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Graph Spectral Feature Learning for Mixed Data of Categorical and Numerical Type

Saswata Sahoo, Souradip Chakraborty

Auto-TLDR; Feature Learning in Mixed Type of Variable by an undirected graph

Abstract Slides Poster

Feature learning in the presence of a mixed type of variables, numerical and categorical types, is important for related modeling problems. In this work, we propose a novel strategy to explicitly model the probabilistic dependence structure among the mixed type of variables by an undirected graph. The dependence structure among different pairs of variables are encoded by a suitable mapping function to estimate the edges of the graph. Spectral decomposition of the graph Laplacian provides the desired feature transformation. We numerically validate the implications of the feature learning strategy on various datasets in terms of data clustering.

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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.

Sparse-Dense Subspace Clustering

Shuai Yang, Wenqi Zhu, Yuesheng Zhu

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

Abstract Slides Poster Similar

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.

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.

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.

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.

N2D: (Not Too) Deep Clustering Via Clustering the Local Manifold of an Autoencoded Embedding

Ryan Mcconville, Raul Santos-Rodriguez, Robert Piechocki, Ian Craddock

Auto-TLDR; Local Manifold Learning for Deep Clustering on Autoencoded Embeddings

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Deep clustering has increasingly been demonstrating superiority over conventional shallow clustering algorithms. Deep clustering algorithms usually combine representation learning with deep neural networks to achieve this performance, typically optimizing a clustering and non-clustering loss. In such cases, an autoencoder is typically connected with a clustering network, and the final clustering is jointly learned by both the autoencoder and clustering network. Instead, we propose to learn an autoencoded embedding and then search this further for the underlying manifold. For simplicity, we then cluster this with a shallow clustering algorithm, rather than a deeper network. We study a number of local and global manifold learning methods on both the raw data and autoencoded embedding, concluding that UMAP in our framework is able to find the best clusterable manifold of the embedding. This suggests that local manifold learning on an autoencoded embedding is effective for discovering higher quality clusters. We quantitatively show across a range of image and time-series datasets that our method has competitive performance against the latest deep clustering algorithms, including out-performing current state-of-the-art on several. We postulate that these results show a promising research direction for deep clustering. The code can be found at https://github.com/rymc/n2d.

Variational Deep Embedding Clustering by Augmented Mutual Information Maximization

Qiang Ji, Yanfeng Sun, Yongli Hu, Baocai Yin

Auto-TLDR; Clustering by Augmented Mutual Information maximization for Deep Embedding

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Clustering is a crucial but challenging task in pattern analysis and machine learning. Recent many deep clustering methods combining representation learning with cluster techniques emerged. These deep clustering methods mainly focus on the correlation among samples and ignore the relationship between samples and their representations. In this paper, we propose a novel end-to-end clustering framework, namely variational deep embedding clustering by augmented mutual information maximization (VCAMI). From the perspective of VAE, we prove that minimizing reconstruction loss is equivalent to maximizing the mutual information of the input and its latent representation. This provides a theoretical guarantee for us to directly maximize the mutual information instead of minimizing reconstruction loss. Therefore we proposed the augmented mutual information which highlights the uniqueness of the representations while discovering invariant information among similar samples. Extensive experiments on several challenging image datasets show that the VCAMI achieves good performance. we achieve state-of-the-art results for clustering on MNIST (99.5%) and CIFAR-10 (65.4%) to the best of our knowledge.

Temporal Pattern Detection in Time-Varying Graphical Models

Federico Tomasi, Veronica Tozzo, Annalisa Barla

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.

Soft Label and Discriminant Embedding Estimation for Semi-Supervised Classification

Fadi Dornaika, Abdullah Baradaaji, Youssof El Traboulsi

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.

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.

Supervised Feature Embedding for Classification by Learning Rank-Based Neighborhoods

Ghazaal Sheikhi, Hakan Altincay

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.

