IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 25, NO. 1, JANUARY 2019 1 TPFlow: Progressive Partition and Multidimensional Pattern Extraction for Large-Scale Spatio-Temporal Data Analysis Dongyu Liu, Panpan Xu, and Liu Ren Fig.
1. The user interface of TPFlow. a Tree View starts with a root node
(a1) representing the original data and visualizes the overall data
partitioning process. Every other node on the tree represents a subset
of data. The system supports a steerable and iterative workflow by
allowing analysts to directly interact with every node (a2, a4, a5, a6).
b c d Each individual chart visualizes the latent patterns
extracted by our tensor-based model. The analysts select multiple nodes
highlighted in different colors on the Tree View (a3) to compare the
patterns across different subsets of data. One interesting pattern here
is that the pink states (d1), located mostly in the northeast
region of Germany, perform significantly different from the other states
(b1, c1, c2). Please refer to the details in Sec. 5.1. Abstract—Consider a multi-dimensional spatio-temporal (ST) dataset where each entry is a numerical measure defined by the corresponding
temporal, spatial and other domain-specific dimensions. A typical
approach to explore such data utilizes interactive visualizations
with multiple coordinated views. Each view displays the aggregated
measures along one or two dimensions. By brushing on the views,
analysts can obtain detailed information. However, this approach often
cannot provide sufficient guidance for analysts to identify patterns
hidden within subsets of data. Without a priori hypotheses, analysts
need to manually select and iterate through different slices to search for patterns, which can be a tedious and lengthy process. In this work, we model multidimensional ST data as tensors and propose a novel piecewise rank-one tensor decomposition algorithm which supports automatically slicing the data
into homogeneous partitions and extracting the latent patterns in each
partition for comparison and visual summarization. The algorithm
optimizes a quantitative measure about how faithfully the extracted
patterns visually represent the original data. Based on
the algorithm
we further propose a visual analytics framework that supports a
top-down, progressive partitioning workflow for level-of-detail multidimensional
ST data exploration. We demonstrate the general applicability and
effectiveness of our technique on three datasets from different
application domains: regional sales trend analysis, customer traffic
analysis in department stores, and taxi trip analysis with origin-destination (OD) data. We further interview domain experts to verify the usability of the prototype. Index Terms—Spatio-temporal data, tensor decomposition, interactive exploration, automatic pattern discoveries 1 INTRODUCTION Dongyu Liu is with the Hong Kong University of Science and Technology. This work was done during his internship at Bosch Research North America. E-mail: [email protected]. Panpan Xu and Liu Ren are with Bosch Research North America, Sunnyvale, CA. E-mail: panpan.xu, [email protected]. Interactive visualization is the key technique for explorative analysis of large-scale multidimensional spatio-temporal (ST) data. However, as the size and the dimensionality of the data increase, more scalable techniques are needed. Data aggregation performs binning and rollup operations on the original data to reduce the number of visual items dis- played, hence improving the perceptual scalability of the visualization techniques. The most popular approaches for multidimensional ST data visualization display aggregated measures along each individual dimen- sion of interest (e.g. spatial, temporal, categorical, numerical) with coordinated views [36,41,45]. For example, consider a traffic volume dataset with the schema (day, hour, region)→ tra f f ic_volume. A typical ST visualization displays the total traffic distributed over hours, Manuscript received 31 Mar. 2018; accepted 1 Aug. 2018. Date of publication 16 Aug. 2018; date of current version 21 Oct. 2018. For information on obtaining reprints of this article, please send e-mail to: [email protected], and reference the Digital Object Identifier below. Digital Object Identifier no. 10.1109/TVCG.2018.2865018 1077-2626 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See