Manifold Adaptive Kernelized Low‐Rank Representation for Semisupervised Image Classification

Abstract

Constructing a powerful graph that can effectively depict the intrinsic connection of data points is the critical step to make the graph-based semisupervised learning algorithms achieve promising performance. Among popular graph construction algorithms, low-rank representation (LRR) is a very competitive one that can simultaneously explore the global structure of data and recover the data from noisy environments. Therefore, the learned low-rank coefficient matrix in LRR can be used to construct the data affinity matrix. Consider the existing problems such as the following: (1) the essentially linear property of LRR makes it not appropriate to process the possible nonlinear structure of data and (2) learning performance can be greatly enhanced by exploring the structure information of data; we propose a new manifold kernelized low-rank representation (MKLRR) model that can perform LRR in the data manifold adaptive kernel space. Specifically, the manifold structure can be incorporated into the kernel space by using graph Laplacian and thus the underlying geometry of data is reflected by the wrapped kernel space. Experimental results of semisupervised image classification tasks show the effectiveness of MKLRR. For example, MKLRR can, respectively, obtain 96.13%, 98.09%, and 96.08% accuracies on ORL, Extended Yale B, and PIE data sets when given 5, 20, and 20 labeled face images per subject.

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“…Graph is an effective data structure to characterize the data relationship [14], based on which many learning tasks can be performed such as clustering [15], dimensionality reduction [16] and semi-supervised learning [8]. Traditionally, graph-based semi-supervised learning models employed a twostage strategy that first constructs a similarity graph and then performs label propagation on this graph [17]- [19]. Obviously, the label propagation performance depends heavily on the graph quality; therefore, such two-stage strategy breaks the inner connections between graph construction and learning tasks, which easily causes the sub-optimality.…”