  In several Machine Learning (ML) clustering and dimensionality reduction
approaches, such as non-negative matrix factorization (NMF), RESCAL, and
K-Means clustering, users must select a hyper-parameter k to define the number
of clusters or components that yield an ideal separation of samples or clean
clusters. This selection, while difficult, is crucial to avoid overfitting or
underfitting the data. Several ML applications use scoring methods (e.g.,
Silhouette and Davies Boulding scores) to evaluate the cluster pattern
stability for a specific k. The score is calculated for different trials over a
range of k, and the ideal k is heuristically selected as the value before the
model starts overfitting, indicated by a drop or increase in the score
resembling an elbow curve plot. While the grid-search method can be used to
accurately find a good k value, visiting a range of k can become time-consuming
and computationally resource-intensive. In this paper, we introduce the Binary
Bleed method based on binary search, which significantly reduces the k search
space for these grid-search ML algorithms by truncating the target k values
from the search space using a heuristic with thresholding over the scores.
Binary Bleed is designed to work with single-node serial, single-node
multi-processing, and distributed computing resources. In our experiments, we
demonstrate the reduced search space gain over a naive sequential search of the
ideal k and the accuracy of the Binary Bleed in identifying the correct k for
NMFk, K-Means pyDNMFk, and pyDRESCALk with Silhouette and Davies Boulding
scores. We make our implementation of Binary Bleed for the NMF algorithm
available on GitHub.
