Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.Comment: 33 pages, 12 figure

Unsupervised Feature Selection with Adaptive Structure Learning

The problem of feature selection has raised considerable interests in the past decade. Traditional unsupervised methods select the features which can faithfully preserve the intrinsic structures of data, where the intrinsic structures are estimated using all the input features of data. However, the estimated intrinsic structures are unreliable/inaccurate when the redundant and noisy features are not removed. Therefore, we face a dilemma here: one need the true structures of data to identify the informative features, and one need the informative features to accurately estimate the true structures of data. To address this, we propose a unified learning framework which performs structure learning and feature selection simultaneously. The structures are adaptively learned from the results of feature selection, and the informative features are reselected to preserve the refined structures of data. By leveraging the interactions between these two essential tasks, we are able to capture accurate structures and select more informative features. Experimental results on many benchmark data sets demonstrate that the proposed method outperforms many state of the art unsupervised feature selection methods

Target Contrastive Pessimistic Discriminant Analysis

Domain-adaptive classifiers learn from a source domain and aim to generalize to a target domain. If the classifier's assumptions on the relationship between domains (e.g. covariate shift) are valid, then it will usually outperform a non-adaptive source classifier. Unfortunately, it can perform substantially worse when its assumptions are invalid. Validating these assumptions requires labeled target samples, which are usually not available. We argue that, in order to make domain-adaptive classifiers more practical, it is necessary to focus on robust methods; robust in the sense that the model still achieves a particular level of performance without making strong assumptions on the relationship between domains. With this objective in mind, we formulate a conservative parameter estimator that only deviates from the source classifier when a lower or equal risk is guaranteed for all possible labellings of the given target samples. We derive the corresponding estimator for a discriminant analysis model, and show that its risk is actually strictly smaller than that of the source classifier. Experiments indicate that our classifier outperforms state-of-the-art classifiers for geographically biased samples.Comment: 9 pages, no figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1706.0808

Adaptive Graph via Multiple Kernel Learning for Nonnegative Matrix Factorization

Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define parts-based, and linear representation of nonnegative data. Recently, Graph regularized NMF (GrNMF) is proposed to find a compact representation,which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In GNMF, an affinity graph is constructed from the original data space to encode the geometrical information. In this paper, we propose a novel idea which engages a Multiple Kernel Learning approach into refining the graph structure that reflects the factorization of the matrix and the new data space. The GrNMF is improved by utilizing the graph refined by the kernel learning, and then a novel kernel learning method is introduced under the GrNMF framework. Our approach shows encouraging results of the proposed algorithm in comparison to the state-of-the-art clustering algorithms like NMF, GrNMF, SVD etc.Comment: This paper has been withdrawn by the author due to the terrible writin

Supervised Classification: Quite a Brief Overview

The original problem of supervised classification considers the task of automatically assigning objects to their respective classes on the basis of numerical measurements derived from these objects. Classifiers are the tools that implement the actual functional mapping from these measurements---also called features or inputs---to the so-called class label---or output. The fields of pattern recognition and machine learning study ways of constructing such classifiers. The main idea behind supervised methods is that of learning from examples: given a number of example input-output relations, to what extent can the general mapping be learned that takes any new and unseen feature vector to its correct class? This chapter provides a basic introduction to the underlying ideas of how to come to a supervised classification problem. In addition, it provides an overview of some specific classification techniques, delves into the issues of object representation and classifier evaluation, and (very) briefly covers some variations on the basic supervised classification task that may also be of interest to the practitioner