TY - CHAP

T1 - Sparse component analysis

T2 - A new tool for data mining

AU - Georgiev, Pando

AU - Theis, Fabian

AU - Cichocki, Andrzej

AU - Bakardjian, Hovagim

PY - 2007

Y1 - 2007

N2 - In many practical problems for data mining the data X under consideration (given as (m × N)-matrix) is of the form X = AS, where the matrices A and S with dimensions mxn and nx N respectively (often called mixing matrix or dictionary and source matrix) are unknown (m ≤ n ≤ N). We formulate conditions (SCA-conditions) under which we can recover A and S uniquely (up to scaling and permutation), such that S is sparse in the sense that each column of S has at least one zero element. We call this the Sparse Component Analysis problem (SCA). We present new algorithms for identification of the mixing matrix (under SCAconditions), and for source recovery (under identifiability conditions). The methods are illustrated with examples showing good performance of the algorithms. Typical examples are EEC and fMRI data sets, in which the SCA algorithm allows us to detect some features of the brain signals. Special attention is given to the application of our method to the transposed system XT = ST AT utilizing the sparseness of the mixing matrix A in appropriate situations. We note that the sparseness conditions could be obtained with some preprocessing methods and no independence conditions for the source signals are imposed (in contrast to Independent Component Analysis). We applied our method to fMRI data sets with dimension (128 × 128 × 98) and to EEC data sets from a 256-channels EEC machine.

AB - In many practical problems for data mining the data X under consideration (given as (m × N)-matrix) is of the form X = AS, where the matrices A and S with dimensions mxn and nx N respectively (often called mixing matrix or dictionary and source matrix) are unknown (m ≤ n ≤ N). We formulate conditions (SCA-conditions) under which we can recover A and S uniquely (up to scaling and permutation), such that S is sparse in the sense that each column of S has at least one zero element. We call this the Sparse Component Analysis problem (SCA). We present new algorithms for identification of the mixing matrix (under SCAconditions), and for source recovery (under identifiability conditions). The methods are illustrated with examples showing good performance of the algorithms. Typical examples are EEC and fMRI data sets, in which the SCA algorithm allows us to detect some features of the brain signals. Special attention is given to the application of our method to the transposed system XT = ST AT utilizing the sparseness of the mixing matrix A in appropriate situations. We note that the sparseness conditions could be obtained with some preprocessing methods and no independence conditions for the source signals are imposed (in contrast to Independent Component Analysis). We applied our method to fMRI data sets with dimension (128 × 128 × 98) and to EEC data sets from a 256-channels EEC machine.

KW - Blind Signal Separation

KW - Clustering

KW - Sparse Component Analysis

UR - http://www.scopus.com/inward/record.url?scp=84976516173&partnerID=8YFLogxK

U2 - 10.1007/978-0-387-69319-4_6

DO - 10.1007/978-0-387-69319-4_6

M3 - Chapter

AN - SCOPUS:84976516173

T3 - Springer Optimization and Its Applications

SP - 91

EP - 116

BT - Springer Optimization and Its Applications

PB - Springer International Publishing

ER -