Abstract--Single-hidden layer feed forward neural networks (SLFNs) are widely used in pattern classification problems, but a huge bottleneck encountered is the slow speed and poor perf or-mance of the traditional iterative gradient-based learnin g algorithms. Although the famous extreme learning machine (ELM) has successfully addressed the problems of slow convergenc e, it still has computational robustness problems brought by inp ut weights and biases randomly assigned. Thus, in order to over - come the aforementioned problems, in this paper, a novel typ e neural network based on Gegenbauer orthogonal polynomials, termed as GNN, is constructed and investigated. This model c ould overcome the computational robustness problems of ELM, whi le still has comparable structural simplicity and approximat ion capability. Based on this, we propose a regularized weights direct determination (R-WDD) based on equality-constrain ed optimization to determine the optimal output weights. The R - WDD tends to minimize the empirical risks and structural ris ks of the network, thus to lower the risk of over fitting and impro ve the generalization ability. This leads us to a the final GNN wi th R-WDD, which is a unified learning mechanism for binary and multi-class classification problems. Finally, as is verifie d in the various comparison experiments, GNN with R-WDD tends to have comparable (or even better) generalization performan ces, computational scalability and efficiency, and classificati on robustness, compared to least square support vector machine ( LS-SVM), ELM with Gaussian kernel. ESEARCHES on artificial feed-forward neural networks (FNNs) have become increasingly active and popular, for it is one of the most powerful tools in artificial intelligenc e field.

If there is one application of Machine Learning that is known to be particularly useful and often successful, that is classification. Classification is the task of assigning a given entry to a single class (e.g. Usually, each entry to be processed is represented numerically as a vector of numbers, which can encode high-level features (e.g. the length of the tail, the presence of stripes or spots, etc.) or low-level ones (e.g. the value of each pixel in an image). Over the years, a lot of different classifiers have been explored by the community, the most popular ones being artificial neural networks, decision trees, support -vector machines, or other algorithms such as k-means clustering. In this article I will focus on neural networks, but the argument can be adapted to other types of classifiers.

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts.

Near real-time damage diagnosis of building structures after extreme events (e.g., earthquakes) is of great importance in structural health monitoring. Unlike conventional methods that are usually time-consuming and require human expertise, pattern recognition algorithms have the potential to interpret sensor recordings as soon as this information is available. This paper proposes a robust framework to build a damage prediction model for building structures. Support vector machines are used to predict the existence as well as the probable location of the damage. The model is designed to consider probabilistic approaches in determining hazard intensity given the existing attenuation models in performance-based earthquake engineering. Performance of the model regarding accurate and safe predictions is enhanced using Bayesian optimization. The proposed framework is evaluated on a reinforced concrete moment frame. Targeting a selected large earthquake scenario, 6,240 nonlinear time history analyses are performed using OpenSees. Simulation results are engineered to extract low-dimensional intensity-based features that can be used as damage indicators. For the given case study, the proposed model achieves a promising accuracy of 83.1% to identify damage location, demonstrating the great potential of model capabilities.

The estimation of f τ( x) is difficult but, more informative than estimation of only mean regression f ( x). The estimation of f τ( x) for different values of τ can briefly describe the different characteristics of the conditional distribution of y/x . In many real world problems, the estimation of mean regression f ( x) is not required or enough, rather they require the estimation of quantile f τ(x). The study of quantile regression problem has initially been started in 1978 by Koenkar and Bassett[1]. Later, it has been briefly discussed and described by Koenker in his book (Koenker, [2]). Koenkar and Bassett [1] proposed the pinball loss function for the estimation of the quantile function f τ(x). For a given quantile τ (0, 1), the pinball loss function was an asymmetric loss function suitable for quantile estimation. It was given by P τ( u) null τu if u 0, (τ 1)u otherwise.

