# Tensor Factorization

## Tensors

We will be talking about tensors but we will skip the introduction to tensor for now.

In this article, we follow a commonly used convention for tensors in physics, the abstract index notation. We will denote tensors as $T^{ab\cdots}_ {\phantom{ab\cdots}cd\cdots}$, where the latin indices such as $^{a}$ are simply a placebo for the slot for this “tensor machine”. For a given basis (coordinate system), we can write down the components of this tensor $T^{\alpha\beta\cdots} _ {\phantom{\alpha\beta\cdots}\gamma\delta\cdots}$.

Planted:
by L Ma;

References:

- Anandkumar, A., Ge, R., Hsu, D., Kakade, S. M., & Telgarsky, M. (2012). Tensor decompositions for learning latent variable models. Journal of Machine Learning Research, 15(1), 2773–2832.
- Tensor Methods in Machine Learning
- Penrose graphical notation
- What is the practical difference between abstract index notation and “ordinary” index notation
- Tensor Decomposition: Fast CNN in your pocket

Dynamic Backlinks:

L Ma (2019). 'Tensor Factorization', Datumorphism, 06 April. Available at: https://datumorphism.leima.is/wiki/machine-learning/factorization/tensor-factorization/.