Least-Squares Log-Density Gradient (LSLDG) directly estimates the gradient of a log-density without going through density estimation. An application of LSLDG is clustering based on mode seeking. The clustering method called LSLDG clustering (LSLDGC) has the following advantages:
We do not need to set the number of clusters in advance.
All the parameters (e.g. bandwidth) can be optimized by cross validation.
It works significantly better than mean-shift clustering in higher-dimensional data.
MATLAB implementation of LSLDGC: LSLDGC.zip
"demo.m" is a demo for clustering.
References
Hiroaki Sasaki, Aapo Hyvärinen and Masashi Sugiyama, “Clustering via Mode Seeking by Direct Estimation of the Gradient of a Log-Density”, the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML/PKDD), Lecture Notes in Computer Science Part Ⅲ, vol. 8726, pp. 19-34, 2014.
Hiroaki Sasaki, Takafumi Kanamori, Aapo Hyvärinen, Gang Niu and Masashi Sugiyama, "Mode-Seeking Clustering and Density Ridge Estimation via Direct Estimation of Density-Derivative-Ratios", arXiv:1707.01711.