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Over the last decades, learning methods using kernels have become very popular. The main reason is that real data analysis often requires nonlinear methods to detect the dependencies that allow successful predictions of properties of interest. Gaussian kernels have been used in many studies such as learning algorithms and data analysis. Most of these studies have shown that the parameter chosen for a Gaussian kernel could have a huge impact on the desired results. Therefore, it is essential to understand this impact on a theoretical level. The main contribution of this paper is to study the effect of the Gaussian kernel bandwidth parameter on how well an empirical operator defined from data approximates its continuous counterpart. Some results in spectral approximations are provided as well as some examples.

This paper generalizes the Attention in Attention (AiA) mechanism, in P. Fang et al., 2019 by employing explicit mapping in reproducing kernel Hilbert spaces to generate attention values of the input feature map. The AiA mechanism models the capacity of building inter-dependencies among the local and global features by the interaction of inner and outer attention modules. Besides a vanilla AiA module, termed linear attention with AiA, two non-linear counterparts, namely, second-order polynomial attention and Gaussian attention, are also proposed to utilize the non-linear properties of the input features explicitly, via the second-order polynomial kernel and Gaussian kernel approximation. The deep convolutional neural network, equipped with the proposed AiA blocks, is referred to as Attention in Attention Network (AiA-Net). The AiA-Net learns to extract a discriminative pedestrian representation, which combines complementary person appearance and corresponding part features. Extensive ablation studies verify the effectiveness of the AiA mechanism and the use of non-linear features hidden in the feature map for attention design. Furthermore, our approach outperforms current state-of-the-art by a considerable margin across a number of benchmarks. In addition, state-of-the-art performance is also achieved in the video person retrieval task with the assistance of the proposed AiA blocks. [ABSTRACT FROM AUTHOR]

A set of good test patterns is a key for accurate lithography modeling. We address three sub-problems in test pattern extraction: (1) Each pattern is associated with one or more gauges, where CD is measured and modeling is performed. We perform gauge clustering in feature space, while the goal is to minimize the number of chosen patterns. (2) Sample patterns do not usually guarantee enough coverage, so once coverage of chosen patterns is identified, some synthetic patterns are systematically generated to fill the empty region in feature space. (3) Pattern representation defines the feature space. We propose to use some Gaussian convolutions (or a few of their principal components) together with image parameter set (IPS) to reflect exposure for optical model and both PEB and development for resist model. Experiments with 1xnm DRAM design demonstrate that lithography modeling through our test pattern extraction and generation is performed with 35% smaller number of test patterns while CD error is reduced by 55%, with pattern extraction in feature space of IPS parameters as a reference. [ABSTRACT FROM AUTHOR]

Aiming at alleviate the detrimental effect of similar object interferences and target state changes in SiamRPN tracker, a Channel Positive and Negative Feedback Network (CPFN) is proposed, in which the Gaussian score map is generated by the feature channels selected by a Gaussian kernel, and the map is combined with the classification branches of SiamRPN. In this way, the feature channels are divided into positive feedback channels and interference channels, and these feature channels are effectively utilized. In addition, a channel weight update strategy is proposed to enhance the robustness of the tracker and avoid template pollution caused by inadequate template update. Extensive experiments on tracking benchmarks including VOT2016, VOT2018, VOT2019, OTB100, UAV123, LaSOT and GOT-10k show that the proposed CPFN outperforms the state-of-the-art methods based on small backbone network in terms of accuracy and achieves high-speed tracking.

Time series normalized difference vegetation index (NDVI) is the primary data for agricultural remote sensing monitoring. Due to the tradeoff between a single sensor's spatial and temporal resolutions and the impacts of cloud coverage, the time series NDVI data cannot serve well for precision agriculture. In this study, a Gaussian kernel-based spatiotemporal fusion model (GKSFM) was developed to fuse high-resolution NDVI (Landsat) and low-resolution NDVI (MODIS) to produce a daily NDVI product at a 30-m spatial resolution. Considering that the NDVI curve of crop in each growing season can be characterized by Gaussian function, GKSFM used the Gaussian kernel to fit the nonlinear relationship between the high-resolution NDVI and the low-resolution NDVI, to obtain a more reasonable temporal increment. The experimental results show that GKSFM outperformed the comparative models in different proportions of cropland/noncropland and different crop phenology. In addition, GKSFM was also applied for crop mapping of Mishan County by fusing the NDVI images during the crop growing season. This study demonstrates that the accuracy of the proposed method can be improved in the midseason of crops.

