Piece wise Laplacian‐based Projection for Interactive Data Exploration and Organization

Abstract

Multidimensional projection has emerged as an important visualization tool in applications involving the visual analysis of high-dimensional data. However, high precision projection methods are either computationally expensive or not flexible enough to enable feedback from user interaction into the projection process. A built-in mechanism that dynamically adapts the projection based on direct user intervention would make the technique more useful for a larger range of applications and data sets. In this paper we propose the Piecewise Laplacian-based Projection (PLP), a novel multidimensional projection technique, that, due to the local nature of its formulation, enables a versatile mechanism to interact with projected data and to allow interactive changes to alter the projection map dynamically, a capability unique of this technique. We exploit the flexibility provided by PLP in two interactive projection-based applications, one designed to organize pictures visually and another to build music playlists. These applications illustrate the usefulness of PLP in handling high-dimensional data in a flexible and highly visual way. We also compare PLP with the currently most promising projections in terms of precision and speed, showing that it performs very well also according to these quality criteria.

Temporal Multivariate Networks

“…[86]. Dimensionality reduction projects a set of high-dimensional attributes into R 2 or R 3 so that similarities between the original attributes are reflected in the low-dimensional distance [61,82,83]. Although such approaches scale well computationally for large sample counts [84], it is hard to visualize both attribute similarity and graph structure in the same embedding.…”

LoCH: A neighborhood-based multidimensional projection technique for high-dimensional sparse spaces

“…Although LSP presents good results in terms of neighborhood preservation, the Laplacian operator involves the solution of a linear system with n variables, which is impracticable for large datasets. Piecewise Laplacian Projection (PLP) [26] handles this problem by solving several small linear systems instead of a large one. This is done by partitioning the dataset into clusters and applying the Laplacian operator onto these clusters.…”

Multidimensional Projection with Radial Basis Function and Control Points Selection

“…Since Pekalska et al's work, a variety of control-points-based techniques have been proposed: L-Isomap [10], L-MDS [11], LSP [21], PLMP [22], LAMP [18] and PLP [23] are a few examples of such methods. Even though control points are central to the aforementioned techniques, most of these works do not approach the problem of how to effectively select control points.…”