Best Approximation by Trigonometric Polynomials of Convolution Classes Generated by Some Linear Combinations of Periodic Kernels

Nonnegative matrix factorization with combined kernels for small data representation

Sleep staging is one of the important areas which is used to diagnose several diseases. People try to obtain models to carry out this operation without human interaction due to the time-consuming and complex nature of classification process. Most of the prior studies use concatenation of the extracted features from the electroencephalography (EEG) signals to obtain a single classifier. However, concatenating different feature views may not always yield better classification performance. This paper proposes a combination of kernels using the genetic algorithm based weight optimization process for sleep stage classification instead of concatenation. Unlike the previous works, our novelty is combining different feature views in a new structure with optimized kernel weights which are obtained from the genetic algorithm. In the proposed model SVM classifiers are trained by distinct feature views namely wavelet decomposition(DWT), autoregressive model based and frequency based energy features. Weighted linear combination of the single kernels is used to construct a new kernel and the performance of the model is compared with traditional kernel function. Experiments are carried out on 10 different patients. The average accuracy of the experiments is considered as final accuracy. The results show that the proposed architecture increases the performance up to approximately 86 % on average. The proposed structure fits better for multi-source data, unlike traditional single kernel methods.

This paper is devoted to a family of interpolation type problems for positive trigonometric polynomials of a given ordern. Via the Riesz-Fejer factorization theorem, they can be viewed as natural generalizations of the partial autocorrelation problem for discrete time signals of lengthn+1. The relevant variables for a specific problem are well-defined linear combinations of the coefficients of the underlying trigonometric polynomial. An efficient method is obtained to characterize the feasibility region of the problem, defined as the set of points having these variables as coordinates. It allows us to determine the boundary of that region by computing the extreme eigen values and the corresponding eigenvectors of certain well-defined Hermitian Toeplitz matrices of ordern+1. The method is an extension of one proposed by Steinhardt to solve the coefficient problem for positive cosine polynomials (which belongs to the family). Other interesting applications are the Nevanlinna-Pick interpolation problem for polynomial functions, and the simple interpolation problem for positive trigonometric polynomials. The close connection between the generalized Steinhardt method and classical techniques based on the polarity theorem for convex cones and on the Hahn-Banach extension theorem are established.

We study when the spaces of Lorentz multipliers from Lp,t → Lp,s are distinct. Our main interest is the case when s < t, the Lorentz-improving multipliers. We prove, for example, that the space of multipliers which map Lp,t → Lp,s is different from those mapping Lp,t → Lp,s if either r = p or p′ and 1/s − 1/t ≠ 1/u − 1/v, or r ≠ p or p′. These results are obtained by making careful estimates of the Lorentz multiplier norms of certain linear combinations of Fejer or Dirichlet kernels. For the case when the first indices are different the linear combination we analyze is in the spirit of a Rudin-Shapiro polynomial.

Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel c...

Feature selection and lung nodule recognition are the core modules of the lung computer-aided detection (Lung CAD) system. To improve the performance of the Lung CAD system, algorithmic research is carried out for the above two parts, respectively. First, in view of the poor interpretability of deep features and the incomplete expression of clinically defined handcrafted features, a feature cascade method is proposed to obtain richer feature information of nodules as the final input of the classifier. Second, to better map the global characteristics of samples, the multiple kernel learning support vector machine (MKL-SVM) algorithm with a linear convex combination of polynomial kernel and sigmoid kernel is proposed. Furthermore, this paper applied the methods for speed contraction factor and roulette strategy, and a mixture of simulated annealing (SA) and particle swarm optimization (PSO) is used for global optimization, so as to solve the problem that the PSO is easy to lose particle diversity and fall into the local optimal solution as well as improve the model's training speed. Therefore, the MKL-SVM algorithm is presented in this paper, which is based on swarm intelligence optimization is proposed for lung nodule recognition. Finally, the algorithm construction experiments are conducted on the cooperative hospital dataset and compared with 8 advanced algorithms on the public dataset LUNA16. The experimental results show that the proposed algorithms can improve the accuracy of lung nodule recognition and reduce the missed detection of nodules.

