Unsupervised detection of semantic correlations in big data

TL;DR

This paper introduces a method to detect semantic correlations in large, high-dimensional binary data by estimating the intrinsic dimension, enabling analysis of complex data structures and neural network representations.

Contribution

It presents a novel algorithm for estimating the intrinsic dimension of big data, which is robust to high dimensionality and reveals semantic correlations in images and text.

Findings

Identified phase transitions in model magnetic systems.

Detected semantic correlations in neural network representations.

Demonstrated robustness of the method in big data scenarios.

Abstract

In real-world data, information is stored in extremely large feature vectors. These variables are typically correlated due to complex interactions involving many features simultaneously. Such correlations qualitatively correspond to semantic roles and are naturally recognized by both the human brain and artificial neural networks. This recognition enables, for instance, the prediction of missing parts of an image or text based on their context. We present a method to detect these correlations in high-dimensional data represented as binary numbers. We estimate the binary intrinsic dimension of a dataset, which quantifies the minimum number of independent coordinates needed to describe the data, and is therefore a proxy of semantic complexity. The proposed algorithm is largely insensitive to the so-called curse of dimensionality, and can therefore be used in big data analysis. We test this approach identifying phase transitions in model magnetic systems and we then apply it to the detection of semantic correlations of images and text inside deep neural networks.