem as an optimization problem, the solution to which turns out to be the minimum spanning tree. Thus, our framework provides the optimal batch of points within the given budget based on the cost and utility functions. We evaluate our method on several data sets and show its superior performance over baseline methods.

Double Manifolds Regularized Non-Negative Matrix Factorization for Data Representation

Jipeng Guo, Shuai Yin, Yanfeng Sun, Yongli Hu

Auto-TLDR; Double Manifolds Regularized Non-negative Matrix Factorization for Clustering

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Non-negative matrix factorization (NMF) is an important method in learning latent data representation. The local geometrical structure can make the learned representation more effectively and significantly improve the performance of NMF. However, most of existing graph-based learning methods are determined by a predefined similarity graph which may be not optimal for specific tasks. To solve the above the problem, we propose the Double Manifolds Regularized NMF (DMR-NMF) model which jointly learns an adaptive affinity matrix with the non-negative matrix factorization. The learned affinity matrix can guide the NMF to fit the clustering task. Moreover, we develop the iterative updating optimization schemes for DMR-NMF, and provide the strict convergence proof of our optimization strategy. Empirical experiments on four different real-world data sets demonstrate the state-of-the-art performance of DMR-NMF in comparison with the other related algorithms.

Low-Cost Lipschitz-Independent Adaptive Importance Sampling of Stochastic Gradients

Huikang Liu, Xiaolu Wang, Jiajin Li, Man-Cho Anthony So

Auto-TLDR; Adaptive Importance Sampling for Stochastic Gradient Descent

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Stochastic gradient descent (SGD) usually samples training data based on the uniform distribution, which may not be a good choice because of the high variance of its stochastic gradient. Thus, importance sampling methods are considered in the literature to improve the performance. Most previous work on SGD-based methods with importance sampling requires the knowledge of Lipschitz constants of all component gradients, which are in general difficult to estimate. In this paper, we study an adaptive importance sampling method for common SGD-based methods by exploiting the local first-order information without knowing any Lipschitz constants. In particular, we periodically changes the sampling distribution by only utilizing the gradient norms in the past few iterations. We prove that our adaptive importance sampling non-asymptotically reduces the variance of the stochastic gradients in SGD, and thus better convergence bounds than that for vanilla SGD can be obtained. We extend this sampling method to several other widely used stochastic gradient algorithms including SGD with momentum and ADAM. Experiments on common convex learning problems and deep neural networks illustrate notably enhanced performance using the adaptive sampling strategy.

RNN Training along Locally Optimal Trajectories via Frank-Wolfe Algorithm

Yun Yue, Ming Li, Venkatesh Saligrama, Ziming Zhang

Auto-TLDR; Frank-Wolfe Algorithm for Efficient Training of RNNs

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We propose a novel and efficient training method for RNNs by iteratively seeking a local minima on the loss surface within a small region, and leverage this directional vector for the update, in an outer-loop. We propose to utilize the Frank-Wolfe (FW) algorithm in this context. Although, FW implicitly involves normalized gradients, which can lead to a slow convergence rate, we develop a novel RNN training method that, surprisingly, even with the additional cost, the overall training cost is empirically observed to be lower than back-propagation. Our method leads to a new Frank-Wolfe method, that is in essence an SGD algorithm with a restart scheme. We prove that under certain conditions our algorithm has a sublinear convergence rate of $O(1/\epsilon)$ for $\epsilon$ error. We then conduct empirical experiments on several benchmark datasets including those that exhibit long-term dependencies, and show significant performance improvement. We also experiment with deep RNN architectures and show efficient training performance. Finally, we demonstrate that our training method is robust to noisy data.

T-SVD Based Non-Convex Tensor Completion and Robust Principal Component Analysis

Tao Li, Jinwen Ma

Auto-TLDR; Non-Convex tensor rank surrogate function and non-convex sparsity measure for tensor recovery

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In this paper, we propose a novel non-convex tensor rank surrogate function and a novel non-convex sparsity measure. The basic idea is to sidestep the bias of $\ell_1-$norm by introducing the concavity. Furthermore, we employ this non-convex penalty in tensor recovery problems such as tensor completion and tensor robust principal component analysis. Due to the concavity, the parameters of these models are difficult to solve. To tackle this problem, we devise a majorization minimization algorithm that can optimize the upper bound of the original function in each iteration, and every sub-problem is solved by the alternating direction multiplier method. We also analyze the theoretical properties of the proposed algorithm. Finally, the experimental results on natural and hyperspectral images demonstrate the efficacy and efficiency of the proposed method.

