Active subspace learning

Many previous studies have shown that naturally occurring data cannot possibly fill up the high dimensional space uniformly, rather it must concentrate around lower dimensional structure. The typical supervised subspace learning algorithms to discover this low dimensional structure include Linear Discriminant Analysis (LDA). For LDA, the training data points are usually pre-given. However, in some real world applications like relevance feedback image retrieval, there is opportunity to interact with the user and actively select the training points for labeling. In this paper, we propose a novel active subspace learning algorithm which selects the most informative data points and uses them for learning an optimal subspace. Using techniques from experimental design, we discuss how to perform data selection in supervised or semi-supervised subspace learning by minimizing the expected error. Experiments on image retrieval show improvement over state-of-the-art methods.

1. Introduction

In many real world applications, objects such as images are usually represented as points in very high dimensional space. However, the naturally occurring data cannot possibly fill up the ambient space uniformly, rather it must concentrate around lower dimensional structure. Subspace learning aims at discover the intrinsic geometrical and discriminant structure in the data. The typical supervised and semi-supervised subspace learning algorithms include Linear Discriminant Analysis (LDA) [10] and Semi-supervised Discriminant Analysis (SDA) [3].