Music is a heavenly way of expressing feelings about the world. The language of music has vast diversity. For centuries, people have indulged in debates to stratisfy between Western and Indian Classical Music. But through this paper, an understanding can be fabricated while differentiating the types of Indian Classical Music. Classical music is one of the essential characteristics of Indian Cultural Heritage. Indian Classical Music is divided into two major parts, i.e. Hindustani and Carnatic. Models have been sculptured and trained to classify between Hindustani and Carnatic Music. In this paper, two approaches are used to implement classification models. MFCCs are used as features and implemented models like DNN (1 Layer, 2 Layers, 3 Layers), CNN (1 Layer, 2 Layers, 3 Layers), RNN-LSTM, SVM (Sigmoid, Polynomial & Gaussian Kernel) as one approach. A 3 channels input is created by merging features like MFCC, Spectrogram and Scalogram and implemented models like VGG-16, CNN (1 Layer, 2 Layers, 3 Layers), ResNet-50 as another approach. 3 Layered CNN and RNN-LSTM model performed best among all the approaches.

A set-valued information system (SVIS) with missing values is known as an incomplete set-valued information system (ISVIS). This article focuses on studying uncertainty measurement for an ISVIS and the optimal selection of subsystems by means of Gaussian kernel. First, the distance between two information values on each attribute in an ISVIS is put forward. Second, the fuzzy $T_{cos}$ -equivalence relation induced by a given subsystem is proposed based on Gaussian kernel. Next, some tools are used to measure the uncertainty of an ISVIS. Moreover, effectiveness analysis is done from a statistical point of view. In the end, the optimal selection of subsystems based on $\delta $ -information granulation and $\delta $ -information amount is given. These results will help us comprehend nature of uncertainty in an ISVIS.

China's soybean supply and demand are seriously imbalanced. It is crucial to improve the level of soybean breeding. Hundred-grain weight is one of the most essential phenotypic parameters for crop breeding. Accurate soybean seed counting is a key step for 100-grain weight. There are several seed counting methods, which have their own limitations one way or the other. Among these, manual counting is time-consuming, electronic automatic seed counter devices are expensive and their counting speed is very slow, and the traditional digital image processing techniques are not suitable for seed counting based on individual pod images. This paper attempted to develop a method that would combine the density estimation-based methods and the convolution neural network (CNN)-based methods to accurately estimate the seed count from an individual soybean pod image with a single perspective. In this paper, we first introduced a new large-scale seed counting dataset, named Soybean-pod. The dataset contains 500 annotated pod images with a total of 32 126 seeds and is the largest annotated dataset for soybean seed counting so far. Simultaneously, we used annotation information to generate a ground-truth density map by convolving a Gaussian kernel and, then, devised a simple but effective method that would elucidate pod images to a seed density map using a two-column CNN (TCNN) and thus accomplish seed counting ultimately. We conducted relevant experiments from three aspects on the new dataset to verify the effectiveness of our model and method, which provided 13.21 mean absolute error (MAE) and 17.62 mean squared error (mse). In addition, our research results showed that deep learning techniques can be easily adapted to precision tasks for plant phenotyping and breeding purposes.

Aspect-level sentiment classification (ASC) is a research hotspot in natural language processing, which aims to infer the sentiment polarity of a particular aspect in an opinion sentence. There are three main influence factors in the aspect-level sentiment classification: the semantic information of the context; the interaction information of the context and aspect; the position information between the aspect and the context. Some researchers have proposed way to solve aspect-level sentiment classification. However, previous work mainly used the average vector of the aspect to calculate the attention score of the context, which introduced the influence of noise words. Moreover, these attention-based approaches simply used relative positions to calculate positional information for contextual and aspect terms and did not provided better semantic information. Based on these above questions, in this paper, we propose the PSRTN model. Firstly, obtaining the position-aware influence propagate between words and aspects by Gaussian kernel and generating the influence vector for each context word. Secondly, capturing global and local information of the context by the R-Transformer, and using the self-attention mechanism to obtain the keywords in the aspect. Finally, context representation of a particular aspect is generated for classification. In order to evaluate the validity of the model, we conduct experiments on SemEval2014 and Twitter. The results show that the accuracy of the PSRTN model can reach 83.8%, 80.9%, and 75.1% on three data sets, respectively.

