# Randomized CP Tensor Decomposition

## TL;DR

This paper introduces a randomized algorithm for efficient approximate CP tensor decomposition, enabling scalable analysis of large tensors with controlled error, supported by theoretical and empirical validation.

## Contribution

It presents a novel randomized method that significantly reduces computation time for CP tensor decomposition on large-scale data.

## Key findings

- Algorithm achieves faster decomposition on massive tensors.
- Approximation error is controllable through oversampling and power iterations.
- Empirical results validate the effectiveness of the proposed method.

## Abstract

The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought after since many high-dimensional tensors have low intrinsic rank relative to the dimension of the ambient measurement space. However, the emergence of `big data' poses significant computational challenges for computing this fundamental tensor decomposition. By leveraging modern randomized algorithms, we demonstrate that coherent structures can be learned from a smaller representation of the tensor in a fraction of the time. Thus, this simple but powerful algorithm enables one to compute the approximate CP decomposition even for massive tensors. The approximation error can thereby be controlled via oversampling and the computation of power iterations. In addition to theoretical results, several empirical results demonstrate the performance of the proposed algorithm.