Fuzzy Principal Components Analysis
Dyomina, Nadezhda (2007)
Tiivistelmä
Due to the large number of characteristics, there is a need to extract the most relevant
characteristicsfrom the input data, so that the amount of information lost in this way is
minimal, and the classification realized with the projected data set is relevant with
respect to the original data. In order to achieve this feature extraction, different
statistical techniques, as well as the principal components analysis (PCA) may be used.
This thesis describes an extension of principal components analysis (PCA) allowing
the extraction ofa finite number of relevant features from high-dimensional fuzzy data
and noisy data. PCA finds linear combinations of the original measurement variables
that describe the significant variation in the data. The comparisonof the two proposed
methods was produced by using postoperative patient data. Experiment results
demonstrate the ability of using the proposed two methods in complex data.
Fuzzy PCA was used in the classificationproblem. The classification was applied by
using the similarity classifier algorithm where total similarity measures weights are
optimized with differential evolution algorithm. This thesis presents the comparison of
the classification results based on the obtained data from the fuzzy PCA.
characteristicsfrom the input data, so that the amount of information lost in this way is
minimal, and the classification realized with the projected data set is relevant with
respect to the original data. In order to achieve this feature extraction, different
statistical techniques, as well as the principal components analysis (PCA) may be used.
This thesis describes an extension of principal components analysis (PCA) allowing
the extraction ofa finite number of relevant features from high-dimensional fuzzy data
and noisy data. PCA finds linear combinations of the original measurement variables
that describe the significant variation in the data. The comparisonof the two proposed
methods was produced by using postoperative patient data. Experiment results
demonstrate the ability of using the proposed two methods in complex data.
Fuzzy PCA was used in the classificationproblem. The classification was applied by
using the similarity classifier algorithm where total similarity measures weights are
optimized with differential evolution algorithm. This thesis presents the comparison of
the classification results based on the obtained data from the fuzzy PCA.