DISGUISED DISCRIMINATION OF LOCALITY-BASED UNSUPERVISED DIMENSIONALITY REDUCTION

Abstract

Many locality-based unsupervised dimensionality reduction (DR) algorithms have recently been proposed and demonstrated to be e®ective to a certain degree in some classi¯cation tasks. In this paper, we aim to show that: (1) a discriminant disposal is intentionally or unintentionally induced from the construction of locality in these unsupervised algorithms, however, such a discrimination is often inconsistent with the actual class information, so here called disguised discrimination; (2) sensitivities of these algorithms to local neighbor parameters stem from the inconsistency between the disguised discrimination and the actual class information; (3) how such inconsistency impacts the classi¯cation performance of these algorithms. The experiments on the benchmark face datasets testify our statements that are expected to provide some insight into the unsupervised leaning based on locality.

A Comparative Study: Globality versus Locality for Graph Construction in Discriminant Analysis

“…Up to date, to our knowledge, there are few particular concerns on these issues. So, pursuing our previous studies on the graph construction and DA [19][20][21], in this paper, we elaborately address the issues involved above. Concretely, firstly, we illustrate the meanings of local compactness, global compactness, local margin, and global margin in DA, as shown in Figure 1; secondly, we formulate globally constructed intraclass and interclass graphs; thirdly, resorting to the relation between the scatter and the structure preservation property of DA based on graph construction, by Proposition 1 and Corollary 2 and Proposition 3 and Corollary 4, we demonstrate that the interclass graph should be globally constructed and the intraclass graph should be locally constructed; finally, by jointly utilizing both the globality and the locality, we develop two DA algorithms; that is, one is Globally marginal and Locally compact Discriminant Analysis (GmLcDA) algorithm based on so-introduced global interclass and local intraclass graphs, and the other is Locally marginal and Globally compact Discriminant Analysis (LmGcDA) based on so-introduced local interclass and global intraclass graphs.…”