Segmentation of Multivariate Mixed Data via Lossy Data Coding and Compression

In this paper, based on ideas from lossy data coding and compression, we present a simple but effective technique for segmenting multivariate mixed data that are drawn from a mixture of Gaussian distributions, which are allowed to be almost degenerate. The goal is to find the optimal segmentation th...

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Vydáno v:IEEE transactions on pattern analysis and machine intelligence Ročník 29; číslo 9; s. 1546 - 1562
Hlavní autoři: Yi Ma, Derksen, H., Wei Hong, Wright, J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Los Alamitos, CA IEEE 01.09.2007
IEEE Computer Society
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Applied sciences
Artificial Intelligence
Asymptotic properties
Bioinformatics
Coding
Compressing
Computer science; control theory; systems
Computer Simulation
Data Clustering
Data compression
Data Compression - methods
Data Interpretation, Statistical
Data Segmentation
Distortion
Exact sciences and technology
Gaussian distribution
Image coding
Image segmentation
Lossy Coding
Lossy Compression
Maximum likelihood estimation
Microarray Data Clustering
Models, Statistical
Multivariate Analysis
Multivariate Mixed Data
Normal Distribution
Optimization
Parameter estimation
Pattern Recognition, Automated - methods
Pattern recognition. Digital image processing. Computational geometry
Phase distortion
Rate Distortion
Segmentation
Segments
Signal processing algorithms
Studies
Cluster analysis
Parameter estimation
Multivariate mixed data
Image processing
Data compression
Degenerate system
DNA chip
data clustering
Modeling
Phase transitions
Outlier
lossy coding
Classification
System identification
Pattern analysis
Deterministic approach
Bioinformatics
microarray data clustering
Mixed distribution
lossy compression
Rate distortion theory
data segmentation
Image segmentation
rate distortion
Gaussian process
Optimal solution
Asymptotic approximation
Artificial intelligence
ISSN:0162-8828, 1939-3539
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Popis
Shrnutí:In this paper, based on ideas from lossy data coding and compression, we present a simple but effective technique for segmenting multivariate mixed data that are drawn from a mixture of Gaussian distributions, which are allowed to be almost degenerate. The goal is to find the optimal segmentation that minimizes the overall coding length of the segmented data, subject to a given distortion. By analyzing the coding length/rate of mixed data, we formally establish some strong connections of data segmentation to many fundamental concepts in lossy data compression and rate-distortion theory. We show that a deterministic segmentation is approximately the (asymptotically) optimal solution for compressing mixed data. We propose a very simple and effective algorithm that depends on a single parameter, the allowable distortion. At any given distortion, the algorithm automatically determines the corresponding number and dimension of the groups and does not involve any parameter estimation. Simulation results reveal intriguing phase-transition-like behaviors of the number of segments when changing the level of distortion or the amount of outliers. Finally, we demonstrate how this technique can be readily applied to segment real imagery and bioinformatic data.
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ISSN:0162-8828
1939-3539
DOI:10.1109/TPAMI.2007.1085