Generative Deep-Neural-Network Mixture Modeling with Semi-Supervised MinMax+EM Learning

Nilay Pande, Suyash Awate

Auto-TLDR; Semi-supervised Deep Neural Networks for Generative Mixture Modeling and Clustering

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Deep neural networks (DNNs) for generative mixture modeling typically rely on unsupervised learning that employs hard clustering schemes, or variational learning with loose / approximate bounds, or under-regularized modeling. We propose a novel statistical framework for a DNN mixture model using a single generative adversarial network. Our learning formulation proposes a novel data-likelihood term relying on a well-regularized / constrained Gaussian mixture model in the latent space along with a prior term on the DNN weights. Our min-max learning increases the data likelihood using a tight variational lower bound using expectation maximization (EM). We leverage our min-max EM learning scheme for semi-supervised learning. Results on three real-world datasets demonstrate the benefits of our compact modeling and learning formulation over the state of the art for mixture modeling and clustering.

A Multi-Task Multi-View Based Multi-Objective Clustering Algorithm

Sayantan Mitra, Sriparna Saha

Auto-TLDR; MTMV-MO: Multi-task multi-view multi-objective optimization for multi-task clustering

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In recent years, multi-view multi-task clustering has received much attention. There are several real-life problems that involve both multi-view clustering and multi-task clustering, i.e., the tasks are closely related, and each task can be analyzed using multiple views. Traditional multi-task multi-view clustering algorithms use single-objective optimization-based approaches and cannot apply too-many regularization terms. However, these problems are inherently some multi-objective optimization problems because conflict may be between different views within a given task and also between different tasks, necessitating a trade-off. Based on these observations, in this paper, we have proposed a novel multi-task multi-view multi-objective optimization (MTMV-MO) algorithm which simultaneously optimizes three objectives, i.e., within-view task relation, within-task view relation and the quality of the clusters obtained. The proposed methodology (MTMV-MO) is evaluated on four different datasets and the results are compared with five state-of-the-art algorithms in terms of Adjusted Rand Index (ARI) and Classification Accuracy (%CoA). MTMV-MO illustrates an improvement of 1.5-2% in terms of ARI and 4-5% in terms of %CoA compared to the state-of-the-art algorithms.

Constrained Spectral Clustering Network with Self-Training

Xinyue Liu, Shichong Yang, Linlin Zong

Auto-TLDR; Constrained Spectral Clustering Network: A Constrained Deep spectral clustering network

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Deep spectral clustering networks have shown their superiorities due to the integration of feature learning and cluster assignment, and the ability to deal with non-convex clusters. Nevertheless, deep spectral clustering is still an ill-posed problem. Specifically, the affinity learned by the most remarkable SpectralNet is not guaranteed to be consistent with local invariance and thus hurts the final clustering performance. In this paper, we propose a novel framework of Constrained Spectral Clustering Network (CSCN) by incorporating pairwise constraints and clustering oriented fine-tuning to deal with the ill-posedness. To the best of our knowledge, this is the first constrained deep spectral clustering method. Another advantage of CSCN over existing constrained deep clustering networks is that it propagates pairwise constraints throughout the entire dataset. In addition, we design a clustering oriented loss by self-training to simultaneously finetune feature representations and perform cluster assignments, which further improve the quality of clustering. Extensive experiments on benchmark datasets demonstrate that our approach outperforms the state-of-the-art clustering methods.

On Learning Random Forests for Random Forest Clustering

Manuele Bicego, Francisco Escolano

Auto-TLDR; Learning Random Forests for Clustering

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In this paper we study the poorly investigated problem of learning Random Forests for distance-based Random Forest clustering. We studied both classic schemes as well as alternative approaches, novel in this context. In particular, we investigated the suitability of Gaussian Density Forests, Random Forests specifically designed for density estimation. Further, we introduce a novel variant of Random Forest, based on an effective non parametric by-pass estimator of the Renyi entropy, which can be useful when the parametric assumption is too strict. An empirical evaluation involving different datasets and different RF-clustering strategies confirms that the learning step is crucial for RF-clustering. We also present a set of practical guidelines useful to determine the most suitable variant of RF-clustering according to the problem under examination.

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.

