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Scalable Direction-Search-Based Approach to Subspace Clustering

Yicong He, George Atia

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

Abstract Slides

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.

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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.

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.

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.

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.

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.

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.

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.

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.

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

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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

3CS Algorithm for Efficient Gaussian Process Model Retrieval

Fabian Berns, Kjeld Schmidt, Ingolf Bracht, Christian Beecks

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

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

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.

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 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.

A Randomized Algorithm for Sparse Recovery

Huiyuan Yu, Maggie Cheng, Yingdong Lu

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

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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.

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.

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.

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.

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.

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.

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.

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.

PIF: Anomaly detection via preference embedding

Filippo Leveni, Luca Magri, Giacomo Boracchi, Cesare Alippi

Auto-TLDR; PIF: Anomaly Detection with Preference Embedding for Structured Patterns

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We address the problem of detecting anomalies with respect to structured patterns. To this end, we conceive a novel anomaly detection method called PIF, that combines the advantages of adaptive isolation methods with the flexibility of preference embedding. Specifically, we propose to embed the data in a high dimensional space where an efficient tree-based method, PI-FOREST, is employed to compute an anomaly score. Experiments on synthetic and real datasets demonstrate that PIF favorably compares with state-of-the-art anomaly detection techniques, and confirm that PI-FOREST is better at measuring arbitrary distances and isolate points in the preference space.

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.

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.

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

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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.

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.

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.

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.

A Novel Adaptive Minority Oversampling Technique for Improved Classification in Data Imbalanced Scenarios

Ayush Tripathi, Rupayan Chakraborty, Sunil Kumar Kopparapu

Auto-TLDR; Synthetic Minority OverSampling Technique for Imbalanced Data

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Imbalance in the proportion of training samples belonging to different classes often poses performance degradation of conventional classifiers. This is primarily due to the tendency of the classifier to be biased towards the majority classes in the imbalanced dataset. In this paper, we propose a novel three step technique to address imbalanced data. As a first step we significantly oversample the minority class distribution by employing the traditional Synthetic Minority OverSampling Technique (SMOTE) algorithm using the neighborhood of the minority class samples and in the next step we partition the generated samples using a Gaussian-Mixture Model based clustering algorithm. In the final step synthetic data samples are chosen based on the weight associated with the cluster, the weight itself being determined by the distribution of the majority class samples. Extensive experiments on several standard datasets from diverse domains show the usefulness of the proposed technique in comparison with the original SMOTE and its state-of-the-art variants algorithms.

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.

Penalized K-Means Algorithms for Finding the Number of Clusters

Behzad Kamgar-Parsi, Behrooz Kamgar-Parsi

Auto-TLDR; Exploring the coefficient of additive penalty in k-means for ideal clusters

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In many applications we want to find the number of clusters in a dataset. A common approach is to use a penalized k-means algorithm with an additive penalty term linear in the number of clusters. Obviously, the number of discovered clusters depends critically on the value of the coefficient of the penalty term, and an open problem is estimating the value of the coefficient in a principled manner. In this paper (a) We derive rigorous bounds for the coefficient of additive penalty in k-means for ideal clusters. Although in practice clusters typically deviate from the ideal assumption, the ideal case serves as a useful guideline. (b) We propose an alternative approach to additive penalty, namely multiplicative penalty, which appears to produce a more reliable signature for the correct number of clusters in most cases. We also empirically investigate certain types of deviations from ideal cluster assumption and show, in particular, that the best way to resolve ambiguous solutions is to combine additive and multiplicative penalties.

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.

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.

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.

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.

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.

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.