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## Project description

## Install the Package from PyPI + Go to the terminal (mac) or command line (windows), copy and paste:pip3 install KTensors or pip3 install KTensors==0.0.5 for a specific version

## install the Package from GitHub

• Go to the terminal (mac) or command line (windows), copy and paste:pip3 install git+https://github.com/Hanchao-Zhang/KTensors.git

• Open a python console, copy and paste: from KTensors import KTensors

### KTensors

KTensors(Psis, K, max_iter=1000).clustering()

input: - Psis: a 3D array of size (n, p, p) where n is the number of matrices and p is the dimension of the positive semi-definite matrices. - K: number of clusters - max_iter: maximum number of iterations, default is 1000, usually finish within 10 iterations

return: - group: a vector of length n, each element is an index of group membership - CPCs: K orthonormal basis matrices of size p by p for each cluster - $mathbf F$: $mathbf F = mathbf B^top mathbfPsi mathbf B$ - $text{diag}(mathbf F)$: $text{diag}(mathbf F) = (mathbf B^top mathbfPsi mathbf B) circ mathbf I$ the diagonal of matrix $mathbf F$ - centers: Mean of each cluster - loss: loss function for each iteration

## Some Tecnical Details

### Loss Function

begin{aligned}mathcal L(mathbf Psi, mathcal P_{mathbf B} (mathbf Psi) ) = Vert mathbf Psi - mathbf B((mathbf B^top mathbf Psi mathbf B) circ mathbb I )mathbf B^top Vert_F^2 = Vertmathbf B^top mathbf Psi mathbf B - (mathbf B^top mathbf Psi mathbf B)circ mathbb I Vert_F^2 end{aligned}

where $mathbb I$ is a identity matrix, and $circ$ is the Hadamard product.

For more technical details, please refer to the paper.

## Project details

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