Feature-Aware Unsupervised Learning with Joint Variational Attention and Automatic Clustering

Wang Ru, Lin Li, Peipei Wang, Liu Peiyu

Auto-TLDR; Deep Variational Attention Encoder-Decoder for Clustering

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Deep clustering aims to cluster unlabeled real-world samples by mining deep feature representation. Most of existing methods remain challenging when handling high-dimensional data and simultaneously exploring the complementarity of deep feature representation and clustering. In this paper, we propose a novel Deep Variational Attention Encoder-decoder for Clustering (DVAEC). Our DVAEC improves the representation learning ability by fusing variational attention. Specifically, we design a feature-aware automatic clustering module to mitigate the unreliability of similarity calculation and guide network learning. Besides, to further boost the performance of deep clustering from a global perspective, we define a joint optimization objective to promote feature representation learning and automatic clustering synergistically. Extensive experimental results show the promising performance achieved by our DVAEC on six datasets comparing with several popular baseline clustering methods.

Interpolation in Auto Encoders with Bridge Processes

Carl Ringqvist, Henrik Hult, Judith Butepage, Hedvig Kjellstrom

Auto-TLDR; Stochastic interpolations from auto encoders trained on flattened sequences

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Auto encoding models have been extensively studied in recent years. They provide an efficient framework for sample generation, as well as for analysing feature learning. Furthermore, they are efficient in performing interpolations between data-points in semantically meaningful ways. In this paper, we introduce a method for generating sequence samples from auto encoders trained on flattened sequences (e.g video sample from auto encoders trained to generate a video frame); as well as a canonical, dimension independent method for generating stochastic interpolations. The distribution of interpolation paths is represented as the distribution of a bridge process constructed from an artificial random data generating process in the latent space, having the prior distribution as its invariant distribution.

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 Embeddings for Image Clustering: An Empirical Study of Triplet Loss Approaches

Kalun Ho, Janis Keuper, Franz-Josef Pfreundt, Margret Keuper

Auto-TLDR; Clustering Objectives for K-means and Correlation Clustering Using Triplet Loss

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In this work, we evaluate two different image clustering objectives, k-means clustering and correlation clustering, in the context of Triplet Loss induced feature space embeddings. Specifically, we train a convolutional neural network to learn discriminative features by optimizing two popular versions of the Triplet Loss in order to study their clustering properties under the assumption of noisy labels. Additionally, we propose a new, simple Triplet Loss formulation, which shows desirable properties with respect to formal clustering objectives and outperforms the existing methods. We evaluate all three Triplet loss formulations for K-means and correlation clustering on the CIFAR-10 image classification dataset.

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.

An Invariance-Guided Stability Criterion for Time Series Clustering Validation

Florent Forest, Alex Mourer, Mustapha Lebbah, Hanane Azzag, Jérôme Lacaille

Auto-TLDR; An invariance-guided method for clustering model selection in time series data

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Time series clustering is a challenging task due to the specificities of this type of data. Temporal correlation and invariance to transformations such as shifting, warping or noise prevent the use of standard data mining methods. Time series clustering has been mostly studied under the angle of finding efficient algorithms and distance metrics adapted to the specific nature of time series data. Much less attention has been devoted to the general problem of model selection. Clustering stability has emerged as a universal and model-agnostic principle for clustering model selection. This principle can be stated as follows: an algorithm should find a structure in the data that is resilient to perturbation by sampling or noise. We propose to apply stability analysis to time series by leveraging prior knowledge on the nature and invariances of the data. These invariances determine the perturbation process used to assess stability. Based on a recently introduced criterion combining between-cluster and within-cluster stability, we propose an invariance-guided method for model selection, applicable to a wide range of clustering algorithms. Experiments conducted on artificial and benchmark data sets demonstrate the ability of our criterion to discover structure and select the correct number of clusters, whenever data invariances are known beforehand.

