TensorPCA or TPCA is shot for Tensor Principal Component Analysis, it is an extension of PCA to tensor (higher dimensional) datasets that estimates tensor factor models. TensorPCA is a Python package that implements the algorithm introduced in the paper Tensor Principal Component Analysis.
For a brief introduction of the tensor factor model, please check out my website.
In your terminal, cd to a directory where you want to save the package, then run
git clone https://github.com/junsupan/TensorPCA
cd TensorPCA
pip install -e .
Functionality of TensorPCA includes
- tensor matricization (unfolding),
- tensor factor model estimation,
- hypothesis test for selecting number of factors,
- generating random tensor data.
Run example.py to check if the package is successfully installed.
For a quick start, we can first randomly generate a 3-dim tensor factor model by the following code:
from TensorPCA.dgp import DGP
R = 2 # rank, number of factors
# tensor size TxNxJ
T = 40
N = 30
J = 20
Y, s, M = DGP((T,N,J),R)
The above code assigns the randomly generated tensor to variable Y, the scale components to variable s, and the vector components to variable M. Note that, s and M are the true parameters that generate the tensor Y.
Then following code inputs the tensor Y into a class of functions:
from TensorPCA.tensorpca import TensorPCA
Z = TensorPCA(Y)
The class has method tensor matricization (unfolding):
Z.unfold(0) # to unfold the tensor in its first dimension
Z.unfold(1) # to unfold the tensor in its second dimension
Z.unfold(2) # to unfold the tensor in its third dimension
We can also estimate the tensor factor model by the code:
s_hat, M_hat = Z.t_pca(2) # to estimate a 2-factor model
Lastly, for the hypothesis
| H0 | H1 |
|---|---|
|
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the number of factors > k, but |
the following code implements the above test in each dimension:
from TensorPCA.hyptest import dist
TW_dist = dist(1, 3) # approximating the statistic distribution with k=1, K=3
Stat, pValue = Z.ranktest(TW_dist)
where k=1, K=3.
The output pValue would reject the null hypothesis because tensor Y has two 2 factors.
Note: The distribution approximation process takes considerable amount of time, thus we have provided pre-created distributions for k=(1,...,9) and K=(k+1,...,10).
If you use TensorPCA in an academic paper, please cite
Babii, Andrii, Eric Ghysels, and Junsu Pan. "Tensor Principal Component Analysis." arXiv preprint arXiv:2212.12981 (2022). https://arxiv.org/abs/2212.12981
If you have any question, please contact junsupan1994@gmail.com