Minh Tuan Pham

Classification and Clustering of Spatial Patterns with Geometric Algebra

In fields of classification and clustering of patterns most conventional methods of feature extraction do not pay much attention to the geometric properties of data, even in cases where the data have spatial features. This paper proposes to use geometric algebra to systematically extract geometric features from data given in a vector space. We show the results of classification of handwritten digits and those of clustering of consumers’ impression with the proposed method.

Feature extractions with geometric algebra for classification of objects

Most conventional methods of feature extraction do not pay much attention to the geometric properties of data, even in cases where the data have spatial features. In this study we introduce geometric algebra to undertake various kinds of feature extraction from spatial data. Geometric algebra is a generalization of complex numbers and of quaternions, and it is able to describe spatial objects and relations between them. This paper proposes to use geometric algebra to systematically extract geometric features from data given in a vector space. We show the results of classification of hand-written digits, which were classified by feature extraction with the proposed method.

A clustering method for geometric data based on approximation using conformal geometric algebra

Clustering is one of the most useful methods for understanding similarity among data. However, most conventional clustering methods do not pay sufficient attention to the geometric properties of data. Geometric algebra (GA) is a generalization of complex numbers and quaternions able to describe spatial objects and the relations between them. This paper uses conformal GA (CGA), which is a part of GA, to transform a vector in a real vector space into a vector in a CGA space and presents a proposed new clustering method using conformal vectors. In particular, this paper shows that the proposed method was able to extract the geometric clusters which could not be detected by conventional methods.

Robust feature extractions from geometric data using geometric algebra

Most conventional methods of feature extraction for pattern recognition do not pay sufficient attention to inherent geometric properties of data, even in the case where the data have spatial features. This paper introduces geometric algebra to extract invariant geometric features from spatial data given in a vector space. Geometric algebra is a multidimensional generalization of complex numbers and of quaternions, and it ables to accurately describe oriented spatial objects and relations between them. This paper proposes to combine several geometric features using Gaussian mixture models. It applies the proposed method to the classification of hand-written digits.

A fast non-empirical tropical cyclone identification method

We propose a high speed non-empirical method to detect centers of tropical cyclones, which is useful to identify tropical cyclones in huge climatology data. In this method, centers of tropical cyclones are detected automatically by iteration of streamline in down-stream direction from some initial positions. We also bend the path of streamline successively to converge on the center of tropical cyclone rapidly. Since this method is free from empirical conditions used in the conventional method, the accuracy is independent of these conditions. Moreover, because the proposed method does not need to check these at all grid points, computational cost is significantly reduced. We compare the accuracy and effectiveness of the method with those of the conventional one for tropical cyclone identification task in observational data. Our method could find almost all tropical cyclones, some of which were not identified by the conventional method. This method will be useful for future huge climatology data, since computational cost does not depend on the number of grid points.