Optimizing explicit feature maps on intervals

Approximating non-linear kernels by finite-dimensional feature maps is a popular approach for accelerating training and evaluation of support vector machines or to encode information into efficient match kernels. We propose a novel method of data independent construction of low-dimensional feature maps. The problem is formulated as a linear program that jointly considers two competing objectives: the quality of the approximation and the dimensionality of the feature map.For both shift-invariant and homogeneous kernels the proposed method achieves better approximation at the same dimensionality or comparable approximations at lower dimensionality of the feature map compared with state-of-the-art methods.     

On feature extraction via kernels.

Using the kernel trick idea and the kernels-as-features idea, we can construct two kinds of nonlinear feature spaces, where linear feature extraction algorithms can be employed to extract nonlinear features. In this correspondence, we study the relationship between the two kernel ideas applied to certain feature extraction algorithms such as linear discriminant analysis, principal component analysis, and canonical correlation analysis. We provide a rigorous theoretical analysis and show that they are equivalent up to different scalings on each feature. These results provide a better understanding of the kernel method.     

Efficient feature size reduction via predictive forward selection

Most of the widely used pattern classification algorithms, such as Support Vector Machines (SVM), are sensitive to the presence of irrelevant or redundant features in the training data. Automatic feature selection algorithms aim at selecting a subset of features present in a given dataset so that the achieved accuracy of the following classifier can be maximized. Feature selection algorithms are generally categorized into two broad categories: algorithms that do not take the following classifier into account (the filter approaches), and algorithms that evaluate the following classifier for each considered feature subset (the wrapper approaches). Filter approaches are typically faster, but wrapper approaches deliver a higher performance. In this paper, we present the algorithm – Predictive Forward Selection – based on the widely used wrapper approach forward selection. Using ideas from meta-learning, the number of required evaluations of the target classifier is reduced by using experience knowledge gained during past feature selection runs on other datasets. We have evaluated our approach on 59 real-world datasets with a focus on SVM as the target classifier. We present comparisons with state-of-the-art wrapper and filter approaches as well as one embedded method for SVM according to accuracy and run-time. The results show that the presented method reaches the accuracy of traditional wrapper approaches requiring significantly less evaluations of the target algorithm. Moreover, our method achieves statistically significant better results than the filter approaches as well as the embedded method.     

Point cloud completion via structured feature maps using a feedback network

Computational Visual Media - In this paper, we tackle the challenging problem of point cloud completion from the perspective of feature learning. Our key observation is that to recover the...     

Towards heart sound classification without segmentation via autocorrelation feature and diffusion maps

Heart sound classification, used for the automatic heart sound auscultation and cardiac monitoring, plays an important role in primary health center and home care. However, one of the most difficult problems for the task of heart sound classification is the heart sound segmentation, especially for classifying a wide range of heart sounds accompanied with murmurs and other artificial noise in the real world. In this study, we present a novel framework for heart sound classification without segmentation based on the autocorrelation feature and diffusion maps, which can provide a primary diagnosis in the primary health center and home care. In the proposed framework, the autocorrelation features are first extracted from the sub-band envelopes calculated from the sub-band coefficients of the heart signal with the discrete wavelet decomposition (DWT). Then, the autocorrelation features are fused to obtain the unified feature representation with diffusion maps. Finally, the unified feature is input into the Support Vector Machines (SVM) classifier to perform the task of heart sound classification. Moreover, the proposed framework is evaluated on two public datasets published in the PASCAL Classifying Heart Sounds Challenge. The experimental results show outstanding performance of the proposed method, compared with the baselines.     

特征加权的核学习方法

提出了一种特征加权的核学习方法,其主要为了解决当前核方法在分类任务中对所有数据特征的同等对待的不足。在分类任务中,数据样本的每个特征所起的作用并不是相同的,有些特征对分类任务有促进作用,应该给予更多的关注。提出的算法集成了多核学习的优势,以加权的方式组合不同的核函数,但所需的计算复杂度更低。实验结果证明,提出的算法与支持向量机、多核学习算法相比,分类准确度优于支持向量机和多核学习算法,在计算复杂度上略高于支持向量机,但远远低于多核学习算法。     

Weighted partition consensus via kernels

The combination of multiple clustering results (clustering ensemble) has emerged as an important procedure to improve the quality of clustering solutions. In this paper we propose a new cluster ensemble method based on kernel functions, which introduces the Partition Relevance Analysis step. This step has the goal of analyzing the set of partition in the cluster ensemble and extract valuable information that can improve the quality of the combination process. Besides, we propose a new similarity measure between partitions proving that it is a kernel function. A new consensus function is introduced using this similarity measure and based on the idea of finding the median partition. Related to this consensus function, some theoretical results that endorse the suitability of our methods are proven. Finally, we conduct a numerical experimentation to show the behavior of our method on several databases by making a comparison with simple clustering algorithms as well as to other cluster ensemble methods.     