Assortative-Constrained Stochastic Block Models

Daniel Gribel, Thibaut Vidal, Michel Gendreau

Auto-TLDR; Constrained Stochastic Block Models for Assortative Communities in Neural Networks

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Stochastic block models (SBMs) are often used to find assortative community structures in networks, such that the probability of connections within communities is higher than in between communities. However, classic SBMs are not limited to assortative structures. In this study, we discuss the implications of this model-inherent indifference towards assortativity or disassortativity, and show that it can lead to undesirable outcomes in datasets which are known to be assortative but which contain a reduced amount of information. To circumvent these issues, we propose a constrained SBM that imposes strong assortativity constraints, along with efficient algorithmic solutions. These constraints significantly boost community-detection capabilities in regimes which are close to the detectability threshold. They also permit to identify structurally-different communities in networks representing cerebral-cortex activity regions.

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

Fadi Dornaika, Ahmad Khoder

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.

Improved Time-Series Clustering with UMAP Dimension Reduction Method

Clément Pealat, Vincent Cheutet, Guillaume Bouleux

Auto-TLDR; Time Series Clustering with UMAP as a Pre-processing Step

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Clustering is an unsupervised machine learning method giving insights on data without early knowledge. Classes of data are return by assembling similar elements together. Giving the increasing of the available data, this method is now applied in a lot of fields with various data types. Here, we propose to explore the case of time series clustering. Indeed, time series are one of the most classic data type, and are present in various fields such as medical or finance. This kind of data can be pre-processed by of dimension reduction methods, such as the recent UMAP algorithm. In this paper, a benchmark of time series clustering is created, comparing the results with and without UMAP as a pre-processing step. UMAP is used to enhance clustering results. For completeness, three different clustering algorithms and two different geometric representation for the time series (Classic Euclidean geometry, and Riemannian geometry on the Stiefel Manifold) are applied. The results are compared with and without UMAP as a pre-processing step on the databases available at UCR Time Series Classification Archive www.cs.ucr.edu/~eamonn/time_series_data/.

Multi-Modal Deep Clustering: Unsupervised Partitioning of Images

Guy Shiran, Daphna Weinshall

Auto-TLDR; Multi-Modal Deep Clustering for Unlabeled Images

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The clustering of unlabeled raw images is a daunting task, which has recently been approached with some success by deep learning methods. Here we propose an unsupervised clustering framework, which learns a deep neural network in an end-to-end fashion, providing direct cluster assignments of images without additional processing. Multi-Modal Deep Clustering (MMDC), trains a deep network to align its image embeddings with target points sampled from a Gaussian Mixture Model distribution. The cluster assignments are then determined by mixture component association of image embeddings. Simultaneously, the same deep network is trained to solve an additional self-supervised task. This pushes the network to learn more meaningful image representations and stabilizes the training. Experimental results show that MMDC achieves or exceeds state-of-the-art performance on four challenging benchmarks. On natural image datasets we improve on previous results with significant margins of up to 11% absolute accuracy points, yielding an accuracy of 70% on CIFAR-10 and 61% on STL-10.

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

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.

Deep Convolutional Embedding for Digitized Painting Clustering

Giovanna Castellano, Gennaro Vessio

Auto-TLDR; A Deep Convolutional Embedding Model for Clustering Artworks

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Clustering artworks is difficult because of several reasons. On one hand, recognizing meaningful patterns in accordance with domain knowledge and visual perception is extremely hard. On the other hand, the application of traditional clustering and feature reduction techniques to the highly dimensional pixel space can be ineffective. To address these issues, we propose to use a deep convolutional embedding model for digitized painting clustering, in which the task of mapping the input raw data to an abstract, latent space is jointly optimized with the task of finding a set of cluster centroids in this latent feature space. Quantitative and qualitative experimental results show the effectiveness of the proposed method. The model is also able to outperform other state-of-the-art deep clustering approaches to the same problem. The proposed method may be beneficial to several art-related tasks, particularly visual link retrieval and historical knowledge discovery in painting datasets.