Fast Subspace Clustering Based on the Kronecker Product

Lei Zhou, Xiao Bai, Liang Zhang, Jun Zhou, Edwin Hancock

Auto-TLDR; Subspace Clustering with Kronecker Product for Large Scale Datasets

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Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is often smaller than the ambient dimension. Spectral clustering, as one of the main approaches to subspace clustering, often takes on a sparse representation or a low-rank representation to learn a block diagonal self-representation matrix for subspace generation. However, existing methods require solving a large scale convex optimization problem with a large set of data, with computational complexity reaches O(N^3) for N data points. Therefore, the efficiency and scalability of traditional spectral clustering methods can not be guaranteed for large scale datasets. In this paper, we propose a subspace clustering model based on the Kronecker product. Due to the property that the Kronecker product of a block diagonal matrix with any other matrix is still a block diagonal matrix, we can efficiently learn the representation matrix which is formed by the Kronecker product of k smaller matrices. By doing so, our model significantly reduces the computational complexity to O(kN^{3/k}). Furthermore, our model is general in nature, and can be adapted to different regularization based subspace clustering methods. Experimental results on two public datasets show that our model significantly improves the efficiency compared with several state-of-the-art methods. Moreover, we have conducted experiments on synthetic data to verify the scalability of our model for large scale datasets.

GraphBGS: Background Subtraction Via Recovery of Graph Signals

Jhony Heriberto Giraldo Zuluaga, Thierry Bouwmans

Auto-TLDR; Graph BackGround Subtraction using Graph Signals

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Background subtraction is a fundamental pre-processing task in computer vision. This task becomes challenging in real scenarios due to variations in the background for both static and moving camera sequences. Several deep learning methods for background subtraction have been proposed in the literature with competitive performances. However, these models show performance degradation when tested on unseen videos; and they require huge amount of data to avoid overfitting. Recently, graph-based algorithms have been successful approaching unsupervised and semi-supervised learning problems. Furthermore, the theory of graph signal processing and semi-supervised learning have been combined leading to new insights in the field of machine learning. In this paper, concepts of recovery of graph signals are introduced in the problem of background subtraction. We propose a new algorithm called Graph BackGround Subtraction (GraphBGS), which is composed of: instance segmentation, background initialization, graph construction, graph sampling, and a semi-supervised algorithm inspired from the theory of recovery of graph signals. Our algorithm has the advantage of requiring less data than deep learning methods while having competitive results on both: static and moving camera videos. GraphBGS outperforms unsupervised and supervised methods in several challenging conditions on the publicly available Change Detection (CDNet2014), and UCSD background subtraction databases.

A Multilinear Sampling Algorithm to Estimate Shapley Values

Ramin Okhrati, Aldo Lipani

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

Sketch-Based Community Detection Via Representative Node Sampling

Mahlagha Sedghi, Andre Beckus, George Atia

Auto-TLDR; Sketch-based Clustering of Community Detection Using a Small Sketch

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This paper proposes a sketch-based approach to the community detection problem which clusters the full graph through the use of an informative and concise sketch. The reduced sketch is built through an effective sampling approach which selects few nodes that best represent the complete graph and operates on a pairwise node similarity measure based on the average commute time. After sampling, the proposed algorithm clusters the nodes in the sketch, and then infers the cluster membership of the remaining nodes in the full graph based on their aggregate similarity to nodes in the partitioned sketch. By sampling nodes with strong representation power, our approach can improve the success rates over full graph clustering. In challenging cases with large node degree variation, our approach not only maintains competitive accuracy with full graph clustering despite using a small sketch, but also outperforms existing sampling methods. The use of a small sketch allows considerable storage savings, and computational and timing improvements for further analysis such as clustering and visualization. We provide numerical results on synthetic data based on the homogeneous, heterogeneous and degree corrected versions of the stochastic block model, as well as experimental results on real-world data.

Aggregating Dependent Gaussian Experts in Local Approximation

Hamed Jalali, Gjergji Kasneci

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.

