Wearing a MASK: Compressed Representations of Variable-Length Sequences Using Recurrent Neural Tangent Kernels
This work addresses a gap in dimensionality reduction techniques for variable-length sequences, which is incremental as it adapts existing methods to a new context.
The paper tackles the challenge of dimensionality reduction for variable-length sequences by extending kernel-based methods using the Recurrent Neural Tangent Kernel (RNTK), resulting in the MASK approach that enables PCA and t-SNE applications on synthetic time series data.
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.