Pattern Recognition in Numerical Data Sets and Color Images through the Typicality Based on the GKPFCM Clustering Algorithm

Abstract

We take the concept of typicality from the field of cognitive psychology, and we apply the meaning to the interpretation of numerical data sets and color images through fuzzy clustering algorithms, particularly the GKPFCM, looking to get better information from the processed data. The Gustafson Kessel Possibilistic Fuzzy c-means (GKPFCM) is a hybrid algorithm that is based on a relative typicality (membership degree, Fuzzy c-means) and an absolute typicality (typicality value, Possibilistic c-means). Thus, using both typicalities makes it possible to learn and analyze data as well as to relate the results with the theory of prototypes. In order to demonstrate these results we use a synthetic data set and a digitized image of a glass, in a first example, and images from the Berkley database, in a second example. The results clearly demonstrate the advantages of the information obtained about numerical data sets, taking into account the different meaning of typicalities and the availability of both values with the clustering algorithm used. This approach allows the identification of small homogeneous regions, which are difficult to find.

Introducing the structural bases of typicality effects in deep learning

“…With the rise of deep neural networks, handcrafted features were replaced with CNN features in prototype learning, thus achieving end-to-end integration in deep networks and high precision and robustness in various image processing tasks. The differences between the great variety of existing approaches can be roughly grouped by: i) the number of prototypes used to represent a category (1-per-class [19,20,23,26,28,29,34], n-perclass [25,27,30,31,33], sparse [18]); ii) the distance measure (or measures combination) used to stand for the similarity between each instance-prototype pair (Euclidean distance [18-20, 25, 26, 30, 31, 33], Mahalanobis distance [19,20], Co-variance distance [29], Cosine distance [26], Learned distance [27,28], Hand-designed distance [33,34]); and iii) the approach used for prototype representation (prototype-template image [18,23], mean vector of embedded features [25,26,28,29,31], learned centroid vector [19,20,27,30,34], learned CNN-tensor [33]).…”

“…In general, prototype learning methods [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] represent the prototype as a centroid vector computed using all category members. In contrast to those proposals that assume the prototype as a centroid element (prototype-object), and based on Rosch's prototype definition, we propose representing the prototype as a semantic entity with a center and boundaries computed using only the typical members.…”

“…Consequently, for each baseline CNN model, we evaluated six PS-Layer model versions:fromscratch-a, fromscratchb, freezing-a, freezing-b, pretrain-a, pretrain-b. Notice that unlike other prototype learning approaches [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], our prototype representation is not updated during the training process. Because the lack of annotated data with the typicality information prevents end-to-end training, our main goal is to evaluate the performance and robustness of the semantic information encapsulated in our prototype's representation.…”

“…This paper relies on cognitive semantic studies related to the Prototype Theory to propose a new perspective to model the central semantic meaning of object categories: the prototype. Unlike other prototype learning approaches [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], we use our prototype representation to capture the concepts of typicality and category membership degree of object's images. Our proposal considers the typicality concept from cognitive psychology, assuming that it is possible to obtain a more natural and interpretable representation of the semantics of the object's image.…”

“…Prototype learning is a representative approach of pattern recognition methods. It has been used in such image processing tasks as Face Recognition [18,25], Image Segmentation [19,28], Static Hand Gesture [25], Few-Shot Learning [23,26,29,31], Clustering [22], Robust Image Classification [20,21,24,30,33,34], CNN Interpretation [27,32], etc. Even though these works proposed a wide variety of methods for prototype learning, most of the approaches focus on using prototype learning to improve the performance/robustness of a specific task.…”