Distance metric has a key role in many machine learning and computer vision algorithms so that choosing an appropriate distance metric has a direct effect on the performance of such algorithms. Recently, distance metric learning using labeled data or other available supervisory information has become a very active research area in machine learning applications. Studies in this area have shown that distance metric learning-based algorithms considerably outperform the commonly used distance metrics such as Euclidean distance. In the kernelized version of the metric learning algorithms, the data points are implicitly mapped into a new feature space using a non-linear kernel function. The associated distance metric is then learned in this new feature space. Utilizing kernel function improves the performance of pattern recognition algorithms, however choosing a proper kernel and tuning its parameter(s) are the main issues in such methods. Using of an appropriate composite kernel instead of a single kernel is one of the best solutions to this problem. In this research study, a Multiple kernel is constructed using the weighted sum of a set of basis kernels. In this framework, we propose different learning approaches to determine the kernels weights. The proposed learning techniques arise from the distance metric learning concepts. These methods are performed within a semi supervised framework where different cost functions are considered and the learning process is performed using a limited amount of supervisory information. The supervisory information is in the form of a small set of similarity and/or dissimilarity pairs. We define four distance metric based cost functions in order to optimize the Multiple kernel weight. In the first structure, the average distance between the similarity pairs is considered as the cost function. The cost function is minimized subject to maximizing of the average distance between the dissimilarity pairs. This is in fact, a commonly used goal in the distance metric learning problem. In the next structure, it is tried to preserve the topological structure of the data by using of the idea of graph Laplacian. For this purpose, we add a penalty term to the cost function which preserves the topological structure of the data. This penalty term is also used in the other two structures. In the third arrangement, the effect of each dissimilarity pair is considered as an independent constraint. Finally, in the last structure, maximization of the distance between the dissimilarity pairs is considered within the cost function not as a constraint. The proposed methods are examined in the clustering application using the kernel k-means clustering algorithm. Both synthetic (a XOR data set) and real data sets (the UCI data) used in the experiments and the performance of the clustering algorithm using single kernels, are considered as the baseline. Our experimental results confirm that using the Multiple kernel not only improves the clustering result but also makes the algorithm independent of choosing the best kernel. The results also show that increasing of the number of constraints, as in the third structures, leads to instability of the algorithm which is expected.

The main objective of this paper is a study of some new generalizations of Hilbert’s and Hardy–Hilbert’s type inequalities. We apply our general results to homogeneous functions. Also, we obtain the best possible constants when the parameters satisfy appropriate conditions.

Extracting and modeling the spatial information content of very high resolution (VHR) images can dramatically increase the performances of urban area classification. However, extracting spatial features is a highly challenging task. During the years, several spatial feature extraction methods have been proposed, most of which are mainly designed for grayscale images. To use these methods for a multispectral image, usually, a dimensionality reduction step is required. As a result, these methods cannot optimally extract the spatial information contents of different bands of a multispectral image. To address this issue, we proposed the use of the region covariance descriptor (RCD) for spatial feature extraction from VHR images. The RCD features consider the covariance matrix of a local neighborhood of each pixel as the features. These features can model both the spatial information and the spectral relationship between bands. The RCD features lie in a Riemannian manifold, on which the common classification algorithms cannot be applied. To overcome this, we used Riemannian kernel functions. Also, we proposed a Multiple kernel learning strategy for combining RCD and spectral features. The proposed strategy was evaluated for classifying a VHR image acquired over the urban area of Tehran, Iran. Furthermore, its obtained results were compared with those of ten other common spatial feature extraction methods. The results showed that the proposed classification strategy using the RCD features yielded at least 5% higher accuracies than the other feature extraction methods.

With a largeamount of multimedia content in the web, storage and retrieval of them by classical learning methods dealt with some major challenges like memory restriction. These limitations in some of learning algorithms like SVM and ANN is so serious that these algorithms cannot be employed in large-scale learning context. kernel Extreme learning Machine (KELM) algorithm is one of the powerful methods in machine learning. learning phase of this method is based on constructing kernel matrix of labeled instances and calculating inverse of it. So, employing this method in large scale learning context with a lot of labeled instances is not feasible. In this research to overcome limitation of employing the KELM in large-scale multi-label learning, a new approach is proposed. The proposed approach is based on prototype selection in neighborhood of each training instance. By using the proposed approach, the size of training set is reduced. So, classical learning methods can be applied on reduced training set. Since multimedia contents are basically multi-label, the proposed prototype selection approach is based on multi-label domains like automatic image annotation. Experimental results on NUS-WIDE large-scale multi-label image set and three other versions include Object, Scene and Lite indicated the effectiveness of the proposed approach in solving the limitation of employing KELM method in large-scale multi-label learning.

Objective: In the present era, businesses have developed to a large extent which has, in turn, forced them to manage their resources and expenditures wisely for the sake of competition. This is mainly because the competitive market has severely reduced the flexibility of companies, which means that their ability respond to different economic situations has reduced and this puts most firms at the constant risk of bankruptcy and contraction. Therefore, in this study, we have tried to predict the bankruptcy of manufacturing companies through preventing the occurrence of such risks. Methods: In this study, the "kernel Extreme learning Machine" has been used as one of the artificial intelligence models for predicting bankruptcy. Given that machine learning methods require an optimization algorithm we have used one of the most up-to-date, "Gray Wolf Algorithm" which has been introduced in 2014. Results: The above model has been implemented on the 136 samples that were collected from the Tehran Stock Exchange between 2015 and 2018. All of the performance evaluation criteria including the classification, accuracy, type error, second-order error and area under the ROC curve showed better performance than the genetic algorithm which was presented and its significance was confirmed by t-test. Conclusion: Considering the gray wolf algorithm’ s high accuracy and its performance compared to the genetic algorithm, it is necessary to use the gray wolf algorithm to predict the bankruptcy of Iranian manufacturing companies either for investment purposes and for validation purposes, or for using internal management of the company.