Software Listing of Author : "Ambarish Jash"

The different low dimensional embeddings are an orthonormal coordinate system generated from a 1. Diffusion process defined on the data 2 . Normalized Laplace Beltrami operator 3. Normalized Focker Plank operator This is a nonlinear dimension reduction technique using the concepts of manifold learning. The image is color coded. (2 data sets which are 2 dimensional each are being clustered using this algorithm using the first three non trivial eigen function of the normalized Focker Plank operator)

  • Platform: Matlab, Scripts

This technique takes advantage of the kernel trick that can be used in PCA. This is a tutorial only and is slow for large data sets. In line 30 the kernel can be changed. Any Kernel should do it. Ref : http://www.eecs.berkeley.edu/~wainwrig/sta...kopf_kernel.pdf

  • Platform: Matlab, Scripts

The Gaussian Kernel can be changed to any desired kernel. However such a change will not dramatically improve results. This is a variant of ridge regression using the kernel trick (Mercers Theorem).

  • Platform: Matlab, Scripts

A gaussian pdf is propagated through the non-linear system and the skewness particularly during the time of bifurcation is observed. To initialize the whole process just run lorenz_att.m. Make sure all the code is in the same directory. The script lorenz_pdf.m saves some images. To modify the directory where the images need to be saved go to line 75 and then to 79 which returns to the code directory. Also line 48 uses the parallel computing toolbox which if you do not have you can comment it out.

  • Platform: Matlab, Scripts

The correlation function calculated from one realization of an ensemble is inherently flawed since the expectation operation does not come into play. Hence it is important to have an idea of the variance in the correlation function.

  • Platform: Matlab, Scripts
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