## 1 Introduction  
Artificial neural networks (ANNs) are widely used pattern recognition tools in chemometrics. The most commonly used neural network for chemists is the back-propagation neural network (BNN). The BNN is a feed forward neural network, usually trained by error back-propagation [1; 2]. BNNs have been applied to a broad range of chemical applications. Recent analytical applications of BNNs in fields such as differential mobility spectrometry [3] and near infrared spectroscopy [4] have been reported in the literature. BNNs have been proven a useful type of ANNs in chemometrics. However, BNNs converge slowly during training especially when the network contains many hidden neurons. This slow and chaotic convergence is partially caused by the simultaneous adjustments of weights of all hidden neurons during the training of BNNs, which is referred to as the \"moving target problem\". To avoid this problem, a network architecture named cascade correlation network (CCN) was proposed by [PERSON] and [PERSON] [5]. A CCN begins its training with a minimal network, which only has an input layer and an output layer. During training, the CCN determines its topology by adding and training one hidden neuron at a time, resulting in a multilayer structure. In this training strategy, the moving target problem is avoided because only weights of single hidden neuron in the network are allowed to change at any time. CCN have been applied to the prediction of the protein secondary structure [6] and estimation of various ion concentrations in river water for water quality monitoring [7]. A temperature constrained cascade correlation network (TCCCN) [8], which combines the advantages of cascade correlation and computational temperature constraints was devised to provide reproducible models. By modifying the sigmoid transfer function, a temperature term is added to constrain the length of the weight vector in the hidden transfer function. The temperature is adjusted so that the magnitude of the first derivative of the covariance between the output and the residual error is maximized. As a result, fast training can be achieved because of the large weight gradient. TCCCNs have been successfully applied to many areas in analytical chemistry, such as identification of toxic industrial chemicals by their ion mobility spectra [9], classification of official and unofficial rhubarb samples based on their infrared reflectance spectrometry [10], and prediction of substructure and toxicity of pesticides from low-resolution mass spectra [11], _etc_. Besides BNNs and CCNs, the radial basis function network (RBFN) is another important type of neural network. A RBFN is a three-layered feed forward network, which applies a radial basis function (RBF) as its hidden layer transfer function. The most commonly applied RBF is the Gaussian function. The determination of the number, centroids and radii of hidden units of RBFN can be achieved by different ways, such as random generation, clustering, and genetic algorithms. The RBFN can also be trained by back-propagation. [PERSON] and [PERSON] developed a type of RBFN that is a self-configuring radial basis function network (SCRBFN) [12]. In a SCRBFN, a linear averaging (LA) clustering algorithm is applied to determine the parameters of the hidden units. Class memberships of the training objects are used during clustering in the LA algorithm. Recently, many novel supervised learning methods have gained increasing popularity, such as the support vector machine (SVM) and Random Forest (RF). The SVM was introduced by [PERSON] [13]. The SVM first maps the training data into high dimension feature space by using kernel functions. An optimal linear decision hyperplane is determined by maximizing the margin between the objects of two classes. The RF method was developed by [PERSON] [14]. It is derived from the decision trees algorithm. During the RF training, many decision trees were trained by the ensemble learning techniques. The classification result is then calculated by voting from all the trees built.