Graph construction using adaptive Local Hybrid Coding scheme

Abstract

It is well known that dense coding with local bases (via Least Square coding schemes) can lead to large quantization errors or poor performances of machine learning tasks. On the other hand, sparse coding focuses on accurate representation without taking into account data locality due to its tendency to ignore the intrinsic structure hidden among the data. Local Hybrid Coding (LHC) (Xiang et al., 2014) was recently proposed as an alternative to the sparse coding scheme that is used in Sparse Representation Classifier (SRC). The LHC blends sparsity and bases-locality criteria in a unified optimization problem. It can retain the strengths of both sparsity and locality. Thus, the hybrid codes would have some advantages over both dense and sparse codes. This paper introduces a data-driven graph construction method that exploits and extends the LHC scheme. In particular, we propose a new coding scheme coined Adaptive Local Hybrid Coding (ALHC). The main contributions are as follows. First, the proposed coding scheme adaptively selects the local and non-local bases of LHC using data similarities provided by Locality-constrained Linear code. Second, the proposed ALHC exploits local similarities in its solution. Third, we use the proposed coding scheme for graph construction. For the task of graph-based label propagation, we demonstrate high classification performance of the proposed graph method on four benchmark face datasets: Extended Yale, PF01, PIE, and FERET.