背景:非常需要开发一种计算方法来分析和利用基因表达数据中包含的信息。非负矩阵因子分解(NMF)在计算生物学中的最新应用已经证明了从大量数据(特别是基因表达微阵列)中获得必要细节的能力。NMF中的一个常见问题是找到退化演示的因素的适当数量等级(r),但是对于哪种技术最适合用于此目的,尚无共识。因此,已经提出了各种技术来选择秩分解(r)的最优值。
目的:在这项工作中,基于肘部方法,提出了一种新的秩选择指标,将其与cophenetic度量进行了有条不紊的比较。
方法:要确定最佳数量等级(r),这项研究集中在基因表达数据集上NMF的单位不变膝盖(UIK)方法。由于UIK方法需要一个极值距离估计器,该估计器最终用于拐点和拐点的识别,在基因表达数据集上使用UIK方法作为目标矩阵,该方法找到了所提出算法的残差平方和的曲率的第一个拐点。
结果:使用急性淋巴细胞白血病和急性髓细胞性白血病样本的基因表达数据对UIK任务进行计算。因此,对不同算法的不同结果进行了比较。所提出的UIK方法易于执行,快,没有先验排序值输入,并且不需要显著影响模型功能的初始参数。
结论:这项研究表明,肘部方法为基因表达数据和精确估计已知维度的模拟突变过程数据提供了可靠的预测。提出的UIK方法比传统方法更快,包括利用共识矩阵作为秩选择标准的度量,同时实现了显着更好的计算效率,而无需视觉检查曲线。最后,基于肘部法的基因表达数据的等级调整方法在理论上可以说优于cophenetic测量。
BACKGROUND: There is a great need to develop a computational approach to analyze and exploit the information contained in gene expression data. The recent utilization of nonnegative matrix factorization (NMF) in computational biology has demonstrated the capability to derive essential details from a high amount of data in particular gene expression microarrays. A common problem in NMF is finding the proper number rank (r) of factors of the degraded demonstration, but no agreement exists on which technique is most appropriate to utilize for this purpose. Thus, various techniques have been suggested to select the optimal value of rank factorization (r).
OBJECTIVE: In this work, a new metric for rank selection is proposed based on the elbow method, which was methodically compared against the cophenetic metric.
METHODS: To decide the optimum number rank (r), this study focused on the unit invariant knee (UIK) method of the NMF on gene expression data sets. Since the UIK method requires an extremum distance estimator that is eventually employed for inflection and identification of a knee point, the proposed method finds the first inflection point of the curvature of the residual sum of squares of the proposed algorithms using the UIK method on gene expression data sets as a target matrix.
RESULTS: Computation was conducted for the UIK task using gene expression data of acute lymphoblastic leukemia and acute myeloid leukemia samples. Consequently, the distinct results of NMF were subjected to comparison on different algorithms. The proposed UIK method is easy to perform, fast, free of a priori rank value input, and does not require initial parameters that significantly influence the model\'s functionality.
CONCLUSIONS: This study demonstrates that the elbow method provides a credible prediction for both gene expression data and for precisely estimating simulated mutational processes data with known dimensions. The proposed UIK method is faster than conventional methods, including metrics utilizing the consensus matrix as a criterion for rank selection, while achieving significantly better computational efficiency without visual inspection on the curvatives. Finally, the suggested rank tuning method based on the elbow method for gene expression data is arguably theoretically superior to the cophenetic measure.