Fuzzy clusterwise regression has been a useful method for investigating cluster-level heterogeneity of observations based on linear regression. This method integrates fuzzy clustering and ordinary least-squares regression, thereby enabling to estimate regression coefficients for each cluster and fuzzy cluster memberships of observations simultaneously. In practice, however, fuzzy clusterwise re...

To date, numerous genetic variants have been identified as associated with diverse phenotypic traits. However, identified associations generally explain only a small proportion of trait heritability and the predictive power of models incorporating only known-associated variants has been small. Multiple regression is a popular framework in which to consider the joint effect of many genetic varia...

Although there exist a number of single color constancy algorithms, none of them can be considered universal. Consequently, how to select and combine existing single algorithms are two important research directions in the field of color constancy. In this paper we use ridge regression, a simple yet effective machine learning approach, to select and combine existing color constancy algorithms. T...

De-duplication Matlab's unique function was used for de-duplicating reviews – each row that appeared more than once was reduced to a single occurrence. This technique can produce some false positives in the case that the same word frequencies occurred in legitimately distinct reviews (since the order of the tokens is not considered), but the chances of this occurring was considered improbable e...

In this paper, we investigate a divide and conquer approach to Kernel Ridge Regression (KRR). Given n samples, the division step involves separating the points based on some underlying disjoint partition of the input space (possibly via clustering), and then computing a KRR estimate for each partition. The conquering step is simple: for each partition, we only consider its own local estimate fo...

Ridge regression is often the method of choice in ill–conditioned systems. A canonical form identifies regions in the parameter space where Ordinary Least Squares (OLS) is problematic. A curious but unrecognized property of ridge solutions emerges: Under spherical errors with or without moments, the relative concentrations of the canonical estimators reverse as the ridge scalar evolves, the est...

Anomalies persist in the foundations of ridge regression as set forth in Hoerl and Kennard (1970) and subsequently. Conventional ridge estimators and their properties do not follow on constraining lengths of solution vectors using LaGrange’s method, as claimed. Estimators so constrained have singular distributions; the proposed solutions are not necessarily minimizing; and heretofore undiscover...