  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. Also, 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.
  Second, 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.
  Third, 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.
