Abstract
Classification, as one of the main task of machine learning, corresponds to the core work of granular computing, namely granulation. Most of granular computing models and related classification methods are uniquely classifying by granule features, but not considering granule structure, especially in information area with widespread application of algebraic structure. In this paper, we propose a granular computing based classification method from algebraic granule structure. First of all, to pre-process the original data in the algebraic granule structure area, we formulate the algebraic structure based granularity with granule structure of an algebraic binary operator. Then, we propose a novel granular computing based classification method as well as related classifying algorithm with congruence partitioning granules and homomorphicly projecting granule structure. Finally, compared with tolerance neighborhood model, rough set model and quotient space model, we prove that the proposed classification method is much more effective and robust while classifying the algebraic structure based granularity. The proposed granular computing based classification method provides an approach for classifying algebraic structure based granularity, and combines granular computing theory and classification theory of machine learning.
Highlights
Granular computing derives early and is widely used in applications
Granulated by a congruence relation, we propose the granular computing based classification method as well as related classifying algorithm, in which the granules are classified into a congruence partition and the granule structure is homomorphicly projected into a coarser granularity
DIFFERENCES AND ANALYSIS From the above experimental examples of classifying algebraic structure based granularity by tolerance neighborhood model, rough set model, quotient space model and our proposed granular computing based classification method, we find the main differences are as follows: tolerance neighborhood model classifies the granules by a tolerance relation and do not consider the granule structure, rough set model classifies the granules by an equivalence relation and do not consider the granule structure too, quotient space model classifies the granules by an equivalence relation and classifies the granule structure into a quotient space, and our proposed method classifies the granules by a congruence relation and classifies the granule structure into a coarse structure by Formula (4) of Definition 2
Summary
Granular computing derives early and is widely used in applications. Zadeh [1] first introduced the concept of information granulation in the context of fuzzy set in 1979, and Lin [2] formally suggested the term of granular computing in 1997. Granulation, as one key work of granular computing, mainly classifies ungrouped granules (fine granularity) into several parts (coarse granularity) and is a down-top approach [12], which is similar to classification of machine learning. The above classical granular computing models of tolerance neighborhood and quotient space are no longer suitable for classifying granularities with granule structure as an algebra, and there are rarely literature to discuss granular computing based classification methods in which the granule structure is viewed as an algebra. Compared with tolerance neighborhood model and quotient space model, we prove through experimental examples that the proposed classification method is much more effective and robust while classifying the algebraic structure based granularity. The upper presents the main focus of our proposed approach including pre-processing process and classifying method in granulation, corresponding to data training and feature selection from machine learning prospective. A customer of 35 year, 2 months, 13 days old, can be classified into a coarser granularity of a 35
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