Description:

The aim is to embed a given data relationship matrix into a low-dimensional Euclidean space such that the point distances / distance ranks correlate best with the original input relationships. Input relationships may be given as (sparse) (asymmetric) distance, dissimilarity, or (negative!) score matrices. Input-output relations are modeled as low-conditioned. (Weighted) Pearson and soft Spearman rank correlation, and unweighted soft Kendall correlation are supported correlation measures for input/output object neighborhood relationships.

Correlation-based multidimensional scaling is implemented for reconstructing pairwise dissimilarity or score relationships in a Euclidean space. Pearson correlation between pairs of objects in source and target space are directly maximized by gradient methods. Alternatively, optimization of Spearman rank correlation and Kendall correlation is achieved by a numerically soft formulation. Scale and shift invariance properties of correlation help circumventing typical norm concentration problems.

Contrary to non-metric MDS based on isotonic regression and high-throughput MDS (HiT-MDS) maximizing Pearson correlation, the implementation is not matrix-conditioned (global) but row-conditioned (local) which allows for embedding asymmetric of relational score matrices. That is, instance-specific similarity profiles are reconstructed rather than global rank or distance relationships.

Changes to previous version:

• Initial release (Ver 1.0): Weighted Pearson and correlation and soft Spearman rank correlation, Tue Dec 4 16:14:51 CET 2012

• Ver 1.1 Added soft Kendall correlation, Fri Mar 8 08:41:09 CET 2013

• Ver 1.2 Added reconstruction of sparse relationship matrices, Fri Jul 26 16:58:37 CEST 2013

BibTeX Entry: Download

Corresponding Paper BibTeX Entry: Download

Supported Operating Systems: Platform Independent

Data Formats: Matlab

Tags: Data Visualization, Mds, Neighbor Embedding, Relational Data, Sparse Data

Archive: download here

Other available revisons

Version	Changelog	Date
1.2	Initial release (Ver 1.0): Weighted Pearson and correlation and soft Spearman rank correlation, Tue Dec 4 16:14:51 CET 2012 Ver 1.1 Added soft Kendall correlation, Fri Mar 8 08:41:09 CET 2013 Ver 1.2 Added reconstruction of sparse relationship matrices, Fri Jul 26 16:58:37 CEST 2013	July 27, 2013, 14:35:36
1.1	Initial release (Ver 1.0): Weighted Pearson and correlation and soft Spearman rank correlation, Tue Dec 4 16:14:51 CET 2012 Ver 1.1 Added soft Kendall correlation, Fri Mar 8 08:41:09 CET 2013	March 11, 2013, 11:47:39
1.0	Initial Announcement on mloss.org.	December 4, 2012, 16:49:24

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