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The TensorProjection Layer is a dimensionality reduction layer proposed by Toshinari Morimoto and Su-Yun Huang. We have implemented our method as a custom hidden layer in TensorFlow.
You can integrate a TensorProjection Layer into a Deep Neural Network defined using TensorFlow Keras. To get started, we recommend installing Python, TensorFlow, and Jupyter Notebook. You can then run the provided code (.ipynb file) using Jupyter Notebook.
Please avoid using very old versions of TensorFlow. The TensorProjection Layer requires the computation of the square root of a positive semi-definite matrix (sqrtm), which is not available in older versions of TensorFlow. Ensure that your version supports this function.
If you decide to incorporate the TensorProjection Layer into your model, we suggest placing it after the final convolutional layer for optimal performance.
The TensorProjection Layer is typically installed after a 2D convolutional layer.
The output of a 2D convolutional layer consists of n 3D tensors, each shaped as [n, p1, p2, p3], where n is the number of observations (i.e., the minibatch size).
The TensorProjection Layer transforms the input tensor from a shape of [n, p1, p2, p3] to [n, q1, q2, q3], where each qk is less than or equal to pk (for k=1, 2, 3).
This transformation is achieved by performing a tensor mode product on each 3D tensor (i=1,2,...,n). The TensorProjection Layer multiplies truncated orthogonal matrices of size [qk, pk] (for k=1, 2, 3) with each tensor.
For further details, please refer to our paper:
https://arxiv.org/abs/2004.04454