3D Pots Configuration System by Optimizing Over Geometric Constraints

Jae Eun Kim, Muhammad Zeeshan Arshad, Seong Jong Yoo, Je Hyeong Hong, Jinwook Kim, Young Min Kim

Auto-TLDR; Optimizing 3D Conﬁgurations for Stable Pottery Restoration from irregular and noisy evidence

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While potteries are common artifacts excavated in archaeological sites, the restoration process relies on the manual cleaning and reassembling shattered pieces. Since the number of possible 3D conﬁgurations is considerably large, the exhaustive manual trial may result in an abrasion on fractured surfaces and even failure to ﬁnd the correct matches. As a result, many recent works suggest virtual reassembly from 3D scans of the fragments. The problem is challenging in the view of the conventional 3D geometric analysis, as it is hard to extract reliable shape features from the thin break lines. We propose to optimize the global conﬁguration by combining geometric constraints with information from noisy shape features. Speciﬁcally, we enforce bijection and continuity of sequence of correspondences given estimates of corners and pair-wise matching scores between multiple break lines. We demonstrate that our pipeline greatly increases the accuracy of correspondences, resulting in the stable restoration of 3D conﬁgurations from irregular and noisy evidence.

Stochastic Runge-Kutta Methods and Adaptive SGD-G2 Stochastic Gradient Descent

Gabriel Turinici, Imen Ayadi

Auto-TLDR; Adaptive Stochastic Runge Kutta for the Minimization of the Loss Function

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The minimization of the loss function is of paramount importance in deep neural networks. Many popular optimization algorithms have been shown to correspond to some evolution equation of gradient flow type. Inspired by the numerical schemes used for general evolution equations, we introduce a second-order stochastic Runge Kutta method and show that it yields a consistent procedure for the minimization of the loss function. In addition, it can be coupled, in an adaptive framework, with the Stochastic Gradient Descent (SGD) to adjust automatically the learning rate of the SGD The resulting adaptive SGD, called SGD-G2, shows good results in terms of convergence speed when tested on standard data-sets.

Low Rank Representation on Product Grassmann Manifolds for Multi-viewSubspace Clustering

Jipeng Guo, Yanfeng Sun, Junbin Gao, Yongli Hu, Baocai Yin

Auto-TLDR; Low Rank Representation on Product Grassmann Manifold for Multi-View Data Clustering

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Clustering high dimension multi-view data with complex intrinsic properties and nonlinear manifold structure is a challenging task since these data are always embedded in low dimension manifolds. Inspired by Low Rank Representation (LRR), some researchers extended classic LRR on Grassmann manifold or Product Grassmann manifold to represent data with non-linear metrics. However, most of these methods utilized convex nuclear norm to leverage a low-rank structure, which was over-relaxation of true rank and would lead to the results deviated from the true underlying ones. And, the computational complexity of singular value decomposition of matrix is high for nuclear norm minimization. In this paper, we propose a new low rank model for high-dimension multi-view data clustering on Product Grassmann Manifold with the matrix tri-factorization which is used to control the upper bound of true rank of representation matrix. And, the original problem can be transformed into the nuclear norm minimization with smaller scale matrices. An effective solution and theoretical analysis are also provided. The experimental results show that the proposed method obviously outperforms other state-of-the-art methods on several multi-source human/crowd action video datasets.

On the Global Self-attention Mechanism for Graph Convolutional Networks

Chen Wang, Deng Chengyuan

Auto-TLDR; Global Self-Attention Mechanism for Graph Convolutional Networks

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Applying Global Self-Attention (GSA) mechanism over features has achieved remarkable success on Convolutional Neural Networks (CNNs). However, it is not clear if Graph Convolutional Networks (GCNs) can similarly benefit from such a technique. In this paper, inspired by the similarity between CNNs and GCNs, we study the impact of the Global Self-Attention mechanism on GCNs. We find that consistent with the intuition, the GSA mechanism allows GCNs to capture feature-based vertex relations regardless of edge connections; As a result, the GSA mechanism can introduce extra expressive power to the GCNs. Furthermore, we analyze the impacts of the GSA mechanism on the issues of overfitting and over-smoothing. We prove that the GSA mechanism can alleviate both the overfitting and the over-smoothing issues based on some recent technical developments. Experiments on multiple benchmark datasets illustrate both superior expressive power and less significant overfitting and over-smoothing problems for the GSA-augmented GCNs, which corroborate the intuitions and the theoretical results.

