A Novel Sampled Clustering Algorithm for Rice Phenotypic Data
Mithun Singh Kapil Ahuja Milind B. Ratnaparkhe
Phenotypic (or Physical) characteristics of plant species are commonly used
to perform clustering. In one of our recent works (Shastri et al. (2021)), we
used a probabilistically sampled (using pivotal sampling) and spectrally
clustered algorithm to group soybean species. These techniques were used to
obtain highly accurate clusterings at a reduced cost. In this work, we extend
the earlier algorithm to cluster rice species. We improve the base algorithm in
three ways. First, we propose a new function to build the similarity matrix in
Spectral Clustering. Commonly, a natural exponential function is used for this
purpose. Based upon the spectral graph theory and the involved Cheeger's
inequality, we propose the use a base "a" exponential function instead. This
gives a similarity matrix spectrum favorable for clustering, which we support
via an eigenvalue analysis.
  Second, the function used to build the similarity matrix in Spectral
Clustering was earlier scaled with a fixed factor (called global scaling).
Based upon the idea of Zelnik-Manor and Perona (2004), we now use a factor that
varies with matrix elements (called local scaling) and works better. Third, to
compute the inclusion probability of a specie in the pivotal sampling
algorithm, we had earlier used the notion of deviation that captured how far
specie's characteristic values were from their respective base values (computed
over all species). A maximum function was used before to find the base values.
We now use a median function, which is more intuitive. We support this choice
using a statistical analysis. With experiments on 1865 rice species, we
demonstrate that in terms of silhouette values, our new Sampled Spectral
Clustering is 61% better than Hierarchical Clustering (currently prevalent).
Also, our new algorithm is significantly faster than Hierarchical Clustering
due to the involved sampling.