Learning Distributions of Image Features by Interactive Fuzzy Lattice Reasoning in Pattern Recognition Applications

Abstract

This paper describes the recognition of image patterns based on novel representation learning techniques by considering higher-level (meta-)representations of numerical data in a mathematical lattice. In particular, the interest here focuses on lattices of (Type-1) Inter vals' Numbers (INs), where an IN represents a distribution of image features including orthogonal moments. A neural classif ier, namely fuzzy lattice reasoning (f lr) fuzzy-ART-MAP (FAM), or f lrFAM for short, is described for learning distributions of INs; hence, Type-2 INs emerge. Four benchmark image pattern recognition applications are demonstrated. The results obtained by the proposed techniques compare well with the results obtained by alternative methods from the literature. Furthermore, due to the isomorphism between the lattice of INs and the lattice of fuzzy numbers, the proposed techniques are straightforward applicable to Type-1 and/or Type-2 fuzzy systems. The far-reaching potential for deep learning in big data applications is also discussed.

Nonparametric Hyperbox Granular Computing Classification Algorithms

“…During the join process, the datum with the class label with the hyperbox granule lies in the hyperbox granule is not considered the join process, such as datum x8 with the class label 1. In this way, the hyperbox granule G 1 = [4,6,7,9] with the blue lines is generated for the data with the class label 1. The same strategy is adopted for the data with the class label 2; two hyperbox granules G 2 = [2, 2, 8, 5] and G 3 = [3, 7, 3, 7] are generated and are shown in Figure 3d.…”

“…In this way, the hyperbox granule 1 [4,6,7,9] G = with the blue lines is generated for the data with the class label 1. The same strategy is adopted for the data with the class label 2; two hyperbox granules 2 [2,2,8,5] G = and 3 [3,7,3,7] G = are generated and are shown in Figure 3d. For the training set S, the achieved granule set is Figure 3d; the granule marked with the blue lines is the granule with class label 1, and the granules with the red lines are the granules with class label 2.…”

“…The discrete inclusion relation method estimates the class labels of inputs based on the discrete inclusion relation between an input with a determined class label and an input without a class label and includes techniques such as random forest (RF) and granular computing (GrC). In this paper, we mainly study the classification algorithm using GrC, especially GrC with the form of hyperbox granule, the superiority and feasibility of which are shown in references [4][5][6][7][8][9][10][11].…”

“…Kaburlasos defined the join operation and the meet operation as inducing granules with different granularity in terms of the theory of lattice computing [5,6]. Kaburlasos defined the fuzzy inclusion measure between two granules on the basis of the defined join operation and meet operation, and the fuzzy lattice reasoning classification algorithm was designed based on the distance between the beginning point and the endpoint of the hyperbox granule [7].…”

“…The second datum x 2 = (7, 6) with the same class label as G 1 is selected to generate the atomic hyperbox granule [76 7 6] which is joined with G 1 and forms the join hyperbox granule[x 2 , x 2 ] ∨ G 1 = [4, 6, 7, 7].Since there are no data with the other class label lying in the join hyperbox granule[x 2 , x 2 ] ∨ G 1 = [4,6,7,7], the G 1 is replaced by the join hyperbox granule, namelyG 1 = [x 2 , x 2 ] ∨ G 1 = [4,6,7,7], as shown inFigure 3b. The third datum x6 with the same class label with G 1 is selected to generate atomic hyperbox granule [x 6 , x 6 ] =[5,9,5,9], which is joined with G 1 and forms the join hyperbox granule [x 6 , x 6 ] ∨ G 1 =[4,6,7,9]. As there are no data with the other class label lying in the join hyperbox granule [x 6 , x 6 ] ∨ G 1 =[4,6,7,9], G 1 is replaced by [x 6 , x 6 ] ∨ G 1 =[4,6,7,9], namely G 1 =[4,6,7,9], as shown in…”