Out-of-focus blur is a common image degradation phenomenon that occurs in case of lens defocusing. The out-of-focus blur kernel is usually modeled as a Gaussian function or a uniform disk in previous work. In this paper, we propose that it can be more accurately depicted using the generalized Gaussian (GG) function. This is motivated by the theoretical analysis of the out-of-focus blur and the practical observation of real blur kernels. We show that as the out-of-focus blur kernels are of specific shapes, the GG function can be further simplified to a single-parameter model. We estimate the parameter of the GG blur kernel from image patches containing step edges, and obtain the clear image by non-blind image deblurring. Experimental results validate that the proposed GG blur kernel estimation algorithm outperforms the state-of-the-art ones deploying either parametric (disk and Gaussian) or nonparametric kernels, and consequently benefits the image deblurring process. [ABSTRACT FROM AUTHOR]

In recent years, many human diseases have been determined to be associated with certain lncRNAs. Only a small percentage of all lncRNA-disease associations (LDAs) have been discovered by researchers. Predicting novel LDAs is time-consuming and costly. It is crucial to propose a method that can effectively identify potential LDAs to solve this problem based on the available datasets. Although some current methods can effectively predict potential LDAs, the prediction accuracy needs to be improved, and there are few known associations. Moreover, there are notable errors in the method of constructing the network and the bipartite graph, which interfere with the final results. A weighted graph regularized collaborative matrix factorization (WGRCMF) method is proposed to predict novel LDAs. We introduce the graph regularization terms into the collaborative matrix factorization. Considering that manifold learning can recover low-dimensional manifold structures from high-dimensional sampled data, we can find low-dimensional manifolds in high-dimensional space. In addition, a weight matrix is also introduced into the method, the significance of which is to prevent unknown associations from contributing to the final prediction matrix. Finally, the prediction accuracy of this method is better than those of other methods. In several cancer cases, we implemented the corresponding simulation experiments. According to the experimental results, the proposed method is feasible and effective. [ABSTRACT FROM AUTHOR]

This paper studies convergence of empirical measures smoothed by a Gaussian kernel. Specifically, consider approximating $P\ast \mathcal {N}_\sigma $ , for $\mathcal {N}_\sigma \triangleq \mathcal {N}(0,\sigma ^{2} \mathrm {I}_{d})$ , by $\hat {P}_{n}\ast \mathcal {N}_\sigma $ under different statistical distances, where $\hat {P}_{n}$ is the empirical measure. We examine the convergence in terms of the Wasserstein distance, total variation (TV), Kullback-Leibler (KL) divergence, and $\chi ^{2}$ -divergence. We show that the approximation error under the TV distance and 1-Wasserstein distance ($\mathsf {W}_{1}$) converges at the rate $e^{O(d)} n^{-1/2}$ in remarkable contrast to a (typical) $n^{-\frac {1}{d}}$ rate for unsmoothed $\mathsf {W}_{1}$ (and $d\ge 3$). Similarly, for the KL divergence, squared 2-Wasserstein distance ($\mathsf {W}_{2}^{2}$), and $\chi ^{2}$ -divergence, the convergence rate is $e^{O(d)} n^{-1}$ , but only if $P$ achieves finite input-output $\chi ^{2}$ mutual information across the additive white Gaussian noise (AWGN) channel. If the latter condition is not met, the rate changes to $\omega \left ({n^{-1}}\right)$ for the KL divergence and $\mathsf {W}_{2}^{2}$ , while the $\chi ^{2}$ -divergence becomes infinite – a curious dichotomy. As an application we consider estimating the differential entropy $h(S+Z)$ , where $S\sim P$ and $Z\sim \mathcal {N}_\sigma $ are independent $d$ -dimensional random variables. The distribution $P$ is unknown and belongs to some nonparametric class, but n independently and identically distributed (i.i.d) samples from it are available. Despite the regularizing effect of noise, we first show that any good estimator (within an additive gap) for this problem must have a sample complexity that is exponential in d. We then leverage the above empirical approximation results to show that the absolute-error risk of the plug-in estimator converges as $e^{O(d)} n^{-1/2}$ , thus attaining the parametric rate in n. This establishes the plug-in estimator as minimax rate-optimal for the considered problem, with sharp dependence of the convergence rate both in n and d. We provide numerical results comparing the performance of the plug-in estimator to that of general-purpose (unstructured) differential entropy estimators (based on kernel density estimation (KDE) or k nearest neighbors (kNN) techniques) applied to samples of $S+Z$. These results reveal a significant empirical superiority of the plug-in to state-of-the-art KDE and kNN methods. As a motivating utilization of the plug-in approach, we estimate information flows in deep neural networks and discuss Tishby’s Information Bottleneck and the compression conjecture, among others. [ABSTRACT FROM AUTHOR]