Compression Strategies and Space-Conscious Representations for Deep Neural Networks

Giosuè Marinò, Gregorio Ghidoli, Marco Frasca, Dario Malchiodi

Auto-TLDR; Compression of Large Convolutional Neural Networks by Weight Pruning and Quantization

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Recent advances in deep learning have made available large, powerful convolutional neural networks (CNN) with state-of-the-art performance in several real-world applications. Unfortunately, these large-sized models have millions of parameters, thus they are not deployable on resource-limited platforms (e.g. where RAM is limited). Compression of CNNs thereby becomes a critical problem to achieve memory-efficient and possibly computationally faster model representations. In this paper, we investigate the impact of lossy compression of CNNs by weight pruning and quantization, and lossless weight matrix representations based on source coding. We tested several combinations of these techniques on four benchmark datasets for classification and regression problems, achieving compression rates up to 165 times, while preserving or improving the model performance.

Signature Features with the Visibility Transformation

Yue Wu, Hao Ni, Terry Lyons, Robin Hudson

Auto-TLDR; The Visibility Transformation for Pattern Recognition

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In this paper we put the visibility transformation on a clear theoretical footing and show that this transform is able to embed the effect of the absolute position of the data stream into signature features in a unified and efficient way. The generated feature set is particularly useful in pattern recognition tasks, for its simplifying role in allowing the signature feature set to accommodate nonlinear functions of absolute and relative values.

Unveiling Groups of Related Tasks in Multi-Task Learning

Jordan Frecon, Saverio Salzo, Massimiliano Pontil

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.

An Efficient Empirical Solver for Localized Multiple Kernel Learning Via DNNs

Ziming Zhang

Auto-TLDR; Localized Multiple Kernel Learning using LMKL-Net

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In this paper we propose solving localized multiple kernel learning (LMKL) using LMKL-Net, a feedforward deep neural network (DNN). In contrast to previous works, as a learning principle we propose parameterizing the gating function for learning kernel combination weights and the multiclass classifier using an attentional network (AN) and a multilayer perceptron (MLP), respectively. Such interpretability helps us better understand how the network solves the problem. Thanks to stochastic gradient descent (SGD), our approach has {\em linear} computational complexity in training. Empirically on benchmark datasets we demonstrate that with comparable or better accuracy than the state-of-the-art, our LMKL-Net can be trained about {\bf two orders of magnitude} faster with about {\bf two orders of magnitude} smaller memory footprint for large-scale learning.

Subspace Clustering Via Joint Unsupervised Feature Selection

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

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.

Automatically Mining Relevant Variable Interactions Via Sparse Bayesian Learning

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

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.

Uniform and Non-Uniform Sampling Methods for Sub-Linear Time K-Means Clustering

Yuanhang Ren, Ye Du

Auto-TLDR; Sub-linear Time Clustering with Constant Approximation Ratio for K-Means Problem

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The $k$-means problem is arguably the most well-known clustering problem in machine learning, and lots of approximation algorithms have been proposed for it. However, many of these algorithms may become infeasible when data is huge. Sub-linear time algorithms with constant approximation ratios are desirable in this scenario. In this paper, we first improve the analysis of the algorithm proposed by \cite{Mohan:2017:BNA:3172077.3172235} by sharpening the approximation ratio from $4(\alpha+\beta)$ to $\alpha+\beta$. Moreover, on mild assumptions of the data, a constant approximation ratio can be achieved in poly-logarithmic time by the algorithm. Furthermore, we propose a novel sub-linear time clustering algorithm called {\it Double-K-M$\text{C}^2$ sampling} as well. Experiments on the data clustering task and the image segmentation task have validated the effectiveness of our algorithms.

Graph Approximations to Geodesics on Metric Graphs

Robin Vandaele, Yvan Saeys, Tijl De Bie

Auto-TLDR; Topological Pattern Recognition of Metric Graphs Using Proximity Graphs

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In machine learning, high-dimensional point clouds are often assumed to be sampled from a topological space of which the intrinsic dimension is significantly lower than the representation dimension. Proximity graphs, such as the Rips graph or kNN graph, are often used as an intermediate representation to learn or visualize topological and geometrical properties of this space. The key idea behind this approach is that distances on the graph preserve the geodesic distances on the unknown space well, and as such, can be used to infer local and global geometric patterns of this space. Prior results provide us with conditions under which these distances are well-preserved for geodesically convex, smooth, compact manifolds. Yet, proximity graphs are ideal representations for a much broader class of spaces, such as metric graphs, i.e., graphs embedded in the Euclidean space. It turns out—as proven in this paper—that these existing conditions cannot be straightforwardly adapted to these spaces. In this work, we provide novel, flexible, and insightful characteristics and results for topological pattern recognition of metric graphs to bridge this gap.

