KMeans_SPD_Matrices​.zip

K-Means Clustering for a Population of Symmetric Positive-Definite (SPD) Matrices

This package contains 8 different K-means clustering techniques, applicable to a group of Symmetric Positive Definite (SPD) matrices. The algorithms are different based on (1) the distance/divergence measures used to compare the samples to the cluster centers, and (2) the corresponding mean computation technique, i.e., incremental vs. non-incremental.
The dissimilarity measures used here are: (1) natural geodesic distance on P(n), (2) Stein distance, (3) LogEuclidean distance and (4) Kullback-Leibler divergence.
Mean computation methods are provided in both the incremental and non-incremental frameworks, based on the aforementioned dissimilarity measures.

If you use this software please cite the following papers:

[1] Guang Cheng, Hesamoddin Salehian, Baba C. Vemuri, €œEfficient Recursive Algorithms for Computing the Mean Diffusion Tensor and Applications to DTI Segmentation, European Conference on Computer Vision (ECCV) 2012.

[2] Jeffrey Ho, Guang Cheng, Hesamoddin Salehian, Baba C. Vemuri, €œRecursive Karcher Expectation Estimators And Geometric Law of Large Numbers, International Conference on Artificial Intelligence and Statistics (AISTATS) 2013.

[3] Hesamoddin Salehian, Guang Cheng, Baba C. Vemuri, Jeffrey Ho, Recursive Estimation of the Stein Center of SPD Matrices & its Applications€, International Conference on Computer Vision (ICCV) 2013.