Quantitative Assessment of Direction-Alignment of Fuzzy Vectors for Pattern Classification and Matching

Pattern matching refers to assessing the degree of similarity between pairs of patterns, while pattern classification deals with inferring the class of an unknown pattern from the knowledge of the training instances for each class. This paper provides a unified approach to pattern matching and classification by representing objects using fuzzy vectors with their attributes graded in membership scales along the axes of the reference frame. Such representation helps in taking the direction cosine of pairs of vectors to determine their degree of similarity (matching). Additionally, the said representation helps in representing the given training instances of each class by fuzzy vectors and the class centroid by the average of the fuzzy vectors of the same class. Determination of the class label of an unknown object thus requires representing it by a fuzzy vector, and projecting it along the unit vectors of class centroids of different classes. The class centroid that comes up with the largest length of projection corresponds to the class of the unknown object. The proposed methods of fuzzy matching and classification yield unexpectedly good matching score and classification accuracy because of i)the judicious choice of the graded membership functions, describing diversity of the fuzzy attributes of the data points along the membership axes, and ii) the benefit of projecting a fuzzy data point vector along the target vector by using the dot product. While the choice of membership functions enhances the qualitative degree in data similarity in diversified fuzzy attribute space, the projection of a fuzzy vector along the unit target vectors offers a measure of directional similarity of the 2 vectors. The proposed techniques have successfully been tested for emotion classification of individuals, and also emotion matching across people of different cultures and origin. Statistical tests undertaken confirm the superiority of the proposed algorithm with their competitors.