Unconstrained Vision Guided UAV Based Safe Helicopter Landing

Arindam Sikdar, Abhimanyu Sahu, Debajit Sen, Rohit Mahajan, Ananda Chowdhury

Auto-TLDR; Autonomous Helicopter Landing in Hazardous Environments from Unmanned Aerial Images Using Constrained Graph Clustering

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In this paper, we have addressed the problem of automated detection of safe zone(s) for helicopter landing in hazardous environments from images captured by an Unmanned Aerial Vehicle (UAV). The unconstrained motion of the image capturing drone (the UAV in our case) makes the problem further difficult. The solution pipeline consists of natural landmark detection and tracking, stereo-pair generation using constrained graph clustering, digital terrain map construction and safe landing zone detection. The main methodological contribution lies in mathematically formulating epipolar constraint and then using it in a Minimum Spanning Tree (MST) based graph clustering approach. We have also made publicly available AHL (Autonomous Helicopter Landing) dataset, a new aerial video dataset captured by a drone, with annotated ground-truths. Experimental comparisons with other competing clustering methods i) in terms of Dunn Index and Davies Bouldin Index as well as ii) for frame-level safe zone detection in terms of F-measure and confusion matrix clearly demonstrate the effectiveness of the proposed formulation.

Supervised Domain Adaptation Using Graph Embedding

Lukas Hedegaard, Omar Ali Sheikh-Omar, Alexandros Iosifidis

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.

Subspace Clustering for Action Recognition with Covariance Representations and Temporal Pruning

Giancarlo Paoletti, Jacopo Cavazza, Cigdem Beyan, Alessio Del Bue

Auto-TLDR; Unsupervised Learning for Human Action Recognition from Skeletal Data

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This paper tackles the problem of human action recognition, defined as classifying which action is displayed in a trimmed sequence, from skeletal data. Albeit state-of-the-art approaches designed for this application are all supervised, in this paper we pursue a more challenging direction: Solving the problem with unsupervised learning. To this end, we propose a novel subspace clustering method, which exploits covariance matrix to enhance the action’s discriminability and a timestamp pruning approach that allow us to better handle the temporal dimension of the data. Through a broad experimental validation, we show that our computational pipeline surpasses existing unsupervised approaches but also can result in favorable performances as compared to supervised methods.

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.

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.

JECL: Joint Embedding and Cluster Learning for Image-Text Pairs

Sean Yang, Kuan-Hao Huang, Bill Howe

Auto-TLDR; JECL: Clustering Image-Caption Pairs with Parallel Encoders and Regularized Clusters

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We propose JECL, a method for clustering image-caption pairs by training parallel encoders with regularized clustering and alignment objectives, simultaneously learning both representations and cluster assignments. These image-caption pairs arise frequently in high-value applications where structured training data is expensive to produce, but free-text descriptions are common. JECL trains by minimizing the Kullback-Leibler divergence between the distribution of the images and text to that of a combined joint target distribution and optimizing the Jensen-Shannon divergence between the soft cluster assignments of the images and text. Regularizers are also applied to JECL to prevent trivial solutions. Experiments show that JECL outperforms both single-view and multi-view methods on large benchmark image-caption datasets, and is remarkably robust to missing captions and varying data sizes.

Feature Extraction and Selection Via Robust Discriminant Analysis and Class Sparsity

Ahmad Khoder, Fadi Dornaika

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.

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.

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.

Bayesian Active Learning for Maximal Information Gain on Model Parameters

Kasra Arnavaz, Aasa Feragen, Oswin Krause, Marco Loog

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.

Single-Modal Incremental Terrain Clustering from Self-Supervised Audio-Visual Feature Learning

Reina Ishikawa, Ryo Hachiuma, Akiyoshi Kurobe, Hideo Saito

Auto-TLDR; Multi-modal Variational Autoencoder for Terrain Type Clustering

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The key to an accurate understanding of terrain is to extract the informative features from the multi-modal data obtained from different devices. Sensors, such as RGB cameras, depth sensors, vibration sensors, and microphones, are used as the multi-modal data. Many studies have explored ways to use them, especially in the robotics field. Some papers have successfully introduced single-modal or multi-modal methods. However, in practice, robots can be faced with extreme conditions; microphones do not work well in the crowded scenes, and an RGB camera cannot capture terrains well in the dark. In this paper, we present a novel framework using the multi-modal variational autoencoder and the Gaussian mixture model clustering algorithm on image data and audio data for terrain type clustering. Our method enables the terrain type clustering even if one of the modalities (either image or audio) is missing at the test-time. We evaluated the clustering accuracy with a conventional multi-modal terrain type clustering method and we conducted ablation studies to show the effectiveness of our approach.

