Asymptotic Theory for Discriminant Analysis in High Dimension Low Sample Size
نویسندگان
چکیده
This paper is based on the author’s thesis, “Pattern recognition based on naive canonical correlations in high dimension low sample size”. This paper is concerned with discriminant analysis for multi-class problems in a High Dimension Low Sample Size (hdlss) context. The proposed discrimination method is based on canonical correlations between the predictors and response vector of class label. We investigate the asymptotic behavior of the discrimination method, and evaluate bounds for its misclassification rate.
منابع مشابه
Improved mean estimation and its application to diagonal discriminant analysis
MOTIVATION High-dimensional data such as microarrays have created new challenges to traditional statistical methods. One such example is on class prediction with high-dimension, low-sample size data. Due to the small sample size, the sample mean estimates are usually unreliable. As a consequence, the performance of the class prediction methods using the sample mean may also be unsatisfactory. T...
متن کاملAsymptotic expansion of the distribution of the studentized linear discriminant function with 2-Step monotone missing data
In discriminant analysis, it is important to evaluate probabilities of misclassification. Therefore some asymptotic approximations have been proposed in case that all the sample vectors do not have missing data. Also it is known that asymptotic expansions of the distribution of discriminant function are useful techniques for considering asymptotic approximation in sample vectors with small dime...
متن کاملAsymptotic Distributions of Estimators of Eigenvalues and Eigenfunctions in Functional Data
Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...
متن کاملDistance weighted discrimination of face images for gender classification
We illustrate the advantages of distance weighted discrimination for classification and feature extraction in a High Dimension Low Sample Size (HDLSS) situation. The HDLSS context is a gender classification problem of face images in which the dimension of the data is several orders of magnitude larger than the sample size. We compare distance weighted discrimination with Fisher’s linear discrim...
متن کاملRobust Centroid Quantile Based ClassiÞcation for High Dimension Low Sample Size Data
A new method of statistical classiÞcation (discrimination) is proposed. The method is most effective for high dimension low sample size data. Its value is demonstrated through a new type of asymptotic analysis, and via a simulation study.
متن کامل