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Latent Structural Similarity Networks for Unsupervised Discovery in Multivariate Time Series

Olusegun Owoeye

TL;DR

The paper addresses unsupervised relational discovery in high-dimensional multivariate time series by proposing latent structural similarity networks. It combines rolling-window representations learned via a sequence-to-sequence LSTM autoencoder with aggregation to per-entity embeddings, then constructs a sparse similarity graph through a cosine similarity threshold in latent space. Key findings on hourly cryptocurrency returns show non-uniform latent structure with 64 edges at a $\tau=0.90$ threshold, of which 16 pairs satisfy Engle–Granger cointegration, illustrating both linear and non-linear types of relationships. The approach provides a domain-agnostic, interpretable discovery layer that isolates relational structure from predictive objectives, enabling flexible, post-hoc analyses across diverse multivariate temporal domains.

Abstract

This paper proposes a task-agnostic discovery layer for multivariate time series that constructs a relational hypothesis graph over entities without assuming linearity, stationarity, or a downstream objective. The method learns window-level sequence representations using an unsupervised sequence-to-sequence autoencoder, aggregates these representations into entity-level embeddings, and induces a sparse similarity network by thresholding a latent-space similarity measure. This network is intended as an analyzable abstraction that compresses the pairwise search space and exposes candidate relationships for further investigation, rather than as a model optimized for prediction, trading, or any decision rule. The framework is demonstrated on a challenging real-world dataset of hourly cryptocurrency returns, illustrating how latent similarity induces coherent network structure; a classical econometric relation is also reported as an external diagnostic lens to contextualize discovered edges.

Latent Structural Similarity Networks for Unsupervised Discovery in Multivariate Time Series

TL;DR

The paper addresses unsupervised relational discovery in high-dimensional multivariate time series by proposing latent structural similarity networks. It combines rolling-window representations learned via a sequence-to-sequence LSTM autoencoder with aggregation to per-entity embeddings, then constructs a sparse similarity graph through a cosine similarity threshold in latent space. Key findings on hourly cryptocurrency returns show non-uniform latent structure with 64 edges at a threshold, of which 16 pairs satisfy Engle–Granger cointegration, illustrating both linear and non-linear types of relationships. The approach provides a domain-agnostic, interpretable discovery layer that isolates relational structure from predictive objectives, enabling flexible, post-hoc analyses across diverse multivariate temporal domains.

Abstract

This paper proposes a task-agnostic discovery layer for multivariate time series that constructs a relational hypothesis graph over entities without assuming linearity, stationarity, or a downstream objective. The method learns window-level sequence representations using an unsupervised sequence-to-sequence autoencoder, aggregates these representations into entity-level embeddings, and induces a sparse similarity network by thresholding a latent-space similarity measure. This network is intended as an analyzable abstraction that compresses the pairwise search space and exposes candidate relationships for further investigation, rather than as a model optimized for prediction, trading, or any decision rule. The framework is demonstrated on a challenging real-world dataset of hourly cryptocurrency returns, illustrating how latent similarity induces coherent network structure; a classical econometric relation is also reported as an external diagnostic lens to contextualize discovered edges.
Paper Structure (30 sections, 2 equations, 2 figures)

This paper contains 30 sections, 2 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Methodology
  4. Problem Setup
  5. Windowing and Normalisation
  6. Sequence-to-Sequence Representation Learning
  7. Latent Aggregation and Similarity
  8. Similarity Network Construction
  9. Robustness and Stability Protocol
  10. Scope and Design Boundaries
  11. Experiments
  12. Data Universe
  13. Preprocessing and Window Construction
  14. Latent Representation Learning
  15. Similarity Network Construction
  16. ...and 15 more sections

Figures (2)

  • Figure 1: Cosine similarity matrix computed between aggregated latent representations for 20 cryptocurrency assets at the 1-hour resolution.
  • Figure 2: Latent similarity network induced using a cosine similarity threshold of 0.90. Nodes represent assets and edges denote retained latent similarity relationships.