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

Zhan Wang, Lizhi Wang, Hua Huang

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.

Detecting Rare Cell Populations in Flow Cytometry Data Using UMAP

Lisa Weijler, Markus Diem, Michael Reiter

Auto-TLDR; Unsupervised Manifold Approximation and Projection for Small Cell Population Detection in Flow cytometry Data

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We present an approach for detecting small cell populations in flow cytometry (FCM) samples based on the combination of unsupervised manifold embedding and supervised random forest classification. Each sample consists of hundred thousands to a few million cells where each cell typically corresponds to a measurement vector with 10 to 50 dimensions. The difficulty of the task is that clusters of measurement vectors formed in the data space according to standard clustering criteria often do not correspond to biologically meaningful sub-populations of cells, due to strong variations in shape and size of their distributions. In many cases the relevant population consists of less than 100 scattered events out of millions of events, where supervised approaches perform better than unsupervised clustering. The aim of this paper is to demonstrate that the performance of the standard supervised classifier can be improved significantly by combining it with a preceding unsupervised learning step involving the Uniform Manifold Approximation and Projection (UMAP). We present an experimental evaluation on FCM data from children suffering from Acute Lymphoblastic Leukemia (ALL) showing that the improvement particularly occurs in difficult samples where the size of the relevant population of leukemic cells is low in relation to other sub-populations. Further, the experiments indicate that on such samples the algorithm also outperforms other baseline methods based on Gaussian Mixture Models.

Tensor Factorization of Brain Structural Graph for Unsupervised Classification in Multiple Sclerosis

Berardino Barile, Marzullo Aldo, Claudio Stamile, Françoise Durand-Dubief, Dominique Sappey-Marinier

Auto-TLDR; A Fully Automated Tensor-based Algorithm for Multiple Sclerosis Classification based on Structural Connectivity Graph of the White Matter Network

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Analysis of longitudinal changes in brain diseases is essential for a better characterization of pathological processes and evaluation of the prognosis. This is particularly important in Multiple Sclerosis (MS) which is the first traumatic disease in young adults, with unknown etiology and characterized by complex inflammatory and degenerative processes leading to different clinical courses. In this work, we propose a fully automated tensor-based algorithm for the classification of MS clinical forms based on the structural connectivity graph of the white matter (WM) network. Using non-negative tensor factorization (NTF), we first focused on the detection of pathological patterns of the brain WM network affected by significant longitudinal variations. Second, we performed unsupervised classification of different MS phenotypes based on these longitudinal patterns, and finally, we used the latent factors obtained by the factorization algorithm to identify the most affected brain regions.

Dependently Coupled Principal Component Analysis for Bivariate Inversion Problems

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

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.

Social Network Analysis Using Knowledge-Graph Embeddings and Convolution Operations

Bonaventure Chidube Molokwu, Shaon Bhatta Shuvo, Ziad Kobti, Narayan C. Kar

Auto-TLDR; RLVECO: Representation Learning via Knowledge- Graph Embeddings and Convolution Operations for Social Network Analysis

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Link prediction and node classification tasks in Social Network Analysis (SNA) remain open research problems with respect to Artificial Intelligence (AI). Thus, the inherent representations about social network structures can be effectively harnessed for training AI models in a bid to predict ties as well as detect clusters via classification of actors with regard to a given social network structure. In this paper, we have proposed a special hybrid model comprising dual layers of Feature Learning (FL): Representation Learning via Knowledge- Graph Embeddings and Convolution Operations (RLVECO). The architecture of RLVECO is tailored towards analyzing and extracting meaningful representations from social network structures so as to aid in link prediction, node classification, and community detection tasks. RLVECO utilizes an edge sampling approach for exploiting features of the social graph via learning the context of each actor with respect to its neighboring actors.

