基于局部空间变稀疏约束的多核学习方法

局部多核学习方法根据样本所在局部空间特性选择特定的核函数组合方式,具有较好的判别能力.本文提出了一种基于局部空间变稀疏约束的多核学习方法,首先依据样本在特征空间的分布情况以软分组的方式将训练数据划分为若干数据子集.以数据子集为单位,根据在相应的局部空间内的核函数相似程度,调整核组合的稀疏程度,使用交替优化的方法进行求解.实验表明本文方法对于区分特征学习和对抗噪声方面具有的优势,因此也使得在图像场景分类问题上的准确率和稳定性得到明显提高.     

IQM2: new image quality measure based on steerable pyramid wavelet transform and structural similarity index

In this paper, we present a new full-reference objective image quality measure—IQM2, based on structural similarity index and steerable pyramid wavelet transform. IQM2 is tested using different number of orientation kernels and seven subjective databases. Finally, IQM2 measure is compared with twelve commonly used full-reference objective measures. Results show that proposed IQM2 measure, using kernel with 2 orientations, provides good correlation with the results of subjective evaluation while keeping computational time lower than other similar performing objective measures.     

一种新的复合核函数及在问句检索中的应用

问句检索在问答系统中有着重要的作用,其核心问题在于研究查询问句与候选问句之间的相似性计算问题,实现问句之间的高精度匹配。该文采用树核函数的方法计算问句之间的结构相似性,并针对原有算法的不足,做了相应的改进。为降低句法解析器性能对树核函数的影响,该文在改进的树核函数基础上,将其与字符串核结合,提出了一种能同时融合问句的句法信息,词性信息和词序信息的复合核函数,用以计算问句之间的综合语义相似性。在社区问答系统Yahoo!Answer的数据上进行测试,相对传统的基于词频的特征向量法,问句检索平均准确率提高了24.02%。     

一族新的布尔核函数及其应用

核机器（Kernel Machine）已成为机器学习领域的热点研究问题。针对只具有离散属性的分类问题，在对合取范式进行深入分析的基础上提出了一族新的布尔核函数。利用这些布尔核函数，可以在布尔逻辑学习、决策树，决策规则学习以及基于项集的学习中，引入核机器技术。实验结果指出，使用结构简单而符合训练数据集特征的布尔核函数，有助于显著提高分类器的性能。     

Minimum class variance support vector machines.

In this paper, a modified class of support vector machines (SVMs) inspired from the optimization of Fisher's discriminant ratio is presented, the so-called minimum class variance SVMs (MCVSVMs). The MCVSVMs optimization problem is solved in cases in which the training set contains less samples that the dimensionality of the training vectors using dimensionality reduction through principal component analysis (PCA). Afterward, the MCVSVMs are extended in order to find nonlinear decision surfaces by solving the optimization problem in arbitrary Hilbert spaces defined by Mercer's kernels. In that case, it is shown that, under kernel PCA, the nonlinear optimization problem is transformed into an equivalent linear MCVSVMs problem. The effectiveness of the proposed approach is demonstrated by comparing it with the standard SVMs and other classifiers, like kernel Fisher discriminant analysis in facial image characterization problems like gender determination, eyeglass, and neutral facial expression detection.     

基于图像核函数的图像目标识别技术研究

核方法已经广泛应用于模式识别的各个领域,但是传统的核函数仅能接受一维矢量作为输入数据,对二维图像数据需要进行一定的预处理.本文从核函数构造的角度出发,以RBF核函数为结构原型,定义了一种输入量为图像数据的新型核函数.从形式上看,本核函数仅在输人数据的类型上有所不同,其他方面完全一致,经典的基于核方法的分类器算法都可以使用本核函数.对UCI数据实验结果表明,本核函数在多种图像识别应用中均有良好的效果.     

用于文本相似度计算的新核函数

为了提高文本相似检测的综合表现,在文本文档相似特征的基础上构造了新的核函数S_Wang核函数。结合文本相似计算过程中的实际情况,将待比对的文本表示成向量,考虑通过2个向量间的乘积和欧氏距离来描述向量之间的相似程度,从而构造了适合文本相似度计算的新核函数。并根据Mercer定理证明了所构造函数可以作为核函数。实验验证了新构造的核函数在文本文档相似度计算中的表现,实验结果表明S_Wang核其相似度计算精度和综合指标均分别优于Cauchy核,潜在语义核（LSK）以及CLA复合核。S_Wang核适用于文本相似度计算。     

Robust penalty-weighted deblurring via kernel adaption using single image

Image blind deconvolution is well known as a challenging, ill-posed problem due to the uncertainty of the blur kernel and the noise condition. Based on our observations, blind deconvolution algorithms tend to generate disconnected and noisy blur kernels, which would yield a serious ringing effect in the restored image if the input image is noisy. Therefore, there is still room for further improvement, especially for noisy images captured under poor illumination conditions. In this paper, we propose a robust blind deconvolution algorithm by adopting a penalty-weighted anisotropic diffusion prior. On one hand, the anisotropic diffusion prior effectively eliminates the discontinuity in the blur kernel caused by the noisy input image during the process of kernel estimation. On the other hand, the weighted penalizer reduces the speckle noise of the blur kernel, thus improving the quality of the restored image. The effectiveness of the proposed algorithm is verified by both synthetic and real images with defocused or motion blur.     