Support vector machine (SVM) database search strategies are presented that aim at the identification of small molecule ligands for targets for which no ligand information is currently available. In pharmaceutical research and chemical biology, this situation is faced, for example, when studying orphan targets or newly identified members of protein families. To investigate methods for de novo ligand identification in the absence of known three-dimensional target structures or active molecules, we have focused on combining sequence and ligand information for closely and distantly related proteins. To provide a basis for these investigations, a set of 11 protease targets from different families was assembled together with more than 2000 inhibitors directed against individual proteases. We have compared SVM approaches that combine protein sequence and ligand information in different ways and utilize 2D fingerprints as ligand descriptors. These methodologies were applied to search for inhibitors of individual proteases not taken into account during learning. A target sequence-ligand kernel and, in particular, a linear combination of multiple target-directed SVMs consistently identified inhibitors with high accuracy including test cases where homology-based similarity searching using data fusion and conventional SVM ranking nearly or completely failed. The SVM linear combination and target-ligand kernel methods described herein are intuitive and straightforward to adopt for ligand prediction against other targets.

Multiple kernel learning is a paradigm which employs a properly constructed chain of kernel functions able to simultaneously analyse different data or different representations of the same data. In this paper, we propose an hybrid classification system based on a linear combination of multiple kernels defined over multiple dissimilarity spaces. The core of the training procedure is the joint optimisation of kernel weights and representatives selection in the dissimilarity spaces. This equips the system with a two-fold knowledge discovery phase: by analysing the weights, it is possible to check which representations are more suitable for solving the classification problem, whereas the pivotal patterns selected as representatives can give further insights on the modelled system, possibly with the help of field-experts. The proposed classification system is tested on real proteomic data in order to predict proteins’ functional role starting from their folded structure: specifically, a set of eight representations are drawn from the graph-based protein folded description. The proposed multiple kernel-based system has also been benchmarked against a clustering-based classification system also able to exploit multiple dissimilarities simultaneously. Computational results show remarkable classification capabilities and the knowledge discovery analysis is in line with current biological knowledge, suggesting the reliability of the proposed system.

Abstract. In this paper we explore semantic segmentation of man-made scenes using fully connected conditional random field (CRF). Images of man-made scenes display strong contextual dependencies in the spatial structures. Fully connected CRFs can model long-range connections within the image of man-made scenes and make use of contextual information of scene structures. The pairwise edge potentials of fully connected CRF models are defined by a linear combination of Gaussian kernels. Using filter-based mean field algorithm, the inference is very efficient. Our experimental results demonstrate that fully connected CRF performs better than previous state-of-the-art approaches on both eTRIMS dataset and LabelMeFacade dataset.

Traditional grasping analysis of mechanical dexterous grippers tends to flatten a multi-finger tactile series into one dimension, which ignores the force coupling between fingers and their different grasping force characteristics. To overcome this problem, this work proposes a novel Adaptive Multi-kernel Dictionary Learning (AMDL) method. First, in order to capture the nonlinear feature similarity of different tactile samples, multiple basic kernel functions are used to map all the training samples into Hilbert space, and the corresponding kernel matrix of each basic kernel is computed respectively. Then, an adaptive kernel weight calculation method is developed to learn the adaptive kernel of each basic kernel. A composite kernel, which is the linear combination of multiple basic kernels by using the learned adaptive weights, is constructed to calculate the multi-dimensional kernel matrix. Finally, this work utilizes the proposed AMDL to fuse grasping tactile information of multiple fingers to further consider the force coupling among them, during which the sparse pattern of the coding vector of each finger’s tactile data is restricted to be consistent. The proposed algorithm is compared with other state-of-the-art algorithms in terms of F1 score on the public BioTac SP tactile dataset and our collected tactile dataset. Its grasping state recognition result shows its validity and feasibility.

