News Release

Balanced-partitioning treemapping method for digital hierarchical dataset

Peer-Reviewed Publication

Beijing Zhongke Journal Publising Co. Ltd.

Comparison among different partitioning approaches

image: Given a sequence of input data belonging to the same hierarchical level, performing a number-balanced partition (a) ensures that the number of nodes in the subsets is balanced and that the temporal coherence is well preserved. However, because the total values of the two subsets vary dramatically (8+9 vs. 1+2), the corresponding rectangles have poor aspect ratios. A greedy searching algorithm for the sizebalanced partition problem (b) sorts all nodes by their sizes in descending order and assigns large nodes first. Even though the two subsets at the first level are perfectly balanced in size, the split at the second level cannot be balanced because of node size variation within the subsets. Like the greedy strategy, the proposed size-balanced partition (c) also orders the input nodes according to their sizes, however, instead of alternatively assigning nodes to the two subsets, the small nodes are kept in the same subset and thus reduce size variation within subsets. This allows for balanced partitions at all hierarchical levels. When there is a need to maintain the order of nodes in the input sequence, the proposed sequence-balanced partition (d) divides the sequence directly without attempting to achieve better temporal coherence when handling dynamic datasets. view more 

Credit: Beijing Zhongke Journal Publising Co. Ltd.

From the problem discussed in the abstract, this study aimed to obtain better visible performance of small elements as well as achieve dynamically stable results, resulting in the input dataset being visualized in a relatively stable position of the treemap. However, satisfactory static and dynamic performance can be difficult to achieve at the same time in one treemapping method and it is for this reason that the study put these two directions into one framework. In the framework, we have three sub-branches: one has good static performance while with worse dynamic performance; one has good dynamic stable results while hard to visualize all small elements; one has static and stable dynamical performance between the former two. 

This study proposed effective treemapping strategies that either maintain near-square aspect ratios for the rectangles of a treemap so that small elements are more visible or create stable layouts for time-dependent sequences (stock market variation with time), while these two aspects can be weighted in their influence. Three alternatives for arranging the results are thus designed: a size-balanced visualization maintains nearsquare aspect ratios, and a number-balanced version preserves the temporal coherence. An in-between is formed by a sequence-balanced partitioning method that maintains both aspects reasonably well.

For better comparison and evaluation, the study introduced a new metric that is defined based on the visual changes. It complements existing measurements for dynamic stability that usually only consider distance and size changes. This metric reflects shape variations, in addition to absolute distance and size changes. By comparing and discussing various methods using this measure in addition to other established measures, the study presented the behavior of the treemapping results with respect to standard datasets.

In the future, it is recommended that studies continue minimizing variances and maintaining temporal coherence. The use of a non-sliced method to divide rectangles is also an interesting exploration direction.

For the number-balanced partitioning method, we can combine hierarchical clustering and layout methods to not just two as close as possible. Moreover, for digit twins, the methods proposed in this study can be used for hierarchical dataset layout and visualization, which can be helpful for digit twin pipelines.

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