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Although distance measures are used in many machine learning algorithms, the literature on the context-independent selection and evaluation of distance measures is limited in the sense that prior knowledge is used. In cluster analysis, current studies evaluate the choice of distance measure after applying unsupervised methods based on error probabilities, implicitly setting the goal of reproducing predefined partitions in data. Such studies use clusters of data that are often based on the context of the data as well as the custom goal of the specific study. Depending on the data context, different properties for distance distributions are judged to be relevant for appropriate distance selection. However, if cluster analysis is based on the task of finding similar partitions of data, then the intrapartition distances should be smaller than the interpartition distances. By systematically investigating this specification using distribution analysis through the mirrored-density (MD plot), it is shown that multimodal distance distributions are preferable in cluster analysis. As a consequence, it is advantageous to model distance distributions with Gaussian mixtures prior to the evaluation phase of unsupervised methods. Experiments are performed on several artificial datasets and natural datasets for the task of clustering.

Data fusion consists of the process of integrating several datasets with some common variables, and other variables available only in partial datasets. The main problem of data fusion can be described as follows. From one source, having X⁰ and Y⁰ datasets (with N⁰ observations by multiple x and y variables, n and m of those, respectively), and from another source, having X¹ data (with N¹ observations by the same nx-variables), we need to estimate the missing portion of the Y¹ data (of size N¹ by m variables) in order to combine all the data into one set. Several algorithms are considered in this work, including estimation of weights proportional to the distances from each ith observation in the X¹ "recipients" dataset to all observations in the X⁰ "donors" dataset. Or we can use a sample balancing technique with the maximum effective base performed by applying ridge-regression for the Gifi system of binaries obtained from the x-variables for the best fit of the "donors" X⁰ data to the margins defined by each respondent in the "recipients" X¹ dataset. Then the weighted regressions of each y in the Y⁰ dataset by all variables in the X⁰ are constructed. For each ith observation in the dataset X⁰, these regressions are used for predicting the y-variables in the Y¹ "recipients" dataset. If X and Y are the same n variables from different sources, the dual partial least squares technique and a special regression model with dummies defining each of the three available sets are used for prediction of the Y¹ data.

In this paper we consider that a group of decision makers rank a set of alternatives by means of weak orders for making a collective decision. Since decision makers could have very different opinions and it should be important to reach a consensuated decision, we have introduced indices of contribution to consensus for each decision maker for prioritizing them in order of their contributions to consensus. These indices are defined by means of a consensus measure which assigns a number between 0 and 1 to each subset of decision makers. For putting in practice this idea, we have introduced a class of consensus measures based on distances on weak orders and we have analyzed some of their properties. We have illustrated the weighted decision procedure with an example.

This article compares different methods for combining abundance data, phylogenetic trees and clinical covariates in a nonparametric setting. In particular we study the output from the principal coordinates analysis on UNIFRAC and WEIGHTED UNIFRAC distances and the output from a double principal coordinate analyses DPCOA using distances computed on the phylogenetic tree.

We also present power comparisons for some of the standard tests of phylogenetic signal between different types of samples. These methods are compared both on simulated and real data sets. Our study shows that DPCoA is less robust to outliers, and more robust to small noisy fluctuations around zero.