There is much evidence that long non-coding RNA (lncRNA) is associated with many diseases. However, it is time-consuming and expensive to identify meaningful lncRNA-disease associations (LDAs) through medical or biological experiments. Therefore, investigating how to identify more meaningful LDAs is necessary, and at the same time it is conducive to the prevention, diagnosis and treatment of complex diseases. Considering the limitations of some current prediction models, a novel model based on bipartite local model with nearest profile-based association inferring, BLM-NPAI, is developed for predicting LDAs. This model predicts novel LDAs from the lncRNA side and the disease side, respectively. More importantly, for some lncRNAs and diseases without any association, the model can also be predicted by their nearest neighbors. Leave-one-out cross validation (LOOCV) and 5-fold cross validation are implemented for BLM-NPAI to evaluate the performance of this model. Our model is superior to current advanced methods in most cases. In addition, to verify the validity and reliability of BLM-NPAI, three disease cases and three lncRNA cases are analyzed to further evaluate BLM-NPAI. Finally, these predicted novel LDAs are confirmed by using the LncRNA-disease database. [ABSTRACT FROM AUTHOR]

We propose a novel framework for performing inhomogeneous template adaptation on temporal three-dimensional data. Templates of interest are first globally translated, scaled and rotated using statistical methods in the form of Procrustes analysis. In this globally adapted form, the data is parameterized to a minimum bounding rectangular prism using a parameterization method known as free-form deformation. The parameterized model is then reduced to a linear least squares problem, which subsequently allows for a robust local template adaptation scheme utilizing a non-parametric formulation. To account for complex noise behaviour encountered in quasi-periodic signals, we ensue to complete the framework with an adaptive noise model. We demonstrate the power of the proposed framework using three applications: firstly, we quantify the ability of the proposed framework to track geometric features of heart disease on a synthetic dataset containing three-dimensional electrocardiogram signals. Next we track these features on a publicly available real dataset (PTB database) to demonstrate its potential in heart disease diagnostics. Lastly, we apply the proposed framework to map three-dimensional velocity profiles using the publicly available Complex Upper-Limb Movements database. [ABSTRACT FROM AUTHOR]

The recent advances of compressive sensing (CS) have witnessed a great potential of efficient compressive data gathering (CDG) in wireless sensor network systems (WSNSs). However, most existing work on CDG mainly focuses on multihop relaying strategies to improve the performance of data gathering. In this paper, we propose a mobile CDG scheme including a random walk-based algorithm and a kernel-based method for sparsifying sensory data from irregular deployments. The proposed scheme allows a mobile collector to harvest data by sequentially visiting a number of nodes along a random path. More importantly, toward building the gap between CS and machine learning theories, we explore a theoretical foundation for understanding the feasibility of the proposed scheme. We prove that the CS matrices, constructed from the proposed random walk algorithm combined with a kernel-based sparsity basis, satisfy the restricted isometry property. Particularly, we also show that ${m=O}({k\log } ({n/k}))$ measurements collected by a mobile collector are sufficient to recover a ${k}$ -sparse signal and ${t=O(k\log (n/k))}$ steps are required to collect these measurements in a network with ${n}$ nodes. Finally, we also present extensive numerical results to validate the effectiveness of the proposed scheme by evaluating the performance in terms of energy consumption and the impact of packet losses. The numerical results demonstrate that the proposed scheme is able to not only significantly reduce communication cost but also combat unreliable wireless links under various packet losses compared to the state-of-the-art schemes, which provides an efficient alternative to data relaying approaches for CDG in WSNS. [ABSTRACT FROM AUTHOR]

