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Discriminant Analysis by Gaussian Mixtures
 Journal of the Royal Statistical Society, Series B
, 1996
"... FisherRao 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 nonn ..."
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Cited by 199 (9 self)
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FisherRao 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 nonnormal settings, especially when the classes are clustered. Low dimensional views are an important byproduct of LDAour new techniques inherit this feature. We are able to control the withinclass spread of the subclass centers relative to the betweenclass 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...
Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis
 Journal of Machine Learning Research
, 2007
"... Reducing the dimensionality of data without losing intrinsic information is an important preprocessing step in highdimensional 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 ..."
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Cited by 115 (11 self)
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Reducing the dimensionality of data without losing intrinsic information is an important preprocessing step in highdimensional 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 nonlinear dimensionality reduction scenarios by applying the kernel trick.
Pattern discovery by residual analysis and recursive partitioning
 IEEE Transactions on Knowledge and Data Engineering
, 1999
"... 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 importa ..."
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Cited by 12 (2 self)
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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.
Choosing the number of factors in Independent Factor Analysis model,Metodološki Zvezki
 Advances in Methodology and Statistics
, 2005
"... Independent Factor Analysis (IFA) has recently been proposed in the signal processing literature as a way to model a set of observed variables through linear combinations of hidden independent ones plus a noise term. Despite the peculiarity of its origin the method can be framed within the latent ..."
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Cited by 2 (0 self)
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Independent Factor Analysis (IFA) has recently been proposed in the signal processing literature as a way to model a set of observed variables through linear combinations of hidden independent ones plus a noise term. Despite the peculiarity of its origin the method can be framed within the latent variable model domain and some parallels with the ordinary Factor Analysis can be drawn. If no prior information on the latent structure is available a relevant issue concerns the correct specification of the model. In this work some methods to detect the number of significant latent variables are investigated. Moreover, since the method defines a probability density function for the latent variables by mixtures of gaussians, the correct number of mixture components must also be determined. This issue will be treated according to two main approaches. The first one amounts to carry out a likelihood ratio test. The other one is based on a penalized form of the likelihood, that leads to the so called information criteria. Some simulations and empirical results on real data sets are finally presented. 1
Independent Factor Discriminant Analysis
"... Abstract. In the general classification context the recourse to the socalled Bayes decision rule requires to estimate the class conditional probability density functions. In this paper we propose a mixture model for the observed variables which is derived by assuming that the data have been generat ..."
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Cited by 1 (0 self)
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Abstract. In the general classification context the recourse to the socalled Bayes decision rule requires to estimate the class conditional probability density functions. In this paper we propose a mixture model for the observed variables which is derived by assuming that the data have been generated by an independent factor model. Independent factor analysis is in fact a generative latent variable model whose structure closely resembles the one of ordinary factor model but it assumes that the latent variables are mutually independent and not necessarily Gaussian. The method therefore provides a dimension reduction together with a semiparametric estimate of the class conditional probability density functions. This density approximation is plugged into the classic Bayes rule and its performance is evaluated both on real and simulated data.
Fault diagnosis of a railway device using semisupervised independent factor
"... analysis with mixing constraints ..."
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COMPARISON OF PARTITION BASED CLUSTERING ALGORITHMS
"... 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 s ..."
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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 kmeans, Representative object based kmedoids 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.
Accelerating Learning Performance of Back Propagation Algorithm by Using Adaptive Gain Together with Adaptive Momentum and Adaptive Learning Rate on Classification Problems
"... The back propagation (BP) algorithm is a very popular learning approach in multilayer feedforward networks. However, the most serious problems associated with the BP are local minima problem and slow convergence speeds. Over the years, many improvements and modifications of the BP learning algorithm ..."
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The back propagation (BP) algorithm is a very popular learning approach in multilayer feedforward networks. However, the most serious problems associated with the BP are local minima problem and slow convergence speeds. Over the years, many improvements and modifications of the BP learning algorithm have been reported. In this research, we propose a new modified BP learning algorithm by introducing adaptive gain together with adaptive momentum and adaptive learning rate into weight update process. By computer simulations, we demonstrate that the proposed algorithm can give a better convergence rate and can find a good solution in early time compare to the conventional BP. We use four common benchmark classification problems to illustrate the improvement in convergence time.