Variable selection in discriminant analysis based on the location model for mixed variables

Abstract

Non-parametric smoothing of the location model is a potential basis for discriminating between groups of objects using mixtures of continuous and categorical variables simultaneously. However, it may lead to unreliable estimates of parameters when too many variables are involved. This paper proposes a method for performing variable selection on the basis of distance between groups as measured by smoothed Kullback-Leibler divergence. Searching strategies using forward, backward and stepwise selections are outlined, and corresponding stopping rules derived from asymptotic distributional results are proposed. Results from a Monte Carlo study demonstrate the feasibility of the method. Examples on real data show that the method is generally competitive with, and sometimes is better than, other existing classification methods.

Variable selection in discriminant analysis for mixed continuous-binary variables and several groups

“…The simulation results clearly show their impact on the performance, and we propose a method based on leave-one-out cross validation for obtaining optimal results. When using this appoach, the obtained results show that the proposal is competitive with that of Mahat et al (2007). All the proofs are given in Section 6.…”

“…To overcome these problems, we propose in this section a non-parametric smoothing procedure for estimating the criterion (5). This procedure is based on smoothing as it is done in Aspakourov and Krzanowki (2000) and Mahat et al (2007). Denote by D the dissimilarity defined on {1, · · · , M } 2 by…”

New Discrimination Procedure of Location Model for Handling Large Categorical Variables

“…This full breast cancer data contains 15 variables comprising of 2 continuous variables, 4 nominal variables with three states each, 6 ordinal variables with eleven states each and 3 binary variables. All the ordinal variables are treated as continuous variables while all the nominal variables are transformed into binary variables according to the past studies (Hamid 2014;Krzanowski 1975;Mahat et al 2007). This pre-processing gives a new dimension with eight continuous and eleven binary variables of a full breast cancer data.…”

“…In particular, the continuous variables are utilized to estimate a set of parameters required in each multinomial cells created by the categorical variables. Based on the natural structure of cLM, all categorical variables need to be converted into binary structure in order to create segmentation called multinomial cells (Krzanowski 1993(Krzanowski , 1983(Krzanowski , 1975Mahat et al 2007). These multinomial cells play an important role in discriminating a new observation into group correctly (Asparoukhov & Krzanowski 2000;Krzanowski 1995).…”

“…Adoption of dimensional reduction such as variable selection or variable extraction can be beneficial to downsizing the variables (Zheng & Zhang 2008). Past studies has implemented different techniques of variable selection in the construction of the location model (Krzanowski 1995(Krzanowski , 1983Mahat et al 2007). In order to use this approach, a subset of variables must be selected carefully without losing much information (Fan & Lv 2010).…”