Graph Convolutional Neural Networks for Power Line Outage Identification

Jia He, Maggie Cheng

Auto-TLDR; Graph Convolutional Networks for Power Line Outage Identification

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In this paper, we consider the power line outage identification problem as a graph signal classification problem, where the signal at each vertex is given as a time series. We propose graph convolutional networks (GCNs) for the task of classifying signals supported on graphs. An important element of the GCN design is filter design. We consider filtering signals in either the vertex (spatial) domain, or the frequency (spectral) domain. Two basic architectures are proposed. In the spatial GCN architecture, the GCN uses a graph shift operator as the basic building block to incorporate the underlying graph structure into the convolution layer. The spatial filter directly utilizes the graph connectivity information. It defines the filter to be a polynomial in the graph shift operator to obtain the convolved features that aggregate neighborhood information of each node. In the spectral GCN architecture, a frequency filter is used instead. A graph Fourier transform operator first transforms the raw graph signal from the vertex domain to the frequency domain, and then a filter is defined using the graph's spectral parameters. The spectral GCN then uses the output from the graph Fourier transform to compute the convolved features. There are additional challenges to classify the time-evolving graph signal as the signal value at each vertex changes over time. The GCNs are designed to recognize different spatiotemporal patterns from high-dimensional data defined on a graph. The application of the proposed methods to power line outage identification shows that these GCN architectures can successfully classify abnormal signal patterns and identify the outage location.

Exact and Convergent Iterative Methods to Compute the Orthogonal Point-To-Ellipse Distance

Siyu Guo, Pingping Hu, Zhigang Ling, He Wen, Min Liu, Lu Tang

Auto-TLDR; Convergent iterative algorithm for orthogonal distance based ellipse fitting

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Computation of the orthogonal distance from a given point to an ellipse is the basis of orthogonal distance based ellipse fitting methods. The problem of this orthogonal distance and the corresponding orthogonal contacting point on the ellipse is investigated, and two algorithms, the exact one and the convergent iterative one, are proposed. The exact algorithm utilizes the closed form solution of quartic equations, but is numerically unstable. The iterative algorithm, however, uses Newton’s method to solve the equation, and starts from an initial solution that is proven to lead to a convergent iteration. The proposed algorithms are compared in experiments with an existing rival. Although the rival algorithm is slightly faster and more accurate in realistic scenarios, divergence is likely to occur. On the other hand, both our exact and iterative algorithms can reliably produce the solution needed. While the exact algorithm encounters numeric instability, the iterative algorithm is only slightly outperformed by the existing rival in speed and accuracy, but at the same time provides more reliable computation process, thus making it a preferable method for the task.

Hierarchical Routing Mixture of Experts

Wenbo Zhao, Yang Gao, Shahan Ali Memon, Bhiksha Raj, Rita Singh

Auto-TLDR; A Binary Tree-structured Hierarchical Routing Mixture of Experts for Regression

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In regression tasks the distribution of the data is often too complex to be fitted by a single model. In contrast, partition-based models are developed where data is divided and fitted by local models. These models partition the input space and do not leverage the input-output dependency of multimodal-distributed data, and strong local models are needed to make good predictions. Addressing these problems, we propose a binary tree-structured hierarchical routing mixture of experts (HRME) model that has classifiers as non-leaf node experts and simple regression models as leaf node experts. The classifier nodes jointly soft-partition the input-output space based on the natural separateness of multimodal data. This enables simple leaf experts to be effective for prediction. Further, we develop a probabilistic framework for the HRME model, and propose a recursive Expectation-Maximization (EM) based algorithm to learn both the tree structure and the expert models. Experiments on a collection of regression tasks validate the effectiveness of our method compared to a variety of other regression models.

Naturally Constrained Online Expectation Maximization

Daniela Pamplona, Antoine Manzanera

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.

Computing Stable Resultant-Based Minimal Solvers by Hiding a Variable

Snehal Bhayani, Zuzana Kukelova, Janne Heikkilä

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.

