# Multilinear Compressive Learning

## TL;DR

Multilinear Compressive Learning leverages the tensor structure of multi-dimensional signals during acquisition and inference, improving efficiency and performance over traditional vector-based methods in high-dimensional data tasks.

## Contribution

The paper introduces a novel multilinear framework that preserves tensor structure in compressive sensing, enhancing efficiency and accuracy in inference tasks.

## Key findings

- Outperforms vector-based methods in object classification and face recognition.
- More memory and computationally efficient than traditional approaches.
- Scales well with increasing signal dimensionality.

## Abstract

Compressive Learning is an emerging topic that combines signal acquisition via compressive sensing and machine learning to perform inference tasks directly on a small number of measurements. Many data modalities naturally have a multi-dimensional or tensorial format, with each dimension or tensor mode representing different features such as the spatial and temporal information in video sequences or the spatial and spectral information in hyperspectral images. However, in existing compressive learning frameworks, the compressive sensing component utilizes either random or learned linear projection on the vectorized signal to perform signal acquisition, thus discarding the multi-dimensional structure of the signals. In this paper, we propose Multilinear Compressive Learning, a framework that takes into account the tensorial nature of multi-dimensional signals in the acquisition step and builds the subsequent inference model on the structurally sensed measurements. Our theoretical complexity analysis shows that the proposed framework is more efficient compared to its vector-based counterpart in both memory and computation requirement. With extensive experiments, we also empirically show that our Multilinear Compressive Learning framework outperforms the vector-based framework in object classification and face recognition tasks, and scales favorably when the dimensionalities of the original signals increase, making it highly efficient for high-dimensional multi-dimensional signals.