A Visual Analytics Framework for Reviewing Multivariate Time-Series Data with Dimensionality Reduction (2008.01645v3)

Abstract: Data-driven problem solving in many real-world applications involves analysis of time-dependent multivariate data, for which dimensionality reduction (DR) methods are often used to uncover the intrinsic structure and features of the data. However, DR is usually applied to a subset of data that is either single-time-point multivariate or univariate time-series, resulting in the need to manually examine and correlate the DR results out of different data subsets. When the number of dimensions is large either in terms of the number of time points or attributes, this manual task becomes too tedious and infeasible. In this paper, we present MulTiDR, a new DR framework that enables processing of time-dependent multivariate data as a whole to provide a comprehensive overview of the data. With the framework, we employ DR in two steps. When treating the instances, time points, and attributes of the data as a 3D array, the first DR step reduces the three axes of the array to two, and the second DR step visualizes the data in a lower-dimensional space. In addition, by coupling with a contrastive learning method and interactive visualizations, our framework enhances analysts' ability to interpret DR results. We demonstrate the effectiveness of our framework with four case studies using real-world datasets.

• The paper introduces MulTiDR, a visual analytics framework that employs a two-step dimensionality reduction process combined with contrastive learning to reveal intrinsic patterns in multivariate time-series data.
• The paper employs PCA and UMAP sequentially to simplify tensor data, enabling clearer visualization and interpretation of complex temporal and variable interactions.
• The paper demonstrates its effectiveness across diverse case studies in environmental monitoring, physical activity analysis, network interactions, and supercomputer log analysis.

Overview of MulTiDR for Multivariate Time-Series Analysis

The paper presents MulTiDR, a visual analytics framework that innovatively addresses challenges in multivariate time-series data through a two-step Dimensionality Reduction (DR) process coupled with interactive visualizations and contrastive learning. This framework provides a cohesive approach to visualize and interpret time-dependent high-dimensional data, which is prevalent across multiple fields, from healthcare to transportation systems.

Methodology and Implementation

The core strategy of MulTiDR involves two DR steps to handle the dimensionality of time-series data represented as third-order tensors. Initially, the data cube comprising instances, time points, and variables is reduced from a three-dimensional array to a two-dimensional matrix through a selected DR technique like PCA. Following this, a second DR operation, typically UMAP, projects the data into a visually interpretable low-dimensional space. This two-step process facilitates the discovery of intrinsic patterns while managing data complexity that usually hinders conventional DR methods.

This approach addresses limitations found in standard tensor unfoldings and ensures that patterns significant to different data axes are adequately captured and presented. MulTiDR supports six distinct combinations of DR steps according to the chosen axis for initial reduction, enabling flexibility in focusing analysis on specific data aspects like instance, variable, or time point similarities.

One innovative aspect of MulTiDR is the integration of contrastive learning (CL) to bolster interpretability. Utilizing a variant of the Contrastive Principal Component Analysis (ccPCA), the framework provides insights into feature contributions by highlighting time points, variables, or instances that most distinctively characterize data clusters. This enables researchers to demystify why clusters form as they do and what underlying features drive their behavior.

Evaluation and Results

The paper evaluates MulTiDR through comprehensive case studies across various domains:

1. Environmental Data Analysis: Seasonal patterns within air quality measures were effectively elucidated using the framework, demonstrating the capacity of MulTiDR to reveal time-dependent anomalies and patterns.
2. Physical Activity Data: Multivariate physical sensor data of different body movements were analyzed to distinguish activity modes, further validating the framework's capabilities in contextually rich temporal datasets.
3. Network Interaction Data: Temporal dynamics and node feature patterns in contact networks were interpreted, demonstrating the effectiveness of MulTiDR in network data, where interactions exhibit complex multivariate dependencies.
4. Supercomputer Log Data: The analysis revealed outliers in compute rack behavior in terms of energy consumption and temperature metrics, showcasing the robustness of MulTiDR to parse through vast datasets for critical insights.

Implications and Future Work

MulTiDR expands beyond conventional limitations of visual analytics frameworks by offering a standardized yet flexible approach to interpret multivariate time-series data. The incorporation of contrastive learning provides theoretical and practical implications in elucidating feature contributions, which can enhance model transparency and decision-making in complex systems.

Potential future developments of MulTiDR involve enhancing its scalability to accommodate even larger datasets and refining interpretability tools to support real-time analytics. Moreover, integrating complementary DR techniques, functional PCA for temporal sustainability analysis, or specific application-driven methods like MSSA, could further enhance the depth and quality of insights obtained from such data-intensive explorations.

In conclusion, the MulTiDR framework significantly contributes to dimensionality reduction practices for multivariate time-series data, advancing both methodological flexibility and analytical depth. As data complexity and volume continue to grow in the field of big data analytics, frameworks like MulTiDR are invaluable in decoding intricate datasets, leading to actionable insights and informed decision-making.