Visual cluster separation using high-dimensional sharpened dimensionality reduction

Abstract

Applying dimensionality reduction (DR) to large, high-dimensional data sets can be challenging when distinguishing the underlying high-dimensional data clusters in a 2D projection for exploratory analysis. We address this problem by first sharpening the clusters in the original high-dimensional data prior to the DR step using Local Gradient Clustering (LGC). We then project the sharpened data from the high-dimensional space to 2D by a user-selected DR method. The sharpening step aids this method to preserve cluster separation in the resulting 2D projection. With our method, end-users can label each distinct cluster to further analyze an otherwise unlabeled data set. Our “High-Dimensional Sharpened DR” (HD-SDR) method, tested on both synthetic and real-world data sets, is favorable to DR methods with poor cluster separation and yields a better visual cluster separation than these DR methods with no sharpening. Our method achieves good quality (measured by quality metrics) and scales computationally well with large high-dimensional data. To illustrate its concrete applications, we further apply HD-SDR on a recent astronomical catalog.

Linking Data Separation, Visual Separation, and Classifier Performance Using Pseudo-labeling by Contrastive Learning

“…In a related vein, (Rodrigues et al, 2019) used the VS in projections to construct so-called decision boundary maps to interpret classification performance (CP) but did not actually use these to improve classifiers. (Kim et al, 2022b;Kim et al, 2022a) showed that one can improve VS by increasing DS, the latter being done by mean shift (Comaniciu and Meer, 2002). However, their aim was to generate easier-to-interpret projections and not use these to build higher-CP classifiers.…”

“…Two key observations were made in this respect (discussed in detail in Sec. 2): O1 Visual separability (VS) in a projection mimics the data separability (DS) in the high dimensional space; O2 Data separability (DS) is key to achieving high classifier performance (CP); These observations have been used in several directions, e.g., using projections to assess DS (VS→DS) (der Maaten et al, 2009); using projections to find which samples get misclassified arXiv:2302.02663v1 [cs.LG] 6 Feb 2023 (VS→CP) (Nonato and Aupetit, 2018); increasing DS to get easier-to-interpret projections (DS→VS) (Kim et al, 2022b); using projections to assess classification difficulty (VS→CP) (Rauber et al, 2017a;Rauber et al, 2017b); and using projections to build better classifiers (VS→CP) (Benato et al, 2018;Benato et al, 2021a). However, to our knowledge, no work so far has explored the relationship between DS, VS, and CP in the context of using pseudo-labeling for machine learning (ML).…”

Hunting for C-rich long-period variable stars in the Milky Way's bar-bulge using unsupervised classification of Gaia BP/RP spectra

“…Other computational/algorithmic improvements have enabled significant speed-ups for UMAP compared to t-SNE although in essence, the algorithms share significant similarities and the t-SNE implementation from Poličar et al (2019) is competitive with UMAP in terms of computational time. Despite its relatively recent creation, the UMAP algorithm has already found use in astrophysics applications (Reis et al 2019;Kim et al 2022;Grondin et al 2023).…”

Visual exploration of high-dimensional data using dimensionality reduction

“…Information Visualization, 21(3):197-219, 2022. [112] • Chapter 3: J. Heo * , Y. Kim * , and J. B. T. M. Roerdink.…”

“…We have also evaluated other nearest-neighbor search algorithms (see Section 2.6.1). Our code is publicly available [110].…”