Discriminant Coordinates for Multivariate Functional Data

• Activity Number: 178
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Lukasz Waszak*+ and Tomasz Gorecki and Miroslaw Krzysko and Waldemar Wolynski
• Companies: Adam Mickiewicz University and Adam Mickiewicz University and Adam Mickiewicz University and Adam Mickiewicz University
• Keywords: Multivariate functional data ; Functional data analysis ; Discriminant coordinates

Abstract

In recent years, methods for representing data by functions or curves have received much attention. Data in the form of a continuous vector function on a given interval are referred to as multivariate functional, i.e. objects are characterized by many features observed at many points in time. Such data can be treated as realizations of multivariate random processes. The results so far known relate only to one-dimensional stochastic processes (Ramsay and Silverman, 2005). Suppose that we are observing independent realizations of a p-dimensional stochastic process belonging to the lth class. Our purpose is to construct the discriminant coordinate based on multivariate functional data, i.e. to construct functional discriminant coordinate such that their between-class variance is maximal compared with the total variance. We present a new method of construction of discriminant coordinates for this type of data. Moreover this construction is illustrated and discussed in the context of analyzing real data sets.