A New Similarity Function for Spectral Clustering with Application to Plant Phenotypic Data
Kapil Ahuja, Mithun Singh, Kuldeep Pathak, Milind B. Ratnaparkhe
TL;DR
This work tackles clustering of plant phenotypic data, where traditional hierarchical clustering underperforms. It introduces a base-$a$ exponential similarity for spectral clustering, with $a>e$, and couples it with local scaling to form a more discriminative affinity matrix, guided by Cheeger’s inequality. The authors provide eigenvalue analyses showing that the proposed similarities reduce Laplacian eigenvalues, and they validate the approach on 2376 soybean and 1865 rice samples, achieving up to 35% improvement over standard spectral clustering and 11% over the previous best on rice. This yields a more accurate clustering framework for plant breeding and phenotypic analysis, with avenues for extending the theory and integrating genetic data.
Abstract
Clustering species of the same plant into different groups is an important step in developing new species of the concerned plant. Phenotypic (or physical) characteristics of plant species are commonly used to perform clustering. Hierarchical Clustering (HC) is popularly used for this task, and this algorithm suffers from low accuracy. In one of the recent works (Shastri et al., 2021), the authors have used the standard Spectral Clustering (SC) algorithm to improve the clustering accuracy. They have demonstrated the efficacy of their algorithm on soybean species. In the SC algorithm, one of the crucial steps is building the similarity matrix. A Gaussian similarity function is the standard choice to build this matrix. In the past, many works have proposed variants of the Gaussian similarity function to improve the performance of the SC algorithm, however, all have focused on the variance or scaling of the Gaussian. None of the past works have investigated upon the choice of base "e" (Euler's number) of the Gaussian similarity function (natural exponential function). Based upon spectral graph theory, specifically the Cheeger's inequality, in this work we propose use of a base "a" exponential function as the similarity function. We also integrate this new approach with the notion of "local scaling" from one of the first works that experimented with the scaling of the Gaussian similarity function (Zelnik-Manor et al., 2004). Using an eigenvalue analysis, we theoretically justify that our proposed algorithm should work better than the existing one. With evaluation on 2376 soybean species and 1865 rice species, we experimentally demonstrate that our new SC is 35% and 11% better than the standard SC, respectively.