原空间中的核SOM分类器

自组织特征映射(SOM)是Kohonen提出的一种人工神经网络模型,其整个学习过程是在输入样本空间内进行,并以欧氏距离为度量.这将导致当输入样本分布结构呈高度非线性时,其分类能力下降.核方法通过核函数实现了一个从低维输入空间到高维特征空间的映射,从而使输入空间中复杂的样本结构在特征空间中变得简单.Donald等人通过核映射将低维输入空间中的非线性问题变换至高维特征空间中,从而使SOM聚类形成于映射后的高维特征空间中.但其缺点是失去了对原输入空间聚类中心及结果的直观刻画;本文采用核方法的目的是为原输入空间诱导出一类异于欧氏距离的新的距离度量,并使原SOM成为特例.而核的多样性进一步可诱导出原空间中不同的度量,导致各种对应SOM分类器的生成.最后,本文侧重通过几种经典的核函数在Benchmark上的试验,对该分类器的性能及可靠性进行了验证.     

Learning adaptive interpolation kernels for fast single-image super resolution

This paper presents a fast single-image super-resolution approach that involves learning multiple adaptive interpolation kernels. Based on the assumptions that each high-resolution image patch can be sparsely represented by several simple image structures and that each structure can be assigned a suitable interpolation kernel, our approach consists of the following steps. First, we cluster the training image patches into several classes and train each class-specific interpolation kernel. Then, for each input low-resolution image patch, we select few suitable kernels of it to make up the final interpolation kernel. Since the proposed approach is mainly based on simple linear algebra computations, its efficiency can be guaranteed. And experimental comparisons with state-of-the-art super-resolution reconstruction algorithms on simulated and real-life examples can validate the performance of our proposed approach.     

Nonuniform Interpolation of Noisy Signals Using Support Vector Machines

The problem of signal interpolation has been intensively studied in the information theory literature, in conditions such as unlimited band, nonuniform sampling, and presence of noise. During the last decade, support vector machines (SVM) have been widely used for approximation problems, including function and signal interpolation. However, the signal structure has not always been taken into account in SVM interpolation. We propose the statement of two novel SVM algorithms for signal interpolation, specifically, the primal and the dual signal model based algorithms. Shift-invariant Mercer's kernels are used as building blocks, according to the requirement of bandlimited signal. The sine kernel, which has received little attention in the SVM literature, is used for bandlimited reconstruction. Well-known properties of general SVM algorithms (sparseness of the solution, robustness, and regularization) are explored with simulation examples, yielding improved results with respect to standard algorithms, and revealing good characteristics in nonuniform interpolation of noisy signals.     

基于核函数的非线性口袋算法

应用满足Mercer条件的核函数设计非线性算法已经成为机器学习领域一项新的非线性技术.核感知器算法利用核思想非线性地推广了线性感知器算法,使其可以处理原始输入空间中的非线性分类问题和高维特征空间中的线性问题.线性口袋算法改进了线性感知器算法,能够直接处理线性不可分问题.为了进一步改进线性口袋算法和核感知器算法,本文提出基于核函数的非线性口袋算法,即核口袋算法,其目标是找到一个使错分样本数最小的非线性判别函数,并证明了其收敛性.核口袋算法的特点是用简单的迭代过程和核函数来实现非线性分类器的设计.基准数据集的实验结果证明核口袋算法的性能优于线性口袋算法和核感知器算法.     

A Max‐Flow‐Based Similarity Measure for Spectral Clustering

In most spectral clustering approaches, the Gaussian kernel‐based similarity measure is used to construct the affinity matrix. However, such a similarity measure does not work well on a dataset with a nonlinear and elongated structure. In this paper, we present a new similarity measure to deal with the nonlinearity issue. The maximum flow between data points is computed as the new similarity, which can satisfy the requirement for similarity in the clustering method. Additionally, the new similarity carries the global and local relations between data. We apply it to spectral clustering and compare the proposed similarity measure with other state‐of‐the‐art methods on both synthetic and real‐world data. The experiment results show the superiority of the new similarity: 1) The max‐flow‐based similarity measure can significantly improve the performance of spectral clustering; 2) It is robust and not sensitive to the parameters.     

