# Intelligent Neural Network Schemes for Multi-Class Classification
## 1 Introduction
It is easily implemented but may be sensitive to the characteristics of the attributes involved. The k-Nearest neighbor (KNN) algorithm [17; 18; 19] classifies each data point by analyzing its nearest neighbors among the training examples. It is intuitive and easily implemented. However, it is computationally intensive. Neural networks are another machine learning technique, carrying out the classification work by passing the input values through multiple layers of neurons that can perform nonlinear transformations on the data. A neural network derives its computing power mainly through its massively parallel, distributed structure and its ability of learning and generalization, which make it possible for neural networks to find good approximate solutions to complex problems that are intractable. There are many types of neural networks. Perhaps the most common one is multiple-layer perceptrons (MLPs). Figure 1: Functionality of classification. An MLP is a class of fully connected, feedforward neural network, consisting of an input layer, an output layer, and a certain number of hidden layers [20; 21]. Each node is a neuron associated with a nonlinear activation function, and the gradient descent backpropagation algorithm is adopted to train the weights and biases involved in the network. In general, trial-and-error is needed to determine the number of hidden layers and the number of neurons in each hidden layer, and long learning time is required by the backpropagation algorithm. Support vector machines (SVMs) are models with associated learning algorithms that analyze data used for classification [22; 23; 24]. Training instances of the separate categories are divided by a gap as wide as possible. One disadvantage is that several key parameters need to be set correctly for SVMs to achieve good classification results. Other limitations include the speed in training and the optimal design for multi-class SVM classifiers [25]. Recently, deep learning neural networks have successfully been applied to analyzing visual imagery [26; 27; 28]. They impose less burden on the user compared to other classification algorithms. The independence from prior knowledge and human effort in feature design is a major advantage. However, deep learning networks are computationally expensive. A large dataset for training is required. Hyperparameter tuning is non-trivial. The radial basis function (RBF) network is another type of neural network for multi-class classification problems. [PERSON] and [PERSON] [29] were the first to develop the RBF network model. An RBF network is a two-layer network. In the first layer, the distances between the input vector and the centers of the basis functions are calculated. The second layer is a standard linearly weighted layer. While MLP uses global activation functions, RBF uses local basis functions, which means that the outputs are close to zero for a point that is far away from the center points. There are pros and cons with RBF networks. The configuration of hyper-parameters, e.g., the fixed number of layers and the choice of basis functions, is much simpler than that of MLP, SVM, or CNN. Unlike the MLP network, RBF can have fewer problems with local minima and the local basis functions adopted by RBF can lead to faster training [30]. Also, the local basis functions can be very useful for adaptive training, in which the network continues to be incrementally trained while it is being used. For new training data coming from a certain region of the input space, the weights of those neurons will not be adjusted if the neurons fall outside that region. However, because of locality, basis centers of the RBF network must be spread throughout the range of the input space. This leads to the problem of the curse of dimensionality and there is a greater likelihood that the network will overfit the training data [31]. In this paper, we develop RBF-based neural network schemes for single-label and multi-label classification, respectively.