A note on between-group PCA

In the context of binary classification with continuous predictors, we proove two properties concerning the connections between Partial Least Squares (PLS) dimension reduction and between-group PCA, and between linear discriminant analysis and between-group PCA. Such methods are of great interest for the analysis of high-dimensional data with continuous predictors, such as microarray gene expression data

Penalized Orthogonal-Components Regression for Large p Small n Data

We propose a penalized orthogonal-components regression (POCRE) for large p small n data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlation to the response residuals. A new penalization framework, implemented via empirical Bayes thresholding, is presented to effectively identify sparse predictors of each component. POCRE is computationally efficient owing to its sequential construction of leading sparse principal components. In addition, such construction offers other properties such as grouping highly correlated predictors and allowing for collinear or nearly collinear predictors. With multivariate responses, POCRE can construct common components and thus build up latent-variable models for large p small n data.Comment: 12 page

Penalized Orthogonal-Components Regression for Large p Small n Data

We propose a penalized orthogonal-components regression (POCRE) for large p small n data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlation to the response residuals. A new penalization framework, implemented via empirical Bayes thresholding, is presented to effectively identify sparse predictors of each component. POCRE is computationally efficient owing to its sequential construction of leading sparse principal components. In addition, such construction offers other properties such as grouping highly correlated predictors and allowing for collinear or nearly collinear predictors. With multivariate responses, POCRE can construct common components and thus build up latent-variable models for large p small n data.Comment: 12 page

Weighted k-Nearest-Neighbor Techniques and Ordinal Classification

In the field of statistical discrimination k-nearest neighbor classification is a well-known, easy and successful method. In this paper we present an extended version of this technique, where the distances of the nearest neighbors can be taken into account. In this sense there is a close connection to LOESS, a local regression technique. In addition we show possibilities to use nearest neighbor for classification in the case of an ordinal class structure. Empirical studies show the advantages of the new techniques

Application of analytic tools for materials selection

The objective of this thesis is the targeted design of new wear resistant materials through the development of analytic frameworks. The building of databases on wear data, whether through calculation or experiment, is a very time-consuming problem with high levels of data uncertainty. For these reasons of small data size and high data uncertainty, the development of a hybrid data analytic framework for accelerating the selection of target materials is needed. In this thesis, the focus is on binary ceramic compounds with the properties of interest as friction coefficient and hardness and with the objective being to minimize friction while improving the wear resistance. These design requirements are generally inversely correlated, further requiring the data science framework that is developed in this thesis. This thesis develops a new hybrid methodology of linking dimensionality reduction (principal component analysis) and association mining to aid in materials selection. The novelty in this developed approach is the linking of multiple data mining methodologies into a single framework, which addresses issues such as physically-meaningful attribute selection, addressing data uncertainty, and identifying specific candidate materials when property trade-offs exist. The result of this thesis is a hybrid methodology for material selection, which is used here for identifying new promising materials for wear resistant applications

PLS dimension reduction for classification of microarray data

PLS dimension reduction is known to give good prediction accuracy in the context of classification with high-dimensional microarray data. In this paper, PLS is compared with some of the best state-of-the-art classification methods. In addition, a simple procedure to choose the number of components is suggested. The connection between PLS dimension reduction and gene selection is examined and a property of the first PLS component for binary classification is proven. PLS can also be used as a visualization tool for high-dimensional data in the classification framework. The whole study is based on 9 real microarray cancer data sets

Clustering of the SOM easily reveals distinct gene expression patterns: results of a reanalysis of lymphoma study

BACKGROUND: A method to evaluate and analyze the massive data generated by series of microarray experiments is of utmost importance to reveal the hidden patterns of gene expression. Because of the complexity and the high dimensionality of microarray gene expression profiles, the dimensional reduction of raw expression data and the feature selections necessary for, for example, classification of disease samples remains a challenge. To solve the problem we propose a two-level analysis. First self-organizing map (SOM) is used. SOM is a vector quantization method that simplifies and reduces the dimensionality of original measurements and visualizes individual tumor sample in a SOM component plane. Next, hierarchical clustering and K-means clustering is used to identify patterns of gene expression useful for classification of samples. RESULTS: We tested the two-level analysis on public data from diffuse large B-cell lymphomas. The analysis easily distinguished major gene expression patterns without the need for supervision: a germinal center-related, a proliferation, an inflammatory and a plasma cell differentiation-related gene expression pattern. The first three patterns matched the patterns described in the original publication using supervised clustering analysis, whereas the fourth one was novel. CONCLUSIONS: Our study shows that by using SOM as an intermediate step to analyze genome-wide gene expression data, the gene expression patterns can more easily be revealed. The "expression display" by the SOM component plane summarises the complicated data in a way that allows the clinician to evaluate the classification options rather than giving a fixed diagnosis