Supervised classification via constrained subspace and tensor sparse representation

SRC, a supervised classifier via sparse representation, has rapidly gained popularity in recent years and can be adapted to a wide range of applications based on the sparse solution of a linear system. First, we offer an intuitive geometric model called constrained subspace to explain the mechanism of SRC. The constrained subspace model connects the dots of NN, NFL, NS, NM. Then, inspired from the constrained subspace model, we extend SRC to its tensor-based variant, which takes as input samples of high-order tensors which are elements of an algebraic ring. A tensor sparse representation is used for query tensors. We verify in our experiments on several publicly available databases that the tensor-based SRC called tSRC outperforms traditional SRC in classification accuracy. Although demonstrated for image recognition, tSRC is easily adapted to other applications involving underdetermined linear systems

Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data

The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel

Neural Collaborative Subspace Clustering

We introduce the Neural Collaborative Subspace Clustering, a neural model that discovers clusters of data points drawn from a union of low-dimensional subspaces. In contrast to previous attempts, our model runs without the aid of spectral clustering. This makes our algorithm one of the kinds that can gracefully scale to large datasets. At its heart, our neural model benefits from a classifier which determines whether a pair of points lies on the same subspace or not. Essential to our model is the construction of two affinity matrices, one from the classifier and the other from a notion of subspace self-expressiveness, to supervise training in a collaborative scheme. We thoroughly assess and contrast the performance of our model against various state-of-the-art clustering algorithms including deep subspace-based ones.Comment: Accepted to ICML 201

Multi-View Face Recognition From Single RGBD Models of the Faces

This work takes important steps towards solving the following problem of current interest: Assuming that each individual in a population can be modeled by a single frontal RGBD face image, is it possible to carry out face recognition for such a population using multiple 2D images captured from arbitrary viewpoints? Although the general problem as stated above is extremely challenging, it encompasses subproblems that can be addressed today. The subproblems addressed in this work relate to: (1) Generating a large set of viewpoint dependent face images from a single RGBD frontal image for each individual; (2) using hierarchical approaches based on view-partitioned subspaces to represent the training data; and (3) based on these hierarchical approaches, using a weighted voting algorithm to integrate the evidence collected from multiple images of the same face as recorded from different viewpoints. We evaluate our methods on three datasets: a dataset of 10 people that we created and two publicly available datasets which include a total of 48 people. In addition to providing important insights into the nature of this problem, our results show that we are able to successfully recognize faces with accuracies of 95% or higher, outperforming existing state-of-the-art face recognition approaches based on deep convolutional neural networks

Randomized Dimension Reduction on Massive Data

Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as symmetric generalized eigendecomposition problems. In this paper we outline how taking into account the low rank structure assumption implicit in these dimension reduction approaches provides both computational and statistical advantages. We adapt recent randomized low-rank approximation algorithms to provide efficient solutions to three dimension reduction methods: Principal Component Analysis (PCA), Sliced Inverse Regression (SIR), and Localized Sliced Inverse Regression (LSIR). A key observation in this paper is that randomization serves a dual role, improving both computational and statistical performance. This point is highlighted in our experiments on real and simulated data.Comment: 31 pages, 6 figures, Key Words:dimension reduction, generalized eigendecompositon, low-rank, supervised, inverse regression, random projections, randomized algorithms, Krylov subspace method