Factor Screening Using Bayesian Active Learning and Gaussian Process Meta-Modelling

Cheng Li, Santu Rana, Andrew William Gill, Dang Nguyen, Sunil Kumar Gupta, Svetha Venkatesh

Auto-TLDR; Data-Efficient Bayesian Active Learning for Factor Screening in Combat Simulations

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In this paper we propose a data-efficient Bayesian active learning framework for factor screening, which is important when dealing with systems which are expensive to evaluate, such as combat simulations. We use Gaussian Process meta-modelling with the Automatic Relevance Determination covariance kernel, which measures the importance of each factor by the inverse of their associated length-scales in the kernel. This importance measures the degree of non-linearity in the simulation response with respect to the corresponding factor. We initially place a prior over the length-scale values, then use the estimated posterior to select the next datum to simulate which maximises the mutual entropy between the length-scales and the unknown simulation response. Our goal-driven Bayesian active learning strategy ensures that we are data-efficient in discovering the correct values of the length-scales compared to either a random-sampling or uncertainty-sampling based approach. We apply our method to an expensive combat simulation and demonstrate the superiority of our approach.

Separation of Aleatoric and Epistemic Uncertainty in Deterministic Deep Neural Networks

Denis Huseljic, Bernhard Sick, Marek Herde, Daniel Kottke

Auto-TLDR; AE-DNN: Modeling Uncertainty in Deep Neural Networks

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Despite the success of deep neural networks (DNN) in many applications, their ability to model uncertainty is still significantly limited. For example, in safety-critical applications such as autonomous driving, it is crucial to obtain a prediction that reflects different types of uncertainty to address life-threatening situations appropriately. In such cases, it is essential to be aware of the risk (i.e., aleatoric uncertainty) and the reliability (i.e., epistemic uncertainty) that comes with a prediction. We present AE-DNN, a model allowing the separation of aleatoric and epistemic uncertainty while maintaining a proper generalization capability. AE-DNN is based on deterministic DNN, which can determine the respective uncertainty measures in a single forward pass. In analyses with synthetic and image data, we show that our method improves the modeling of epistemic uncertainty while providing an intuitively understandable separation of risk and reliability.

Motion Segmentation with Pairwise Matches and Unknown Number of Motions

Federica Arrigoni, Tomas Pajdla, Luca Magri

Auto-TLDR; Motion Segmentation using Multi-Modelfitting andpermutation synchronization

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In this paper we address motion segmentation, that is the problem of clustering points in multiple images according to a number of moving objects. Two-frame correspondences are assumed as input without prior knowledge about trajectories. Our method is based on principles from ''multi-model fitting'' and ''permutation synchronization'', and - differently from previous techniques working under the same assumptions - it can handle an unknown number of motions. The proposed approach is validated on standard datasets, showing that it can correctly estimate the number of motions while maintaining comparable or better accuracy than the state of the art.

A Spectral Clustering on Grassmann Manifold Via Double Low Rank Constraint

Xinglin Piao, Yongli Hu, Junbin Gao, Yanfeng Sun, Xin Yang, Baocai Yin

Auto-TLDR; Double Low Rank Representation for High-Dimensional Data Clustering on Grassmann Manifold

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High-dimension data clustering is a fundamental topic in machine learning and data mining areas. In recent year, researchers have proposed a series of effective methods based on Low Rank Representation (LRR) which could explore low-dimension subspace structure embedded in original data effectively. The traditional LRR methods usually treat original data as samples in Euclidean space. They generally adopt linear metric to measure the distance between two data. However, high-dimension data (such as video clip or imageset) are always considered as non-linear manifold data such as Grassmann manifold. Therefore, the traditional linear Euclidean metric would be no longer suitable for these special data. In addition, traditional LRR clustering method always adopt nuclear norm as low rank constraint which would lead to suboptimal solution and decrease the clustering accuracy. In this paper, we proposed a new low rank method on Grassmann manifold for high-dimension data clustering task. In the proposed method, a double low rank representation approach is proposed by combining the nuclear norm and bilinear representation for better construct the representation matrix. The experimental results on several public datasets show that the proposed method outperforms the state-of-the-art clustering methods.