Correlative Matrix Mapping, CMM 1.1

marc strickert — Tue, 05 Jul 2011 15:15:21 -0000

Correlative Matrix Mapping (CMM): If X is a real-valued data matrix (row data vectors) and L the matrix with associated information (row 'label' vectors), then a linear mapping V is computed such that their distance matrices D_X^V and D_L, respectively, are mapped to provide maximum correlation r(D_X^V, D_L) = max. The matrix entries (D_X^V)_ij = sqrt( (x^i-x^j) * V * V' * (x^i-x^j) ) describe the adaptive (Mahalanobis-like) matrix distance between data vectors x^i and x^j with V being optimized according to the maximum correlation mapping criterion induced by D_L.

Correlative Matrix Mapping (CMM) was formerly (before a naming conflict was recognized) known as Multivariate Subspace Regression (MSR) by Strickert, Soto, Vazquez (http://www.dice.ucl.ac.be/esann/proceedings/papers.php?ann=2010).

CMM supersedes Supervised Attribute Relevance Detection using Cross Comparisons (SARDUX) by Strickert, Soto, Vazquez (http://dig.ipk-gatersleben.de/sardux/sardux.html)

The CMM approach is related to canonical correlation analysis, but transforms only the data space to match the well-known static 'label' distance relationships.

mloss.org Correlative Matrix Mapping, CMM

Correlative Matrix Mapping, CMM 1.1