K-Tensors: Clustering Positive Semi-Definite Matrices<img src="./ktensorlogo.png" align="right" width="150" />
========================================================================================================================
[](http://www.repostatus.org/#active) [](https://travis-ci.org/stephenslab/clusteringCPC) [](https://codecov.io/gh/stephenslab/clusteringCPC) [](https://cran.r-project.org/package=clusteringCPC) [](https://cran.r-project.org/package=clusteringCPC)
## Install the Package from PyPI
+ Go to the terminal (mac) or command line (windows), copy and paste:`pip3 install KTensors` or `pip3 install KTensors==0.1.7` 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`
## About the Package
### `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
- $\mathbf F$: $\mathbf F = \mathbf B^\top \mathbf\Psi \mathbf B$
- $\text{diag}(\mathbf F)$: $\text{diag}(\mathbf F) = (\mathbf B^\top \mathbf\Psi \mathbf B) \circ \mathbf I$ the diagonal of matrix $\mathbf F$
- centers: Mean of each cluster
- loss: loss function for each iteration
### `KMetrics`
`KMetrics(Psis, K, metrics)`
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
- metrics: a string of metrics, including 'euclidean', 'affine_invariant', 'log_euclidean', 'log_det', and 'symmetric_stein'.
output:
- a vector of length n, each element is an index of group membership
- loss function for each iteration
## Some Tecnical Details
### Loss Function
$$\begin{aligned}\mathcal L(\mathbf \Psi, \mathcal P_{\mathbf B} (\mathbf \Psi) ) = \Vert \mathbf \Psi - \mathbf B((\mathbf B^\top \mathbf \Psi \mathbf B) \circ \mathbb I )\mathbf B^\top \Vert_F^2 = \Vert\mathbf B^\top \mathbf \Psi \mathbf B - (\mathbf B^\top \mathbf \Psi \mathbf B)\circ \mathbb I \Vert_F^2 \end{aligned}$$
where $\mathbb I$ is a identity matrix, and $\circ$ is the Hadamard product.
For more technical details, please refer to the paper.
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"description": "K-Tensors: Clustering Positive Semi-Definite Matrices<img src=\"./ktensorlogo.png\" align=\"right\" width=\"150\" />\n========================================================================================================================\n\n\n[](http://www.repostatus.org/#active) [](https://travis-ci.org/stephenslab/clusteringCPC) [](https://codecov.io/gh/stephenslab/clusteringCPC) [](https://cran.r-project.org/package=clusteringCPC) [](https://cran.r-project.org/package=clusteringCPC)\n\n## Install the Package from PyPI\n+ Go to the terminal (mac) or command line (windows), copy and paste:`pip3 install KTensors` or `pip3 install KTensors==0.1.7` for a specific version\n\n## install the Package from GitHub\n\n+ Go to the terminal (mac) or command line (windows), copy and paste:`pip3 install git+https://github.com/Hanchao-Zhang/KTensors.git`\n+ Open a python console, copy and paste: `from KTensors import KTensors`\n\n\n## About the Package\n\n### `KTensors`\n\n`KTensors(Psis, K, max_iter=1000).clustering()`\n\ninput:\n- 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.\n- K: number of clusters\n- max_iter: maximum number of iterations, default is 1000, usually finish within 10 iterations\n\nreturn:\n- group: a vector of length n, each element is an index of group membership\n- CPCs: K orthonormal basis matrices of size p by p for each cluster\n- $\\mathbf F$: $\\mathbf F = \\mathbf B^\\top \\mathbf\\Psi \\mathbf B$\n- $\\text{diag}(\\mathbf F)$: $\\text{diag}(\\mathbf F) = (\\mathbf B^\\top \\mathbf\\Psi \\mathbf B) \\circ \\mathbf I$ the diagonal of matrix $\\mathbf F$\n- centers: Mean of each cluster\n- loss: loss function for each iteration\n\n### `KMetrics`\n\n`KMetrics(Psis, K, metrics)`\ninput:\n- 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.\n- K: number of clusters\n- metrics: a string of metrics, including 'euclidean', 'affine_invariant', 'log_euclidean', 'log_det', and 'symmetric_stein'.\n\noutput:\n- a vector of length n, each element is an index of group membership\n- loss function for each iteration\n\n## Some Tecnical Details\n\n### Loss Function\n\n$$\\begin{aligned}\\mathcal L(\\mathbf \\Psi, \\mathcal P_{\\mathbf B} (\\mathbf \\Psi) ) = \\Vert \\mathbf \\Psi - \\mathbf B((\\mathbf B^\\top \\mathbf \\Psi \\mathbf B) \\circ \\mathbb I )\\mathbf B^\\top \\Vert_F^2 = \\Vert\\mathbf B^\\top \\mathbf \\Psi \\mathbf B - (\\mathbf B^\\top \\mathbf \\Psi \\mathbf B)\\circ \\mathbb I \\Vert_F^2 \\end{aligned}$$\n\nwhere $\\mathbb I$ is a identity matrix, and $\\circ$ is the Hadamard product.\n\nFor more technical details, please refer to the paper. \n\n",
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