Feature Grouping and Sparse Principal Component Analysis

Sparse Principal Component Analysis (SPCA) is widely used in data processing and dimension reduction; it uses the lasso to produce modified principal components with sparse loadings for better interpretability. However, sparse PCA never considers an additional grouping structure where the loadings share similar coefficients (i.e., feature grouping), besides a special group with all coefficients being zero (i.e., feature selection). In this paper, we propose a novel method called Feature Grouping and Sparse Principal Component Analysis (FGSPCA) which allows the loadings to belong to disjoint homogeneous groups, with sparsity as a special case. The proposed FGSPCA is a subspace learning method designed to simultaneously perform grouping pursuit and feature selection, by imposing a non-convex regularization with naturally adjustable sparsity and grouping effect. To solve the resulting non-convex optimization problem, we propose an alternating algorithm that incorporates the difference-of-convex programming, augmented Lagrange and coordinate descent methods. Additionally, the experimental results on real data sets show that the proposed FGSPCA benefits from the grouping effect compared with methods without grouping effect.Comment: 21 pages, 5 figures, 2 table

Learning Rank Reduced Interpolation with Principal Component Analysis

In computer vision most iterative optimization algorithms, both sparse and dense, rely on a coarse and reliable dense initialization to bootstrap their optimization procedure. For example, dense optical flow algorithms profit massively in speed and robustness if they are initialized well in the basin of convergence of the used loss function. The same holds true for methods as sparse feature tracking when initial flow or depth information for new features at arbitrary positions is needed. This makes it extremely important to have techniques at hand that allow to obtain from only very few available measurements a dense but still approximative sketch of a desired 2D structure (e.g. depth maps, optical flow, disparity maps, etc.). The 2D map is regarded as sample from a 2D random process. The method presented here exploits the complete information given by the principal component analysis (PCA) of that process, the principal basis and its prior distribution. The method is able to determine a dense reconstruction from sparse measurement. When facing situations with only very sparse measurements, typically the number of principal components is further reduced which results in a loss of expressiveness of the basis. We overcome this problem and inject prior knowledge in a maximum a posterior (MAP) approach. We test our approach on the KITTI and the virtual KITTI datasets and focus on the interpolation of depth maps for driving scenes. The evaluation of the results show good agreement to the ground truth and are clearly better than results of interpolation by the nearest neighbor method which disregards statistical information.Comment: Accepted at Intelligent Vehicles Symposium (IV), Los Angeles, USA, June 201

Unsupervised Learning of Individuals and Categories from Images

Motivated by the existence of highly selective, sparsely firing cells observed in the human medial temporal lobe (MTL), we present an unsupervised method for learning and recognizing object categories from unlabeled images. In our model, a network of nonlinear neurons learns a sparse representation of its inputs through an unsupervised expectation-maximization process. We show that the application of this strategy to an invariant feature-based description of natural images leads to the development of units displaying sparse, invariant selectivity for particular individuals or image categories much like those observed in the MTL data

FAStEN: an efficient adaptive method for feature selection and estimation in high-dimensional functional regressions

Functional regression analysis is an established tool for many contemporary scientific applications. Regression problems involving large and complex data sets are ubiquitous, and feature selection is crucial for avoiding overfitting and achieving accurate predictions. We propose a new, flexible, and ultra-efficient approach to perform feature selection in a sparse high dimensional function-on-function regression problem, and we show how to extend it to the scalar-on-function framework. Our method combines functional data, optimization, and machine learning techniques to perform feature selection and parameter estimation simultaneously. We exploit the properties of Functional Principal Components, and the sparsity inherent to the Dual Augmented Lagrangian problem to significantly reduce computational cost, and we introduce an adaptive scheme to improve selection accuracy. Through an extensive simulation study, we benchmark our approach to the best existing competitors and demonstrate a massive gain in terms of CPU time and selection performance without sacrificing the quality of the coefficients' estimation. Finally, we present an application to brain fMRI data from the AOMIC PIOP1 study