尺度核函数支撑矢量机

本文提出了一种可容许的支撑矢量机核—尺度核.该尺度核函数可以被看作是一个具有平移因子的多维尺度函数,它能作为平方可积空间的子空间上一组完备的基函数.在此意义上,采用尺度核函数的支撑矢量机,可以认为是在尺度空间中寻找最佳的尺度系数.因此在理论上尺度核函数支撑矢量机能够以零误差逼近某一空间上的任何目标函数,文中给出的仿真实验进一步验证了它的可行性和有效性.     

一种基于稀疏编码的多核学习图像分类方法

 本文提出一种基于稀疏编码的多核学习图像分类方法.传统稀疏编码方法对图像进行分类时,损失了空间信息,本文采用对图像进行空间金字塔多划分方式为特征加入空间信息限制.在利用非线性SVM方法进行图像分类时,空间金字塔的各层分别形成一个核矩阵,本文使用多核学习方法求解各个核矩阵的权重,通过核矩阵的线性组合来获取能够对整个分类集区分能力最强的核矩阵.实验结果表明了本文所提出图像分类方法的有效性和鲁棒性.对Scene Categories场景数据集可以达到83.10%的分类准确率,这是当前该数据集上能达到的最高分类准确率.     

基于矩阵模式的最小类内散度支持向量机

 基于最小类内散度支持向量机(MCSVMs)提出一种新的矩阵模式的最小类内散度支持向量机(MCSVMs^matrix).同时为了更好地解决非线性分类问题,将Mercer核函数引入到MCSVMs^matrix方法中,并提出基于矩阵模式的非线性支持向量机:Ker-MCSVMs^matrix.上述两种方法不但继承了MCSVMs的优点,而且由于将矩阵模式的类内散度矩阵引入到支持向量机中,从而在理论上可以较好地解决了MCSVMs方法在处理小样本高维数据集时类内散度矩阵奇异性问题,同时降低了求解类内散度矩阵及其逆矩阵和权重矢量的时间、空间复杂度.因此,在一定程度上提高了分类精度.实验结果也表明MCSVMs^matrix、Ker-MCSVMs matrix具有上述优势.     

Identification of cubic systems using higher order moments ofi.i.d. signals

A simple method for estimating the Volterra kernels of cubic systems with a zero-mean i.i.d. input is presented. This method significantly reduces the computational complexity of Volterra kernel estimation compared to the non-i.i.d. and non-Gaussian input case     

Topology-based kernels with application to inference problems in Alzheimer's disease

Alzheimer's disease (AD) research has recently witnessed a great deal of activity focused on developing new statistical learning tools for automated inference using imaging data. The workhorse for many of these techniques is the support vector machine (SVM) framework (or more generally kernel-based methods). Most of these require, as a first step, specification of a kernel matrix K between input examples (i.e., images). The inner product between images I(i) and I(j) in a feature space can generally be written in closed form and so it is convenient to treat K as "given." However, in certain neuroimaging applications such an assumption becomes problematic. As an example, it is rather challenging to provide a scalar measure of similarity between two instances of highly attributed data such as cortical thickness measures on cortical surfaces. Note that cortical thickness is known to be discriminative for neurological disorders, so leveraging such information in an inference framework, especially within a multi-modal method, is potentially advantageous. But despite being clinically meaningful, relatively few works have successfully exploited this measure for classification or regression. Motivated by these applications, our paper presents novel techniques to compute similarity matrices for such topologically-based attributed data. Our ideas leverage recent developments to characterize signals (e.g., cortical thickness) motivated by the persistence of their topological features, leading to a scheme for simple constructions of kernel matrices. As a proof of principle, on a dataset of 356 subjects from the Alzheimer's Disease Neuroimaging Initiative study, we report good performance on several statistical inference tasks without any feature selection, dimensionality reduction, or parameter tuning.     

Approximating large convolutions in digital images

Computing discrete two-dimensional (2-D) convolutions is an important problem in image processing. In mathematical morphology, an important variant is that of computing binary convolutions, where the kernel of the convolution is a 0-1 valued function. This operation can be quite costly, especially when large kernels are involved. We present an algorithm for computing convolutions of this form, where the kernel of the binary convolution is derived from a convex polygon. Because the kernel is a geometric object, we allow the algorithm some flexibility in how it elects to digitize the convex kernel at each placement, as long as the digitization satisfies certain reasonable requirements. We say that such a convolution is valid. Given this flexibility we show that it is possible to compute binary convolutions more efficiently than would normally be possible for large kernels. Our main result is an algorithm which, given an mxn image and a k-sided convex polygonal kernel K, computes a valid convolution in O(kmn) time. Unlike standard algorithms for computing correlations and convolutions, the running time is independent of the area or perimeter of K, and our techniques do not rely on computing fast Fourier transforms. Our algorithm is based on a novel use of Bresenham's (1965) line-drawing algorithm and prefix-sums to update the convolution incrementally as the kernel is moved from one position to another across the image.