Structure preserving t-SNE of matrix framed data

Across various fields, we can align data elements into a matrix frame with both row and column indices, forming what we refer to as matrix-framed data. These elements can take various forms, such as scalars, vectors, time series, matrices, or arrays. Existing data visualization methods aim to represent data elements of different groups without considering the underlying two-dimensional structure present in matrix-framed data. To address this limitation, we introduce a novel visualization method called Matrix t-SNE, designed to effectively embed matrix elements into a low-dimensional Euclidean space while preserving both row-wise and column-wise group structures. Our approach extends the classical t-SNE algorithm to accommodate matrix-framed data, providing a detailed algorithmic framework for embedding such data into low-dimensional representations. To demonstrate the effectiveness of Matrix t-SNE, we apply it to three real-world datasets: exergame, gene expression, and temperature. Our results show that Matrix t-SNE achieves more effective separation of elements according to latent row-wise and column-wise group structures compared to the classical t-SNE.