In this paper, we investigate the problem of optimizing complex multivariate performance measures to learn classifiers for pattern classification problems. For the first time, the multi-kernel learning is considered to construct a classifier to optimize a given nonlinear and non-smooth multivariate classifier performance measure. We estimate and optimize the upper bound of the given multivariate performance measure, instead of optimizing it directly. Moreover, to solve the problem of kernel function selection and kernel parameter tuning, we proposed to construct an optimal kernel by weighted linear combination of some candidate kernels. The learning of the classifier parameter and the kernel weight are unified in a single objective function considering minimizing the upper bound of the given multivariate performance measure. The objective function is optimized with regard to classifier parameter and kernel weight alternately in an iterative algorithm. The developed algorithm is evaluated on two different pattern classification methods with regard to various multivariate performance measure optimization problems. The experiment results show the proposed algorithm outperforms the competing methods.

The paper presents a novel framework for learning the hash functions for indexing through Multiple Kernel Learning. The Distance Based Hashing function is applied which does the object projection to hash space by preserving inter object distances. In recent works, the kernel matrix has been proved to be more accurate representation of similarity in various recognition problems. Our framework learns the optimal kernel for hashing by parametrized linear combination of base kernels. A novel application of Genetic Algorithm for the optimization of kernel combination parameters is presented. We also define new texture based feature representation for images. Our proposed framework can also be applied for optimal combination of multiple sources for indexing. The evaluation of the proposed framework is presented for CIFAR-10 dataset by applying individual and combination of different features. Additionally, the primary experimental results with MNIST dataset is also presented.

Automatic action recognition in videos is a challenging computer vision task that has become an active research area in recent years. Existing strategies usually use kernel-based learning algorithms that considers a simple combination of different features completely disregarding how such features should be integrated to fit the given problem. Since a given feature is most suitable to describe a given image/video property, the adaptive weighting of such features can improve the performance of the learning algorithm. In this paper, we investigated the use of the Multiple Kernel Learning (MKL) algorithm to adaptive search for the best linear relation among the considered features. MKL is an extension of the support vector machines (SVMs) to work with a weighted linear combination of several single kernels. This approach allows to simultaneously estimate the weights for the multiple kernels combination as well as the underlying SVM parameters. In order to prove the validity of the MKL approach, we considered a descriptor composed of multiple features aligned with dense trajectories. We experimented our approach on a database containing 36 cooking actions. Results confirm that the use of MKL improves the classification performance.

Fault diagnosis is very important for condition based maintenance. Recently, deep learning models are introduced to learn hierarchical representations from raw data instead of using hand-crafted features, which exhibit excellent performance. The success of current deep learning lies in: 1) the training (source domain) and testing (target domain) datasets are from the same feature distribution; 2) Enough labeled data with fault information exist. However, because the machine operates under a non-stationary working condition, the trained model built on the source domain can not be directly applied on the target domain. Moreover, since no sufficient labeled or even unlabeled data are available in target domain, collecting the labeled data and building the model from scratch is time-consuming and expensive. Motivated by transfer learning (TL), we present a new fault diagnosis method, which generalizes convolutional neural network (CNN) to TL scenario. Two layers with regard to task-specific features are adapted in a layer-wise way to regularize the parameters of CNN. What's more, the domain loss is calculated by a linear combination of multiple Gaussian kernels so that the ability of adaptation is enhanced compared to single kernel. Through these two means, the distribution discrepancy is reduced and the transferable features are learned. The proposed method is validated by transfer fault diagnosis experiments. Compared to CNN without domain adaptation and shallow transfer learning methods, the proposed method gets the best performance for fault classification.

Kernel methods have been successfully used in many practical machine learning problems. Choosing a suitable kernel is left to the practitioner. A common way to an automatic selection of optimal kernels is to learn a linear combination of element kernels. In this paper, a novel framework of multiple kernel learning is proposed based on conditional entropy minimization criterion. For the proposed framework, three multiple kernel learning algorithms are derived. The algorithms are experimentally shown to be comparable to or outperform kernel Fisher discriminant analysis and other multiple kernel learning algorithms on benchmark data sets.