# Pattern Classification Based on RBF Networks with Self-Constructing Clustering and Hybrid Learning
## 1 Introduction  
Pattern classification is a process related to categorization, concerned with classifying patterns into one or more categories. It plays an important role in many fields, such as media, medicine, science, business, and security [1; 2; 3; 4; 5]. A classification problem can be converted to multiple binary classification problems in two ways, one-vs-rest (OvR) and one-vs-one (OvO), by creating several systems each of which is responsible for one category. However, OvR may suffer from unbalanced learning, since typically the set of negative training data is much larger than the set of positive training data. In contrast, OvO may suffer from ambiguities: two or more categories may receive the same number of votes and one category has to be picked arbitrarily. Therefore, researchers tend to seek other ways to solve classification problems. In general, classification tasks can be divided into two kinds: single-label and multi-label. Single-label classification concerns classifying a pattern to only one category, but multi-label classification may classify a pattern to one or more categories. Many algorithms, based on multilayered perceptrons (MLP) [6], decision trees [7; 8], k-nearest neighbors (KNN) [9], probability-basedclassifiers [10], support vector machines (SVM) [11; 12], or random vector functional-link (RVFL) networks [13; 14], have been developed for pattern classification. Most developed algorithms are for single-label classification. KNN [9] is a lazy learning algorithm. It is based on similarity between input patterns and training data. The category to which the input pattern belongs to is determined by its k-nearest neighbors. Decision tree methods [7; 15] build decision trees, e.g., ID3 and C4.5, from a set of training data using the concept of information entropy. An unseen pattern traverses down from the root of the tree until reaching a leaf which tells the category to which the unseen is assigned. Probability-based classifiers [16; 17] assume independence among features. These classifiers can be trained for the estimation of parameters necessary for classification. MLP [18; 19; 20] is a feedforward multi-layer network model consisting of several layers of nodes, with two adjacent layers fully connected to each other. Each node in the network is associated with an activation function, linear or nonlinear. RVFL networks [13; 14; 21] are also fully-connected feedforward networks, with only one single hidden layer. The weights between input and hidden nodes are assigned to random values. The values of the weights between hidden and output nodes, instead, are learned from training patterns. An RBF network [22; 23; 24; 25; 26; 27] is a two-layer network, using radial basis functions as the activation functions in the hidden layer. The output of the network is a linear combination of the outputs from the hidden layer. In SVM [11; 12], training patterns are mapped into the points in a high-dimensional space and the points of different categories are separated in the space by a gap as wide as possible. For an unseen pattern, the same mapping is performed and the classification is predicted according to the side of the gap it falls on. For solving multi-label classification problems [28], two approaches are generally adopted [29]: In one approach, a multi-label classification task is transformed to several single-label classification tasks which are instead solved by single-label classification methods. In the other approach, the capability of a specific single-label classification algorithm is extended to handle directly the multi-label data [30; 31; 32; 33]. Since first introduced in 1988 by [PERSON] [34], RBF networks have been becoming popular in classification applications. However, as pointed out in [34; 35], in the construction phase of such networks, there are several issues encountered, such as the determination of the number of nodes in the hidden layer, the form and initialization of the basis functions, and the learning of the parameters involved in the networks.