Binary descriptors are drawing increasing interest as they enable faster processing in a lower memory footprint, which are suitable to large-scale and real-time vision applications. However, the performance of most existing binary descriptors tends to be inferior to those of the competing floating-point descriptors. In this paper, by considering each bit might contribute differently to the robustness and distinctiveness, a novel binary descriptor based on binary weights learning is proposed, referred to as a robust weighted binary descriptor (RWBD). Technically, each bit of RWBD is built upon difference tests of pairwise complementary information sampling with varying Gaussian kernels, leading to a more informative and robust description. Furthermore, RWBD imposes different emphases on all bits utilizing the learned binary weights, which can significantly improve the discriminative power and preserve the fast matching advantage. Extensive experiments on the publicly challenging benchmarks, including image matching and object recognition data sets, clearly demonstrate the effectiveness and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

One-class classification (OCC) builds models using only the samples from one class (the target class) so as to predict whether a new-coming sample belongs to the target class or not. OCC widely exists in many application fields, such as fault detection. As an effective tool for OCC, one-class SVM (OCSVM) with the Gaussian kernel has received much attention recently. However, its kernel parameter selection greatly affects its performance and is still an open problem. This paper proposes a novel method to solve this problem. First, an effective way is presented to measure the distances from the samples to the OCSVM enclosing surfaces. Then based on this measurement, an optimization objective function for the parameter selection is put forward. Extensive experiments are conducted on various data sets, and the results verify the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

Object extraction from remote sensing images has long been an intensive research topic in the field of surveying and mapping. Most past methods are devoted to handling just one type of object, and little attention has been paid to improving the computational efficiency. In recent years, level set evolution (LSE) has been shown to be very promising for object extraction in the field of image processing because it can handle topological changes automatically while achieving high accuracy. However, the application of state-of-the-art LSEs is compromised by laborious parameter tuning and expensive computation. In this paper, we proposed two fast LSEs for man-made object extraction from high spatial resolution remote sensing images. We replaced the traditional mean curvature-based regularization term by a Gaussian kernel, and it is mathematically sound to do that. Thus, we can use a larger time step in the numerical scheme to expedite the proposed LSEs. Compared with existing methods, the proposed LSEs are significantly faster. Most importantly, they involve much fewer parameters while achieving better performance. Their advantages over other state-of-the-art approaches have been verified by a range of experiments. [ABSTRACT FROM PUBLISHER]

Movement related potentials (MRPs) are used as features in many brain-computer interfaces (BCIs) based on electroencephalogram (EEG). MRP feature extraction is challenging since EEG is noisy and varies between subjects. Previous studies used spatial and spatio-temporal filtering methods to deal with these problems. However, they did not optimize temporal information or may have been susceptible to overfitting when training data are limited and the feature space is of high dimension. Furthermore, most of these studies manually select data windows and low-pass frequencies. We propose an adaptive spatio-temporal (AST) filtering method to model MRPs more accurately in lower dimensional space. AST automatically optimizes all parameters by employing a Gaussian kernel to construct a low-pass time-frequency filter and a linear ridge regression (LRR) algorithm to compute a spatial filter. Optimal parameters are simultaneously sought by minimizing leave-one-out cross-validation error through gradient descent. Using four BCI datasets from 12 individuals, we compare the performances of AST filter to two popular methods: the discriminant spatial pattern filter and regularized spatio-temporal filter. The results demonstrate that our AST filter can make more accurate predictions and is computationally feasible. [ABSTRACT FROM AUTHOR]