Learning Sparse Deep Neural Networks Using Efficient Structured Projections on Convex Constraints for Green AI

Michel Barlaud, Frederic Guyard

Auto-TLDR; Constrained Deep Neural Network with Constrained Splitting Projection

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In recent years, deep neural networks (DNN) have been applied to different domains and achieved dramatic performance improvements over state-of-the-art classical methods. These performances of DNNs were however often obtained with networks containing millions of parameters and which training required heavy computational power. In order to cope with this computational issue a huge literature deals with proximal regularization methods which are time consuming.\\ In this paper, we propose instead a constrained approach. We provide the general framework for our new splitting projection gradient method. Our splitting algorithm iterates a gradient step and a projection on convex sets. We study algorithms for different constraints: the classical $\ell_1$ unstructured constraint and structured constraints such as the nuclear norm, the $\ell_{2,1} $ constraint (Group LASSO). We propose a new $\ell_{1,1} $ structured constraint for which we provide a new projection algorithm We demonstrate the effectiveness of our method on three popular datasets (MNIST, Fashion MNIST and CIFAR). Experiments on these datasets show that our splitting projection method with our new $\ell_{1,1} $ structured constraint provides the best reduction of memory and computational power. Experiments show that fully connected linear DNN are more efficient for green AI.

Revisiting Graph Neural Networks: Graph Filtering Perspective

Hoang Nguyen-Thai, Takanori Maehara, Tsuyoshi Murata

Auto-TLDR; Two-Layers Graph Convolutional Network with Graph Filters Neural Network

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In this work, we develop quantitative results to the learnability of a two-layers Graph Convolutional Network (GCN). Instead of analyzing GCN under some classes of functions, our approach provides a quantitative gap between a two-layers GCN and a two-layers MLP model. From the graph signal processing perspective, we provide useful insights to some flaws of graph neural networks for vertex classification. We empirically demonstrate a few cases when GCN and other state-of-the-art models cannot learn even when true vertex features are extremely low-dimensional. To demonstrate our theoretical findings and propose a solution to the aforementioned adversarial cases, we build a proof of concept graph neural network model with different filters named Graph Filters Neural Network (gfNN).

Transferable Model for Shape Optimization subject to Physical Constraints

Lukas Harsch, Johannes Burgbacher, Stefan Riedelbauch

Auto-TLDR; U-Net with Spatial Transformer Network for Flow Simulations

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The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture is used to learn the underlying physical behaviour of fluid flows. The network is used to infer the solution of flow simulations which will be shown for a wide range of generic channel flow simulations. Physical meaningful quantities can be computed on the obtained solution, e.g. the total pressure difference or the forces on the objects. A Spatial Transformer Network with thin-plate-splines is used for the interaction between the physical constraints and the geometric representation of the objects. Thus, a transformation from an initial to a target geometry is performed such that the object is fulfilling the given constraints. This method is fully differentiable i.e., gradient informations can be used for the transformation. This can be seen as an inverse design process. The advantage of this method over many other proposed methods is, that the physical constraints are based on the inferred flow field solution. Thus, we can apply a transferable model to varying problem setups, which is not limited to a given set of geometry parameters or physical quantities.

Learning Stable Deep Predictive Coding Networks with Weight Norm Supervision

Guo Ruohao

Auto-TLDR; Stability of Predictive Coding Network with Weight Norm Supervision

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Predictive Coding Network (PCN) is an important neural network inspired by visual processing models in neuroscience. It combines the feedforward and feedback processing and has the architecture of recurrent neural networks (RNNs). This type of network is usually trained with backpropagation through time (BPTT). With infinite recurrent steps, PCN is a dynamic system. However, as one of the most important properties, stability is rarely studied in this type of network. Inspired by reservoir computing, we investigate the stability of hierarchical RNNs from the perspective of dynamic systems, and propose a sufficient condition for their echo state property (ESP). Our study shows the global stability is determined by stability of the local layers and the feedback between neighboring layers. Based on it, we further propose Weight Norm Supervision, a new algorithm that controls the stability of PCN dynamics by imposing different weight norm constraints on different parts of the network. We compare our approach with other training methods in terms of stability and prediction capability. The experiments show that our algorithm learns stable PCNs with a reliable prediction precision in the most effective and controllable way.

