Naohisa Sakamoto

Naoki Okami, Kazuki Miyake, Naohisa Sakamoto et al.

Comparing tensors and identifying their (dis)similar structures is fundamental in understanding the underlying phenomena for complex data. Tensor decomposition methods help analysts extract tensors' essential characteristics and aid in visual analytics for tensors. In contrast to dimensionality reduction (DR) methods designed only for analyzing a matrix (i.e., second-order tensor), existing tensor decomposition methods do not support flexible comparative analysis. To address this analysis limitation, we introduce a new tensor decomposition method, named tensor unified linear comparative analysis (TULCA), by extending its DR counterpart, ULCA, for tensor analysis. TULCA integrates discriminant analysis and contrastive learning schemes for tensor decomposition, enabling flexible comparison of tensors. We also introduce an effective method to visualize a core tensor extracted from TULCA into a set of 2D visualizations. We integrate TULCA's functionalities into a visual analytics interface to support analysts in interpreting and refining the TULCA results. We demonstrate the efficacy of TULCA and the visual analytics interface with computational evaluations and two case studies, including an analysis of log data collected from a supercomputer.

Fnu Shilpika, Takanori Fujiwara, Naohisa Sakamoto et al.

Many real-world applications involve analyzing time-dependent phenomena, which are intrinsically functional, consisting of curves varying over a continuum (e.g., time). When analyzing continuous data, functional data analysis (FDA) provides substantial benefits, such as the ability to study the derivatives and to restrict the ordering of data. However, continuous data inherently has infinite dimensions, and for a long time series, FDA methods often suffer from high computational costs. The analysis problem becomes even more challenging when updating the FDA results for continuously arriving data. In this paper, we present a visual analytics approach for monitoring and reviewing time series data streamed from a hardware system with a focus on identifying outliers by using FDA. To perform FDA while addressing the computational problem, we introduce new incremental and progressive algorithms that promptly generate the magnitude-shape (MS) plot, which conveys both the functional magnitude and shape outlyingness of time series data. In addition, by using an MS plot in conjunction with an FDA version of principal component analysis, we enhance the analyst's ability to investigate the visually-identified outliers. We illustrate the effectiveness of our approach with two use scenarios using real-world datasets. The resulting tool is evaluated by industry experts using real-world streaming datasets.

Takanori Fujiwara, Shilpika, Naohisa Sakamoto et al.

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.