Robust Discriminative Clustering with Sparse Regularizers

International audienceClustering high-dimensional data often requires some form of dimensionality reduction, where clustered variables are separated from " noise-looking " variables. We cast this problem as finding a low-dimensional projection of the data which is well-clustered. This yields a one-dimensional projection in the simplest situation with two clusters, and extends naturally to a multi-label scenario for more than two clusters. In this paper, (a) we first show that this joint clustering and dimension reduction formulation is equivalent to previously proposed discriminative clustering frameworks, thus leading to convex relaxations of the problem; (b) we propose a novel sparse extension, which is still cast as a convex relaxation and allows estimation in higher dimensions; (c) we propose a natural extension for the multi-label scenario; (d) we provide a new theoretical analysis of the performance of these formulations with a simple probabilistic model, leading to scalings over the form d = O(√ n) for the affine invariant case and d = O(n) for the sparse case, where n is the number of examples and d the ambient dimension; and finally, (e) we propose an efficient iterative algorithm with running-time complexity proportional to O(nd 2), improving on earlier algorithms which had quadratic complexity in the number of examples

Temporal Model Adaptation for Person Re-Identification

Person re-identification is an open and challenging problem in computer vision. Majority of the efforts have been spent either to design the best feature representation or to learn the optimal matching metric. Most approaches have neglected the problem of adapting the selected features or the learned model over time. To address such a problem, we propose a temporal model adaptation scheme with human in the loop. We first introduce a similarity-dissimilarity learning method which can be trained in an incremental fashion by means of a stochastic alternating directions methods of multipliers optimization procedure. Then, to achieve temporal adaptation with limited human effort, we exploit a graph-based approach to present the user only the most informative probe-gallery matches that should be used to update the model. Results on three datasets have shown that our approach performs on par or even better than state-of-the-art approaches while reducing the manual pairwise labeling effort by about 80%

Utilizing Class Information for Deep Network Representation Shaping

Statistical characteristics of deep network representations, such as sparsity and correlation, are known to be relevant to the performance and interpretability of deep learning. When a statistical characteristic is desired, often an adequate regularizer can be designed and applied during the training phase. Typically, such a regularizer aims to manipulate a statistical characteristic over all classes together. For classification tasks, however, it might be advantageous to enforce the desired characteristic per class such that different classes can be better distinguished. Motivated by the idea, we design two class-wise regularizers that explicitly utilize class information: class-wise Covariance Regularizer (cw-CR) and class-wise Variance Regularizer (cw-VR). cw-CR targets to reduce the covariance of representations calculated from the same class samples for encouraging feature independence. cw-VR is similar, but variance instead of covariance is targeted to improve feature compactness. For the sake of completeness, their counterparts without using class information, Covariance Regularizer (CR) and Variance Regularizer (VR), are considered together. The four regularizers are conceptually simple and computationally very efficient, and the visualization shows that the regularizers indeed perform distinct representation shaping. In terms of classification performance, significant improvements over the baseline and L1/L2 weight regularization methods were found for 21 out of 22 tasks over popular benchmark datasets. In particular, cw-VR achieved the best performance for 13 tasks including ResNet-32/110.Comment: Published in AAAI 201

Estimating functional brain networks by incorporating a modularity prior

Functional brain network analysis has become one principled way of revealing informative organization architectures in healthy brains, and providing sensitive biomarkers for diagnosis of neurological disorders. Prior to any post hoc analysis, however, a natural issue is how to construct “ideal” brain networks given, for example, a set of functional magnetic resonance imaging (fMRI) time series associated with different brain regions. Although many methods have been developed, it is currently still an open field to estimate biologically meaningful and statistically robust brain networks due to our limited understanding of the human brain as well as complex noises in the observed data. Motivated by the fact that the brain is organized with modular structures, in this paper, we propose a novel functional brain network modeling scheme by encoding a modularity prior under a matrix-regularized network learning framework, and further formulate it as a sparse low-rank graph learning problem, which can be solved by an efficient optimization algorithm. Then, we apply the learned brain networks to identify patients with mild cognitive impairment (MCI) from normal controls. We achieved 89.01% classification accuracy even with a simple feature selection and classification pipeline, which significantly outperforms the conventional brain network construction methods. Moreover, we further explore brain network features that contributed to MCI identification, and discovered potential biomarkers for personalized diagnosis

DSL: Discriminative Subgraph Learning via Sparse Self-Representation

The goal in network state prediction (NSP) is to classify the global state (label) associated with features embedded in a graph. This graph structure encoding feature relationships is the key distinctive aspect of NSP compared to classical supervised learning. NSP arises in various applications: gene expression samples embedded in a protein-protein interaction (PPI) network, temporal snapshots of infrastructure or sensor networks, and fMRI coherence network samples from multiple subjects to name a few. Instances from these domains are typically ``wide'' (more features than samples), and thus, feature sub-selection is required for robust and generalizable prediction. How to best employ the network structure in order to learn succinct connected subgraphs encompassing the most discriminative features becomes a central challenge in NSP. Prior work employs connected subgraph sampling or graph smoothing within optimization frameworks, resulting in either large variance of quality or weak control over the connectivity of selected subgraphs. In this work we propose an optimization framework for discriminative subgraph learning (DSL) which simultaneously enforces (i) sparsity, (ii) connectivity and (iii) high discriminative power of the resulting subgraphs of features. Our optimization algorithm is a single-step solution for the NSP and the associated feature selection problem. It is rooted in the rich literature on maximal-margin optimization, spectral graph methods and sparse subspace self-representation. DSL simultaneously ensures solution interpretability and superior predictive power (up to 16% improvement in challenging instances compared to baselines), with execution times up to an hour for large instances.Comment: 9 page