Generalized principal component analysis (GPCA)

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 27; no. 12; pp. 1945 - 1959
• Main Authors: Vidal, R., Yi Ma, Sastry, S.
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01.12.2005; IEEE Computer Society; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Application software; Applied sciences; Artificial Intelligence; Cluster Analysis; Clustering algorithms; Computer science; control theory; systems; Computer Simulation; Computer vision; Data points; Derivatives; dimensionality reduction; dynamic scenes and motion segmentation; Exact sciences and technology; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Imaging, Three-Dimensional - methods; Index Terms- Principal component analysis (PCA); Information Storage and Retrieval - methods; Iterative algorithms; Kernel; Machine learning; Mathematical analysis; Mathematical models; Matrix decomposition; Models, Statistical; Motion segmentation; Pattern Recognition, Automated - methods; Pattern recognition. Digital image processing. Computational geometry; Polynomials; Principal Component Analysis; Principal components analysis; Segmentation; Studies; subspace segmentation; Subspaces; temporal video segmentation; Three dimensional; Vectors (mathematics); Veronese map; subspace segmentation; Computer vision; dynamic scenes and motion segmentation; Veronese map; temporal video segmentation; Multiple view; Index Terms-Principal component analysis (PCA); Image segmentation; Dimension reduction; dimensionality reduction; Multidimensional database; Scene analysis; Tridimensional image; EM algorithm; Pattern analysis; Principal component analysis

This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a...