Discriminative variable selection for clustering with the sparse Fisher-EM algorithm

The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results. Existing approaches have demonstrated the efficiency of variable selection for clustering but turn out to be either very time consuming or not sparse enough in high-dimensional spaces. This work proposes to perform a selection of the discriminative variables by introducing sparsity in the loading matrix of the Fisher-EM algorithm. This clustering method has been recently proposed for the simultaneous visualization and clustering of high-dimensional data. It is based on a latent mixture model which fits the data into a low-dimensional discriminative subspace. Three different approaches are proposed in this work to introduce sparsity in the orientation matrix of the discriminative subspace through $\ell_{1}$-type penalizations. Experimental comparisons with existing approaches on simulated and real-world data sets demonstrate the interest of the proposed methodology. An application to the segmentation of hyperspectral images of the planet Mars is also presented

Twin Learning for Similarity and Clustering: A Unified Kernel Approach

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise and outliers. Thus the learned similarity matrix is often not suitable, let alone optimal, for the subsequent clustering. In addition, nonlinear similarity often exists in many real world data which, however, has not been effectively considered by most existing methods. To tackle these two challenges, we propose a model to simultaneously learn cluster indicator matrix and similarity information in kernel spaces in a principled way. We show theoretical relationships to kernel k-means, k-means, and spectral clustering methods. Then, to address the practical issue of how to select the most suitable kernel for a particular clustering task, we further extend our model with a multiple kernel learning ability. With this joint model, we can automatically accomplish three subtasks of finding the best cluster indicator matrix, the most accurate similarity relations and the optimal combination of multiple kernels. By leveraging the interactions between these three subtasks in a joint framework, each subtask can be iteratively boosted by using the results of the others towards an overall optimal solution. Extensive experiments are performed to demonstrate the effectiveness of our method.Comment: Published in AAAI 201

Clustering based on Mixtures of Sparse Gaussian Processes

Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in machine learning. In this article, we focus on proposing a joint formulation for both clustering and dimensionality reduction. When a probabilistic model is desired, one possible solution is to use the mixture models in which both cluster indicator and low dimensional space are learned. Our algorithm is based on a mixture of sparse Gaussian processes, which is called Sparse Gaussian Process Mixture Clustering (SGP-MIC). The main advantages to our approach over existing methods are that the probabilistic nature of this model provides more advantages over existing deterministic methods, it is straightforward to construct non-linear generalizations of the model, and applying a sparse model and an efficient variational EM approximation help to speed up the algorithm

Grassmann Learning for Recognition and Classification

Computational performance associated with high-dimensional data is a common challenge for real-world classification and recognition systems. Subspace learning has received considerable attention as a means of finding an efficient low-dimensional representation that leads to better classification and efficient processing. A Grassmann manifold is a space that promotes smooth surfaces, where points represent subspaces and the relationship between points is defined by a mapping of an orthogonal matrix. Grassmann learning involves embedding high dimensional subspaces and kernelizing the embedding onto a projection space where distance computations can be effectively performed. In this dissertation, Grassmann learning and its benefits towards action classification and face recognition in terms of accuracy and performance are investigated and evaluated. Grassmannian Sparse Representation (GSR) and Grassmannian Spectral Regression (GRASP) are proposed as Grassmann inspired subspace learning algorithms. GSR is a novel subspace learning algorithm that combines the benefits of Grassmann manifolds with sparse representations using least squares loss §¤1-norm minimization for improved classification. GRASP is a novel subspace learning algorithm that leverages the benefits of Grassmann manifolds and Spectral Regression in a framework that supports high discrimination between classes and achieves computational benefits by using manifold modeling and avoiding eigen-decomposition. The effectiveness of GSR and GRASP is demonstrated for computationally intensive classification problems: (a) multi-view action classification using the IXMAS Multi-View dataset, the i3DPost Multi-View dataset, and the WVU Multi-View dataset, (b) 3D action classification using the MSRAction3D dataset and MSRGesture3D dataset, and (c) face recognition using the ATT Face Database, Labeled Faces in the Wild (LFW), and the Extended Yale Face Database B (YALE). Additional contributions include the definition of Motion History Surfaces (MHS) and Motion Depth Surfaces (MDS) as descriptors suitable for activity representations in video sequences and 3D depth sequences. An in-depth analysis of Grassmann metrics is applied on high dimensional data with different levels of noise and data distributions which reveals that standardized Grassmann kernels are favorable over geodesic metrics on a Grassmann manifold. Finally, an extensive performance analysis is made that supports Grassmann subspace learning as an effective approach for classification and recognition