Quantization of eigen subspace for sparse representation

Onur Yilmaz; Ali N. Akansu

doi:10.1109/TSP.2015.2430831

Quantization of eigen subspace for sparse representation

Onur Yilmaz, Ali N. Akansu

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English (US)
Article number	7103342
Pages (from-to)	3616-3625
Number of pages	10
Journal	IEEE Transactions on Signal Processing
Volume	63
Issue number	14
DOIs	https://doi.org/10.1109/TSP.2015.2430831
State	Published - Jul 15 2015

All Science Journal Classification (ASJC) codes

Signal Processing
Electrical and Electronic Engineering

Keywords

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

Access to Document

10.1109/TSP.2015.2430831

Cite this

@article{eec366f8ba4541f788341cbe9c9d46a1,

title = "Quantization of eigen subspace for sparse representation",

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

author = "Onur Yilmaz and Akansu, {Ali N.}",

note = "Publisher Copyright: {\textcopyright} 1991-2012 IEEE.",

year = "2015",

month = jul,

day = "15",

doi = "10.1109/TSP.2015.2430831",

language = "English (US)",

volume = "63",

pages = "3616--3625",

journal = "IEEE Transactions on Signal Processing",

issn = "1053-587X",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "14",

}

TY - JOUR

T1 - Quantization of eigen subspace for sparse representation

AU - Yilmaz, Onur

AU - Akansu, Ali N.

PY - 2015/7/15

Y1 - 2015/7/15

N2 - 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.

AB - 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.

KW - Arcsine distribution

KW - Karhunen-Loeve Transform (KLT)

KW - Lloyd-Max quantizer

KW - cardinality reduction

KW - dimension reduction

KW - eigen decomposition

KW - midtread (zero-zone) pdf-optimized quantizer

KW - principal component analysis (PCA)

KW - sparse matrix

KW - subspace methods

KW - transform coding

UR - http://www.scopus.com/inward/record.url?scp=84933556841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84933556841&partnerID=8YFLogxK

U2 - 10.1109/TSP.2015.2430831

DO - 10.1109/TSP.2015.2430831

M3 - Article

AN - SCOPUS:84933556841

SN - 1053-587X

VL - 63

SP - 3616

EP - 3625

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 14

M1 - 7103342

ER -

Quantization of eigen subspace for sparse representation

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this