Wearing a MASK: Compressed Representations of Variable-Length Sequences Using Recurrent Neural Tangent Kernels

TL;DR

This paper introduces MASK, a novel kernel-based method leveraging Recurrent Neural Tangent Kernels to effectively reduce dimensionality of variable-length sequences, enabling better visualization and analysis of complex time series data.

Contribution

The paper extends kernel methods to variable-length sequences using RNTK, introducing MASK, which adapts PCA and t-SNE for such data types.

Findings

MASK effectively separates synthetic time series data.

The approach generalizes existing fixed-length sequence methods.

Demonstrates improved visualization of variable-length sequences.

Abstract

High dimensionality poses many challenges to the use of data, from visualization and interpretation, to prediction and storage for historical preservation. Techniques abound to reduce the dimensionality of fixed-length sequences, yet these methods rarely generalize to variable-length sequences. To address this gap, we extend existing methods that rely on the use of kernels to variable-length sequences via use of the Recurrent Neural Tangent Kernel (RNTK). Since a deep neural network with ReLu activation is a Max-Affine Spline Operator (MASO), we dub our approach Max-Affine Spline Kernel (MASK). We demonstrate how MASK can be used to extend principal components analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE) and apply these new algorithms to separate synthetic time series data sampled from second-order differential equations.