Fisher-Rao linear discriminant analysis (LDA) is a valuable tool for multigroup classification. LDA is equivalent to maximum likelihood classification assuming Gaussian distributions for each class. In this paper, we fit Gaussian mixtures to each class to facilitate effective classification in non-normal settings, especially when the classes are clustered. Low dimensional views are an important by-product of LDA---our new techniques inherit this feature. We are able to control the within-class spread of the subclass centers relative to the between-class spread. Our technique for fitting these models permits a natural blend with nonparametric versions of LDA. Keywords: Classification, Pattern Recognition, Clustering, Nonparametric, Penalized. 1 Introduction In the generic classification or discrimination problem, the outcome of interest G falls into J unordered classes, which for convenience we denote by the set J = f1; 2; 3; \Delta \Delta \Delta Jg. We wish to build a rule for pred...

Reducing the dimensionality of data without losing intrinsic information is an important preprocessing step in high-dimensional data analysis. Fisher discriminant analysis (FDA) is a traditional technique for supervised dimensionality reduction, but it tends to give undesired results if samples in a class are multimodal. An unsupervised dimensionality reduction method called localitypreserving projection (LPP) can work well with multimodal data due to its locality preserving property. However, since LPP does not take the label information into account, it is not necessarily useful in supervised learning scenarios. In this paper, we propose a new linear supervised dimensionality reduction method called local Fisher discriminant analysis (LFDA), which effectively combines the ideas of FDA and LPP. LFDA has an analytic form of the embedding transformation and the solution can be easily computed just by solving a generalized eigenvalue problem. We demonstrate the practical usefulness and high scalability of the LFDA method in data visualization and classification tasks through extensive simulation studies. We also show that LFDA can be extended to non-linear dimensionality reduction scenarios by applying the kernel trick.

AbstractÐIn this paper, a novel method of pattern discovery is proposed. It is based on the theoretical formulation of a contingency table of events. Using residual analysis and recursive partitioning, statistically significant events are identified in a data set. These events constitute the important information contained in the data set and are easily interpretable as simple rules, contour plots, or parallel axes plots. In addition, an informative probabilistic description of the data is automatically furnished by the discovery process. Following a theoretical formulation, experiments with real and simulated data will demonstrate the ability to discover subtle patterns amid noise, the invariance to changes of scale, cluster detection, and discovery of multidimensional patterns. It is shown that the pattern discovery method offers the advantages of easy interpretation, rapid training, and tolerance to noncentralized noise. Index TermsÐPattern discovery, residual analysis, recursive partitioning, events, contingency tables.

Data mining refers to extracting or “mining” knowledge from large amounts of data. Clustering is one of the most important research areas in the field of data mining. Clustering means creating groups of objects based on their features in such a way that the objects belonging to the same groups are similar and those belonging in different groups are dissimilar. In this paper, the most representative partition based clustering algorithms are described and categorized based on their basic approach. The best algorithm is found out based on their performance. Two of the clustering algorithms, namely, Centroid based k-means, Representative object based k-medoids are implemented by using JAVA and their performance is analyzed based on their clustering quality. The randomly distributed data points are taken as input to these algorithms and clusters are found out for each algorithm. The algorithm’s performance is analyzed by different runs on the input data points. The experimental results are given as both graphical as well as tabular representation.