Integrating joint feature selection into subspace learning: A formulation of 2DPCA for outliers robust feature selection

© 2019 Elsevier Ltd Since the principal component analysis and its variants are sensitive to outliers that affect their performance and applicability in real world, several variants have been proposed to improve the robustness. However, most of the existing methods are still sensitive to outliers and are unable to select useful features. To overcome the issue of sensitivity of PCA against outliers, in this paper, we introduce two-dimensional outliers-robust principal component analysis (ORPCA) by imposing the joint constraints on the objective function. ORPCA relaxes the orthogonal constraints and penalizes the regression coefficient, thus, it selects important features and ignores the same features that exist in other principal components. It is commonly known that square Frobenius norm is sensitive to outliers. To overcome this issue, we have devised an alternative way to derive objective function. Experimental results on four publicly available benchmark datasets show the effectiveness of joint feature selection and provide better performance as compared to state-of-the-art dimensionality-reduction methods

A Survey on Metric Learning for Feature Vectors and Structured Data

The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This has led to the emergence of metric learning, which aims at automatically learning a metric from data and has attracted a lot of interest in machine learning and related fields for the past ten years. This survey paper proposes a systematic review of the metric learning literature, highlighting the pros and cons of each approach. We pay particular attention to Mahalanobis distance metric learning, a well-studied and successful framework, but additionally present a wide range of methods that have recently emerged as powerful alternatives, including nonlinear metric learning, similarity learning and local metric learning. Recent trends and extensions, such as semi-supervised metric learning, metric learning for histogram data and the derivation of generalization guarantees, are also covered. Finally, this survey addresses metric learning for structured data, in particular edit distance learning, and attempts to give an overview of the remaining challenges in metric learning for the years to come.Comment: Technical report, 59 pages. Changes in v2: fixed typos and improved presentation. Changes in v3: fixed typos. Changes in v4: fixed typos and new method

Flexible unsupervised feature extraction for image classification

Dimensionality reduction is one of the fundamental and important topics in the fields of pattern recognition and machine learning. However, most existing dimensionality reduction methods aim to seek a projection matrix W such that the projection W T x is exactly equal to the true low-dimensional representation. In practice, this constraint is too rigid to well capture the geometric structure of data. To tackle this problem, we relax this constraint but use an elastic one on the projection with the aim to reveal the geometric structure of data. Based on this context, we propose an unsupervised dimensionality reduction model named flexible unsupervised feature extraction (FUFE) for image classification. Moreover, we theoretically prove that PCA and LPP, which are two of the most representative unsupervised dimensionality reduction models, are special cases of FUFE, and propose a non-iterative algorithm to solve it. Experiments on five real-world image databases show the effectiveness of the proposed model