Graph Embedding Exploiting Subclasses

Abstract

Abstract-Recently, subspace learning methods for Dimensionality Reduction (DR), like Subclass Discriminant Analysis (SDA) and Clustering-based Discriminant Analysis (CDA), which use subclass information for the discrimination between the data classes, have attracted much attention. In parallel, important work has been accomplished on Graph Embedding (GE), which is a general framework unifying several subspace learning techniques. In this paper, GE has been extended in order to integrate subclass discriminant information resulting to the novel Subclass Graph Embedding (SGE) framework. The kernelization of SGE is also presented. It is shown that SGE comprises a generalization of the typical GE including subclass DR methods. In this vein, the theoretical link of SDA and CDA methods with SGE is established. The efficacy and power of the SGE has been substantiated by comparing subclass DR methods versus a diversity of unimodal methods all pertaining to the SGE framework via a series of experiments on various real-world data.

Steady state visual evoked potential detection using Subclass Marginal Fisher Analysis

“…Subclass Marginal Fisher Analysis has its inception in Subclass Graph Embedding (SGE), which is a general framework for developing algorithms that reduce the dimensionality of high-dimensional data samples [11]. In SGE, we seek for a projection matrix V ∈ R n×m so that every vector x ∈ R n lying in the initial space can be projected to a lowdimensional vector y ∈ R m , with m < n via: y = V T x.…”

“…SMFA belongs to a general category of techniques, known as Subspace Learning (SL) [10], which in the process of feature extraction reduce the dimensionality of the raw data, while retaining as much discriminant information as possible. In general, SL methods have been applied to many different classification domains with noticeable success [11]. Amongst them, Linear Discriminant Analysis (LDA) [12] and Multi-Linear Regression (MLR) [4] have become baseline approaches, and a multitude of other methods build on them.…”

Speed-up and multi-view extensions to Subclass Discriminant Analysis

“…In this paper, we propose a speed-up approach for SDA and its kernelized form, i.e., Kernel Subclass Discriminant Analysis (KSDA) [16]. The proposed approach is based on graph embedding [9,17] and exploitation of the structure of the between-class Laplacian matrix.…”