Density maps are one of the most common and powerful lightning data applications, and they are more efficient the more detailed they are. When working with CG lightning data from lightning location systems, some aspects must be included in the analysis to overcome network performance variations. Two parameters are typically used to evaluate system performance: detection efficiency (DE) and location accuracy (LA).For the Brazilian National Integrated Lightning Detection Network, DE is typically evaluated by models, and LA is analyzed through confidence ellipses. This paper presents climatological analysis of lightning activity, including the most recent relative DE model developed in Brazil, as well as an adapted kernel smoothing method based on confidence ellipses [called Gaussian kernel based on confidence ellipses (GKBCE)] as approaches to minimize and/or include the spatial variation of the system's performance in the analysis. The maps are produced over the central-south portion of Brazil (mainly along ITAIPU power transmission lines), using 11 years of data available from the network (from January 1999 to December 2009). The model increased density by ~20% over the entire region, without making considerable changes to the spatial pattern. The GKBCE seems to work well in smoothing, obtaining better results than the standard cell count (quadrat) method, by working independently of the grid size (allowing the creation of high-resolution maps), and by including location errors in the analysis. The use of these procedures might result in more detailed maps and more suitable results when analyzing lightning data. [ABSTRACT FROM PUBLISHER]

A direct implementation of the bilateral filter requires O(\sigmas^{2}) operations per pixel, where \sigmas is the (effective) width of the spatial kernel. A fast implementation of the bilateral filter that required O(1) operations per pixel with respect to \sigmas was recently proposed. This was done by using trigonometric functions for the range kernel of the bilateral filter, and by exploiting their so-called shiftability property. In particular, a fast implementation of the Gaussian bilateral filter was realized by approximating the Gaussian range kernel using raised cosines. Later, it was demonstrated that this idea could be extended to a larger class of filters, including the popular non-local means filter. As already observed, a flip side of this approach was that the run time depended on the width \sigmar of the range kernel. For an image with dynamic range [0,T], the run time scaled as O(T^2/\sigma^2r) with \sigmar. This made it difficult to implement narrow range kernels, particularly for images with large dynamic range. In this paper, we discuss this problem, and propose some simple steps to accelerate the implementation, in general, and for small \sigmar in particular. We provide some experimental results to demonstrate the acceleration that is achieved using these modifications. [ABSTRACT FROM PUBLISHER]

Recently, anomaly detection (AD) has attracted considerable interest in a wide variety of hyperspectral remote sensing applications. The goal of this unsupervised technique of target detection is to identify the pixels with significantly different spectral signatures from the neighboring background. Kernel methods, such as kernel-based support vector data description (SVDD) (K-SVDD), have been presented as the successful approach to AD problems. The most commonly used kernel is the Gaussian kernel function. The main problem using the Gaussian kernel-based AD methods is the optimal setting of sigma. In an attempt to address this problem, this paper proposes a direct and adaptive measure for Gaussian K-SVDD (GK-SVDD). The proposed measure is based on a geometric interpretation of the GK-SVDD. Experimental results are presented on real and synthetically implanted targets of the target detection blind-test data sets. Compared to previous measures, the results demonstrate better performance, particularly for subpixel anomalies. [ABSTRACT FROM PUBLISHER]

Feature selection for classification in high-dimensional spaces can improve generalization, reduce classifier complexity, and identify important, discriminating feature "markers." For support vector machine (SVM) classification, a widely used technique is recursive feature elimination (RFE).We demonstrate that RFE is not consistent with margin maximization, central to the SVM learning approach. We thus propose explicit margin-based feature elimination (MFE) for SVMs and demonstrate both improved margin and improved generalization, compared with RFE. Moreover, for the case of a nonlinear kernel, we show that RFE assumes that the squared weight vector 2-norm is strictly decreasing as features are eliminated. We demonstrate this is not true for the Gaussian kernel and, consequently, RFE may give poor results in this case. MFE for nonlinear kernels gives better margin and generalization. We also present an extension which achieves further margin gains, by optimizing only two degrees of freedom--the hyperplane's intercept and its squared 2-norm--with the weight vector orientation fixed. We finally introduce an extension that allows margin slackness. We compare against several alternatives, including RFE and a linear programming method that embeds feature selection within the classifier design. On high-dimensional gene microarray data sets, University of California at Irvine (UCI) repository data sets, and Alzheimer's disease brain image data, MFE methods give promising results. [ABSTRACT FROM AUTHOR]