ABSTRACT. Classification using high-dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high-throughput data. The impact of dimensionality on classifications is largely poorly understood. In a seminal paper, Bickel and Levina (2004) show that the Fisher discriminant performs poorly due to diverging spectra and they propose to use the independence rule to overcome the problem. We first demonstrate that even for the independence classification rule, classification using all the features can be as bad as the random guessing due to noise accumulation in estimating population centroids in high-dimensional feature space. In fact, we demonstrate further that almost all linear discriminants can perform as bad as the random guessing. Thus, it is paramountly important to select a subset of important features for high-dimensional classification, resulting in Features Annealed Independence Rules (FAIR). The conditions under which all the important features can be selected by the two-sample t-statistic are established. The choice of the optimal number of features, or equivalently, the threshold value of the test statistics are proposed based on an upper bound of the classification error. Simulation studies and real data analysis support our theoretical results and demonstrate convincingly the advantage of our new classification procedure.

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Detection of biotic stress (Venturia inaequalis) in apple trees using hyperspectral data: Non-parametric statistical approaches and physiological implications

Artificial Neural Networks are useful for pattern recognition and also popular as classification mechanisms in medical decision support systems despite the fact that they are unstable predictors An important application of Gene Expression Data is classification of biological samples or prediction of clinical and outcomes. In this paper a method is proposed that combines statistical technique and Artificial Neural Network(ANN) to identify the prostate cancer diseased genes from normal genes and classify them using metrics call values. The system has 5 steps: 1.Data Collection along with filtering 2. Pre-processing of data using the gene selection method 3.Dimension reduction using statistical method 4.Classification using neural networks. 5. Comparing the results of gene selection followed by ANN and dimension reduction followed by ANN with varying number of predictors chosen from the gene selection method. The subset of genes that contribute significantly to the success of the neural classifiers are identified.

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