Quantization of Eigen Subspace for Sparse Representation

IEEE Transactions on Signal Processing, Vol. 63, No. 14, July 2015

10 Pages Posted: 1 Dec 2015

See all articles by Onur Yilmaz

Onur Yilmaz

New Jersey Institute of Technology

Ali Akansu

New Jersey Institute of Technology

Date Written: July 15, 2015

Abstract

We propose sparse Karhunen-Loeve Transform (SKLT) method to sparse eigen subspaces. The sparsity (cardinality reduction) is achieved through the pdf-optimized quantization of basis function (vector) set. It may be considered an extension of the simple and soft thresholding (ST) methods. The merit of the proposed framework for sparse representation is presented for auto-regressive order one, AR(1),discrete process and empirical correlation matrix of stock returns for NASDAQ-100 index. It is shown that SKLT is efficient to implement and outperforms several sparsity algorithms reported in the literature.

Keywords: Arcsine distribution, cardinality reduction, dimension reduction, eigen decomposition, Karhunen–Loeve Transform (KLT), Lloyd-Max quantizer, midtread (zero-zone) pdf-optimized quantizer, principal component analysis (PCA), sparse matrix, subspace methods, transform coding

JEL Classification: C6

Suggested Citation

Yilmaz, Onur and Akansu, Ali, Quantization of Eigen Subspace for Sparse Representation (July 15, 2015). IEEE Transactions on Signal Processing, Vol. 63, No. 14, July 2015, Available at SSRN: https://ssrn.com/abstract=2697308

Onur Yilmaz

New Jersey Institute of Technology ( email )

University Heights
Newark, NJ 07102
United States

Ali Akansu (Contact Author)

New Jersey Institute of Technology ( email )

University Heights
Newark, NJ 07102
United States

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