Multi-point Dimensionality Reduction to Improve Projection Layout Reliability
Abstract: In ordinary Dimensionality Reduction (DR), each data instance in a high dimensional space (original space), is mapped to one point in a low dimensional space (visual space). This builds a layout of projected points that attempts to preserve as much as possible some property of data such as distances, neighbourhood relationships, and/or topology structures, but with the ultimate goal of approximating semantic properties of data. The approximation of semantic properties, is achieved by preserving geometric properties or topology structures in visual space. In this paper, the first general algorithm of Multi-point Dimensionality Reduction is introduced on where each data instance can be mapped to possibly more than one point in visual space with the aim of improving reliability, usability and interpretability of dimensionality reduction. Furthermore, by allowing the points in visual space to be split into two layers while maintaining the possibility of having more than one projection per data instance, the benefit of separating more reliable points from less reliable points is discussed. The proposed algorithm in this paper, named Layered Vertex Splitting Data Embedding (LVSDE), is built upon and extends a combination of ordinary DR and graph drawing techniques. Based on the experiments of this paper, the particular proposed algorithm (LVSDE) practically outperforms popular ordinary DR methods visually in terms of semantics, group separation, subgroup detection or combinational group detection.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Novi_Quadrianto1
Submission Number: 802
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