In this chapter, a novel semi-supervised dimensionality reduction algorithm
is proposed, namely Sparsity Preserving Projection based Constrained Graph
Embedding (SPP-CGE). Sparsity Preserving Projection (SPP) is an unsupervised
dimensionality reduction method. It aims to preserve the sparse reconstructive
relationship of the data obtained by solving a L1 objective function. Label information
is used as additional constraints for graph embedding in the SPP-CGE algorithm. In
SPP-CGE, both the intrinsic structure and the label information of the data are used. In
addition, to deal with new incoming samples, out-of-sample extension of SPP-CGE is
also proposed. Promising experimental results on several popular face databases
illustrate the effectiveness of the proposed method.
Keywords: Affinity matrix, Constrained graph embedding, Dimensionality
reduction, Eigenvalue problem, Face recognition, Graph embedding, ISOMAP,
Laplacian eigenmaps, Laplacian matrix, Linear discriminant analysis, Locality
preserving projection, Locally linear embedding, Multidimensional scaling,
Neighborhood preserving embedding, Principal component analysis, Projection
matrix, Recognition rate, Semi-supervised learning, Sparse representation,
Sparsity preserving projection.