Graph Discovery for Visual Test Generation

Neil Hallonquist, Laurent Younes, Donald Geman

Auto-TLDR; Visual Question Answering over Graphs: A Probabilistic Framework for VQA

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We consider the problem of uncovering an unknown attributed graph, where both its edges and vertices are hidden from view, through a sequence of binary questions about it. In order to select questions efficiently, we define a probability distribution over graphs, with randomness not just over edges, but over vertices as well. We then sequentially select questions so as to: (1) minimize the expected entropy of the random graph, given the answers to the previous questions in the sequence; and (2) to instantiate the vertices that compose the graph. We propose some basic question spaces, from which to select questions, that vary in their capacity. We apply this framework to the problem of test generation in Visual Question Answering (VQA), where semantic questions are used to evaluate vision systems over rich image representations. To do this, we use a restricted question vocabulary, resulting in image representations that take the form of scene graphs; by defining a distribution over them, a consistent set of probabilities is associated with the questions, and used in their selection.

Expectation-Maximization for Scheduling Problems in Satellite Communication

Werner Bailer, Martin Winter, Johannes Ebert, Joel Flavio, Karin Plimon

Auto-TLDR; Unsupervised Machine Learning for Satellite Communication Using Expectation-Maximization

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In this paper we address unsupervised machine learning for two use cases in satellite communication, which are scheduling problems: (i) Ka-band frequency plan optimization and (ii) dynamic configuration of an active antenna array satellite. We apply approaches based on the Expectation-Maximization (EM) framework to both of them. We compare against baselines of currently deployed solutions, and show that they can be significantly outperformed by the EM-based approach. In addition, the approaches can be applied incrementally, thus supporting fast adaptation to small changes in the input configuration.

Supervised Classification Using Graph-Based Space Partitioning for Multiclass Problems

Nicola Yanev, Ventzeslav Valev, Adam Krzyzak, Karima Ben Suliman

Auto-TLDR; Box Classifier for Multiclass Classification

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We introduce and investigate in multiclass setting an efficient classifier which partitions the training data by means of multidimensional parallelepipeds called boxes. We show that multiclass classification problem at hand can be solved by integrating the heuristic minimum clique cover approach and the k-nearest neighbor rule. Our algorithm is motivated an algorithm for partitioning a graph into a minimal number of maximal. The main advantage of the new classifier called Box classifier is that it optimally utilizes the geometrical structure of the training set by decomposing the l-class problem (l > 2) into l binary classification problems. We discuss computational complexity of the proposed Box classifier. The extensive experiments performed on the simulated and real data for binary and multiclass problems show that in almost all cases the Box classifier performs significantly better than k-NN, SVM and decision trees.

Learning Connectivity with Graph Convolutional Networks

Hichem Sahbi

Auto-TLDR; Learning Graph Convolutional Networks Using Topological Properties of Graphs

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Learning graph convolutional networks (GCNs) is an emerging field which aims at generalizing convolutional operations to arbitrary non-regular domains. In particular, GCNs operating on spatial domains show superior performances compared to spectral ones, however their success is highly dependent on how the topology of input graphs is defined. In this paper, we introduce a novel framework for graph convolutional networks that learns the topological properties of graphs. The design principle of our method is based on the optimization of a constrained objective function which learns not only the usual convolutional parameters in GCNs but also a transformation basis that conveys the most relevant topological relationships in these graphs. Experiments conducted on the challenging task of skeleton-based action recognition shows the superiority of the proposed method compared to handcrafted graph design as well as the related work.

Label Self-Adaption Hashing for Image Retrieval

Jianglin Lu, Zhihui Lai, Hailing Wang, Jie Zhou

Auto-TLDR; Label Self-Adaption Hashing for Large-Scale Image Retrieval

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Hashing has attracted widespread attention in image retrieval because of its fast retrieval speed and low storage cost. Compared with supervised methods, unsupervised hashing methods are more reasonable and suitable for large-scale image retrieval since it is always difficult and expensive to collect true labels of the massive data. Without label information, however, unsupervised hashing methods can not guarantee the quality of learned binary codes. To resolve this dilemma, this paper proposes a novel unsupervised hashing method called Label Self-Adaption Hashing (LSAH), which contains effective hashing function learning part and self-adaption label generation part. In the first part, we utilize anchor graph to keep the local structure of the data and introduce joint sparsity into the model to extract effective features for high-quality binary code learning. In the second part, a self-adaptive cluster label matrix is learned from the data under the assumption that the nearest neighbor points should have a large probability to be in the same cluster. Therefore, the proposed LSAH can make full use of the potential discriminative information of the data to guide the learning of binary code. It is worth noting that LSAH can learn effective binary codes, hashing function and cluster labels simultaneously in a unified optimization framework. To solve the resulting optimization problem, an Augmented Lagrange Multiplier based iterative algorithm is elaborately designed. Extensive experiments on three large-scale data sets indicate the promising performance of the proposed LSAH.