JOURNAL OF L A T EX CLASS FILES, VOL., NO., 1 Single V ersus Union: Nonparallel Support V ector Machine Frameworks Chun-Na Li, Y uan-Hai Shao, Huajun Wang, Y u-Ting Zhao, Ling-Wei Huang, Naihua Xiu and Nai-Y ang Deng Abstract --Considering the classification problem, we summarize the nonparallel support vector machines with the nonparallel hyperplanes to two types of frameworks. It solves a series of small optimization problems to obtain a series of hyperplanes, but is hard to measure the loss of each sample. The other type constructs all the hyperplanes simultaneously, and it solves one big optimization problem with the ascertained loss of each sample. We give the characteristics of each framework and compare them carefully. In addition, based on the second framework, we construct a max-min distance-based nonparallel support vector machine for multiclass classification problem, called NSVM. Experimental results on benchmark data sets and human face databases show the advantages of our NSVM. I NTRODUCTION F OR binary classification problem, the generalized eigenvalue proximal support vector machine (GEPSVM) was proposed by Mangasarian and Wild [1] in 2006, which is the first nonparallel support vector machine. It aims at generating two nonparallel hyperplanes such that each hyperplane is closer to its class and as far as possible from the other class. GEPSVM is effective, particularly when dealing with the "Xor"-type data [1]. This leads to extensive studies on nonparallel support vector machines (NSVMs) [2]-[5].

Emotion recognition based on EEG has become an active research area. As one of the machine learning models, CNN has been utilized to solve diverse problems including issues in this domain. In this work, a study of CNN and its spatiotemporal feature extraction has been conducted in order to explore capabilities of the model in varied window sizes and electrode orders. Our investigation was conducted in subject-independent fashion. Results have shown that temporal information in distinct window sizes significantly affects recognition performance in both 10-fold and leave-one-subject-out cross validation. Spatial information from varying electrode order has modicum effect on classification. SVM classifier depending on spatiotemporal knowledge on the same dataset was previously employed and compared to these empirical results. Even though CNN and SVM have a homologous trend in window size effect, CNN outperformed SVM using leave-one-subject-out cross validation. This could be caused by different extracted features in the elicitation process.

Many kinds of data are naturally amenable to being treated as sequences. An example is text data, where a text may be seen as a sequence of words. Another example is clickstream data, where a data instance is a sequence of clicks made by a visitor to a website. This is also common for data originating in the domains of speech processing and computational biology. Using such data with statistical learning techniques can often prove to be cumbersome since most of them only allow fixed-length feature vectors as input. In casting the data to fixed-length feature vectors to suit these techniques, we lose the convenience, and possibly information, a good sequence-based representation can offer. The framework of rational kernels partly addresses this problem by providing an elegant representation for sequences, for algorithms that use kernel functions. In this report, we take a comprehensive look at this framework, its various extensions and applications. We start with an overview of the core ideas, where we look at the characterization of rational kernels, and then extend our discussion to extensions, applications and use at scale. Rational kernels represent a family of kernels, and thus, learning an appropriate rational kernel instead of picking one, suggests a convenient way to use them; we explore this idea in our concluding section. Rational kernels are not as popular as the many other learning techniques in use today; however, we hope that this summary effectively shows that not only is their theory well-developed, but also that various practical aspects have been carefully studied over time.

Dynamic Multi-objective Optimization Problems (DMOPs) refer to optimization problems that objective functions will change with time. Solving DMOPs implies that the Pareto Optimal Set (POS) at different moments can be accurately found, and this is a very difficult job due to the dynamics of the optimization problems. The POS that have been obtained in the past can help us to find the POS of the next time more quickly and accurately. Therefore, in this paper we present a Support Vector Machine (SVM) based Dynamic Multi-Objective Evolutionary optimization Algorithm, called SVM-DMOEA. The algorithm uses the POS that has been obtained to train a SVM and then take the trained SVM to classify the solutions of the dynamic optimization problem at the next moment, and thus it is able to generate an initial population which consists of different individuals recognized by the trained SVM. The initial populuation can be fed into any population based optimization algorithm, e.g., the Nondominated Sorting Genetic Algorithm II (NSGA-II), to get the POS at that moment. The experimental results show the validity of our proposed approach.

One way to recognise an object is to study how the echo has been shaped during the interaction with the target. Wideband sonar allows the study of the energy distribution for a large range of frequencies. The frequency distribution contains information about an object, including its inner structure. This information is a key for automatic recognition. The scattering by a target can be quantitatively described by its Form Function. The Form Function can be calculated based on the data of the initial pulse, reflected pulse and parameters of a medium where the pulse is propagating. In this work spherical objects are classified based on their filler material - water or air. We limit the study to spherical 2 layered targets immersed in water. The Form Function is used as a descriptor and fed into a Neural Network classifier, Multilayer Perceptron (MLP). The performance of the classifier is compared with Support Vector Machine (SVM) and the Form Function descriptor is examined in contrast to the Time and Frequency Representation of the echo.