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Change point, prediction and classification with functional data (CD)

By: Rathi, Poonam.
Material type: materialTypeLabelBookPublisher: Ahmedabad Indian Institute of Management Ahmedabad 2018Description: 185 p.Subject(s): Change Point | Prediction | Classification | Functional Data | Underlying Gaussian ProcessDDC classification: TH 2018-11 Summary: Functional data consists of a collection of curves or functions dened on a nite subset of some interval. In this dissertation, we discuss change point, prediction and classication with functional data. In change point problem, assuming that the functional data are random sample paths coming from an underlying Gaussian Process, we have introduced a new method for change point detection based on generalized likelihood ratio test. The covariance function used is a suitably modied version of the powered exponential covariance function to accommodate the correlation between dierent seasons of the year. The generalized likelihood ratio test statistic is derived in this functional setup. This method is applied for detecting the presence of change point in the temperature record of nine Indian cities available for the period, 1961-2013. Further, we have explored in detail, the relation of the magnitude of temperature change with the geographical location of the cities. We found that there has been a rise in the average temperature for all cities except one during this period. The magnitude of warming is found to be not uniform and varying across the cities. The cities located in higher altitudes are seen to have warmed more than those located in the plains and warming has occurred more in the winter season. The estimated change points for most of the cities lie within the period 1994 - 2001. The ndings suggest that immediate policy measures may be required to ensure that no further warming happens in these cities. In the prediction problem, we propose new methods for predicting functional data assuming as before that these are random sample paths of an underlying Gaussian Process. We propose two new predictors namely CE-Predictor and k-NN Predictor for such data. When the data is a mixture of two Gaussian processes, we additionally propose two new predictors: KM-Predictor and FC-Predictor. These methods cluster the initial training data into two classes and then the partially observed curve is classied in one of the two classes and subsequently, a prediction is made. We apply our methods to three real life datasets, namely growth curve of girls, annual temperature of Ahmedabad city and railway availability curves. It appears that the KM-Predictor performs quite well for all these data sets. In the classication problem with functional data, we provide a comparison of ve classiers of which three are depth based, one is neighborhood based and the last one is centroid based through various experiments. We experiment with both balanced and unbalanced data as well as with equally spaced and unequally spaced data to check the robustness of classication performance of these methods. It appears that the method based on Fraiman and Muniz depth performs best in most of the experiments followed by the method based on h-modal depth.
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Reference TH 2018-11 (Browse shelf) Not for Issue CD002565

Functional data consists of a collection of curves or functions dened on a nite subset
of some interval. In this dissertation, we discuss change point, prediction and
classication with functional data.
In change point problem, assuming that the functional data are random sample paths
coming from an underlying Gaussian Process, we have introduced a new method for
change point detection based on generalized likelihood ratio test. The covariance
function used is a suitably modied version of the powered exponential covariance
function to accommodate the correlation between dierent seasons of the year. The
generalized likelihood ratio test statistic is derived in this functional setup. This
method is applied for detecting the presence of change point in the temperature record
of nine Indian cities available for the period, 1961-2013. Further, we have explored
in detail, the relation of the magnitude of temperature change with the geographical
location of the cities. We found that there has been a rise in the average temperature
for all cities except one during this period. The magnitude of warming is found to be
not uniform and varying across the cities. The cities located in higher altitudes are
seen to have warmed more than those located in the plains and warming has occurred
more in the winter season. The estimated change points for most of the cities lie within
the period 1994 - 2001. The ndings suggest that immediate policy measures may be
required to ensure that no further warming happens in these cities.
In the prediction problem, we propose new methods for predicting functional data
assuming as before that these are random sample paths of an underlying Gaussian
Process. We propose two new predictors namely CE-Predictor and k-NN Predictor
for such data. When the data is a mixture of two Gaussian processes, we additionally
propose two new predictors: KM-Predictor and FC-Predictor. These methods cluster
the initial training data into two classes and then the partially observed curve is
classied in one of the two classes and subsequently, a prediction is made. We apply our
methods to three real life datasets, namely growth curve of girls, annual temperature
of Ahmedabad city and railway availability curves. It appears that the KM-Predictor
performs quite well for all these data sets.
In the classication problem with functional data, we provide a comparison of ve
classiers of which three are depth based, one is neighborhood based and the last one
is centroid based through various experiments. We experiment with both balanced and
unbalanced data as well as with equally spaced and unequally spaced data to check the
robustness of classication performance of these methods. It appears that the method
based on Fraiman and Muniz depth performs best in most of the experiments followed
by the method based on h-modal depth.

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