A New Geodesic-Based Feature for Characterization of 3D Shapes: Application to Soft Tissue Organ Temporal Deformations

Karim Makki, Amine Bohi, Augustin Ogier, Marc-Emmanuel Bellemare

Auto-TLDR; Spatio-Temporal Feature Descriptors for 3D Shape Characterization from Point Clouds

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Spatio-temporal feature descriptors are of great importance for characterizing the local changes of 3D deformable shapes. In this study, we propose a method for characterizing 3D shapes from point clouds and we show a direct application on a study of organ temporal deformations. As an example, we characterize the behavior of the bladder during forced respiratory motion with a reduced number of 3D surface points: first, a set of equidistant points representing the vertices of quadrilateral mesh for the organ surface are tracked throughout a long dynamic MRI sequence using a large deformation diffeomorphic metric mapping (LDDMM) framework. Second, a novel 3D shape descriptor invariant to translation, scale and rotation is proposed for characterizing the temporal organ deformations by employing an Eulerian Partial Differential Equations (PDEs) methodology. We demonstrate the robustness of our feature on both synthetic 3D shapes and realistic dynamic Magnetic Resonance Imaging (MRI) data sequences portraying the bladder deformation during a forced breathing exercise. Promising results are obtained, showing that the proposed feature may be useful for several computer vision applications such as medical imaging, aerodynamics and robotics.

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

Manolis Lourakis, George Terzakis

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.

Sparse-Dense Subspace Clustering

Shuai Yang, Wenqi Zhu, Yuesheng Zhu

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.

Adaptive Sampling of Pareto Frontiers with Binary Constraints Using Regression and Classification

Raoul Heese, Michael Bortz

Auto-TLDR; Adaptive Optimization for Black-Box Multi-Objective Optimizing Problems with Binary Constraints

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We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification models, which act as a surrogate for the optimization goals and allow us to suggest multiple design points at once in each iteration. The proposed acquisition function is intuitively understandable and can be tuned to the demands of the problems at hand. We also present a novel ellipsoid truncation method to speed up the expected hypervolume calculation in a straightfoward way for regression models with a normal probability density. We benchmark our approach with an evolutionary algorithm on multiple test problems.

Probabilistic Latent Factor Model for Collaborative Filtering with Bayesian Inference

Jiansheng Fang, Xiaoqing Zhang, Yan Hu, Yanwu Xu, Ming Yang, Jiang Liu

Auto-TLDR; Bayesian Latent Factor Model for Collaborative Filtering

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Latent Factor Model (LFM) is one of the most successful methods for Collaborative filtering (CF) in the recommendation system, in which both users and items are projected into a joint latent factor space. Base on matrix factorization applied usually in pattern recognition, LFM models user-item interactions as inner products of factor vectors of user and item in that space and can be efficiently solved by least square methods with optimal estimation. However, such optimal estimation methods are prone to overfitting due to the extreme sparsity of user-item interactions. In this paper, we propose a Bayesian treatment for LFM, named Bayesian Latent Factor Model (BLFM). Based on observed user-item interactions, we build a probabilistic factor model in which the regularization is introduced via placing prior constraint on latent factors, and the likelihood function is established over observations and parameters. Then we draw samples of latent factors from the posterior distribution with Variational Inference (VI) to predict expected value. We further make an extension to BLFM, called BLFMBias, incorporating user-dependent and item-dependent biases into the model for enhancing performance. Extensive experiments on the movie rating dataset show the effectiveness of our proposed models by compared with several strong baselines.

Graph Signal Active Contours

Olivier Lezoray

Auto-TLDR; Adaptation of Active Contour Without Edges for Graph Signal Processing

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With the advent of data living on vertices of graphs, there is much interest in processing the so-called graph signals for partitioning tasks. As active contours have had much impact in the image processing community, their formulation on graphs is of importance to the field of graph signal processing. This paper proposes an adaptation on graphs of a model that combines the Geodesic Active Contour and the Active Contour Without Edges models. In addition, specific terms depending on graphs are introduced in the formulation. This adaptation is solved using a level set formulation with a gradient descent that can be expressed as a morphological front evolution process. Experimental results on different kinds of graphs signals show the benefit of the approach.