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.

翻译：在多种机器学习（ML）聚类与降维方法中，例如非负矩阵分解（NMF）、RESCAL和K-Means聚类，用户必须选择一个超参数k来定义能够实现样本理想分离或清晰聚类的簇或成分的数量。这一选择虽然困难，但对于避免数据过拟合或欠拟合至关重要。若干ML应用使用评分方法（如轮廓系数和戴维斯-鲍尔丁指数）来评估特定k值下的聚类模式稳定性。该方法通过对一个k值范围内的多次试验计算得分，并启发式地选择理想的k值，通常选取模型开始出现过拟合（表现为得分下降或上升，类似于肘部曲线图）之前的k值。虽然网格搜索方法可用于精确找到一个好的k值，但遍历一个k值范围可能非常耗时且计算资源密集。本文介绍了一种基于二分搜索的二进制渗流方法，该方法通过对得分进行阈值化处理的启发式策略，从搜索空间中截断目标k值，从而显著减少了这些基于网格搜索的ML算法的k值搜索空间。二进制渗流设计用于单节点串行、单节点多处理以及分布式计算资源。在我们的实验中，我们展示了相较于朴素的顺序搜索理想k值，该方法在搜索空间缩减方面的收益，以及二进制渗流在使用轮廓系数和戴维斯-鲍尔丁指数为NMFk、K-Means pyDNMFk和pyDRESCALk算法识别正确k值时的准确性。我们将用于NMF算法的二进制渗流实现代码发布于GitHub。