On the additive decomposition for polynomic maps

A polynomic operator can be represented asT= Ltauwhere τ is an imbedding of the input Hilbert resolution space into the appropriate Hilbert scale, andLis a mapping of the Hilbert resolution space that results from closing the span of the Hilbert scale with respect to a naturally defined inner product, into the output Hilbert resolution space. This paper demonstrates the relationship between the strongly causal (strongly anticausal, memoryless) components ofLandT.     

An application-independent methodology of feature recognition with explicit representation of feature interaction

The existing feature-based design and feature recognition methods cannot fulfil the requirements of automated process planning. It is now recognized that satisfactory modelling of interactions between features is necessary for developing an automated process planning system. The selection of an optimum manufacturing process for a part needs to be considered at the conceptual design phase to incorporate the capabilities and constraints of the process in design. This paper describes a methodology of feature recognition that is independent of manufacturing process and explicitly generates geometric feature interactions in a part. The paper illustrates generation of feature sets for shape-forming processes, and describes a method to convert the process-independent features into machinable volumes and tool paths for material removal processes.     

Self-organizing feature maps with self-adjusting learningparameters

Presents an extension of the self-organizing learning algorithm of feature maps in order to improve its convergence to neighborhood preserving maps. The Kohonen learning algorithm is controlled by two learning parameters, which have to be chosen empirically because there exists neither rules nor a method for their calculation. Consequently, often time consuming parameter studies have to precede before a neighborhood preserving feature map is obtained. To circumvent those lengthy numerical studies, here, a method is presented and incorporated into the learning algorithm which determines the learning parameters automatically. Therefore, system models of the learning and organizing process are developed in order to be followed and predicted by linear and extended Kalman filters. The learning parameters are optimal within the system models, so that the self-organizing process converges automatically to a neighborhood preserving feature map of the learning data.     

Asymptotic level density in topological feature maps

The Kohonen algorithm entails a topology conserving mapping of an input pattern space X subsetR(n) characterized by an a priori probability distribution P(x), xinX, onto a discrete lattice of neurons r with virtual positions w(r)inX. Extending results obtained by Ritter (1991) the authors show in the one-dimensional case for an arbitrary monotonously decreasing neighborhood function h(|r-r'|) that the point density D(W(r)) of the virtual net is a polynomial function of the probability density P(x) with D(w(r))~P(alpha)(w(r)). Here the distortion exponent is given by alpha=(1+12R)/3(1+6R) and is determined by the normalized second moment R of the neighborhood function. A Gaussian neighborhood interaction is discussed and the analytical results are checked by means of computer simulations.     

Spatio-temporal feature maps using gated neuronal architecture

In this paper, Kohonen's self-organizing feature map is modified by a novel technique of allowing the neurons in the feature map to compete in a selective manner. The selective competition is achieved by grating the N-dimensional feature space using a spatial frequency and setting a criterion for the neurons to compete based on the region in which the input pattern resides. The spatial grating and selective competition are achieved by introducing a gated neuronal architecture in the feature map. As the selection criterion changes with time, it generates a time sequence of winning node indexes providing more input information and potentially allowing higher classification performance. These time sequences are then used to predict the class label of the input pattern more accurately. Three possible class label prediction algorithms are formulated based on evidential reasoning method and Bayes conditional probability theorem. These are tested on real world 8-class texture and a synthetic 12-class 3D object recognition problems. The classification performance is then compared with the results obtained by using a standard statistical linear discriminant analysis.     

Visual feature analysis by the self-organising maps

The Self-Organising Map (SOM) is an Artificial Neural Network (ANN) model consisting of a regular grid of processing units. A model of some multidimensional observation, e.g. a class of digital images, is associated with each unit. The map attempts to represent all the available observations using a restricted set of models. In unsupervised learning, the models become ordered on the grid so that similar models are close to each other. We review here the objective functions and learning rules related to the SOM, starting from vector coding based on a Euclidean metric and extending the theory of arbitrary metrics and to a subspace formalism, in which each SOM unit represents a subspace of the observation space. It is shown that this Adaptive-Subspace SOM (ASSOM) is able to create sets of wavelet- and Gabor-type filters when randomly displaced or moving input patterns are used as training data. No analytical functional form for these filters is thereby postulated. The same kind of adaptive system can create many other kinds of invariant visual filters, like rotation or scale-invariant filters, if there exist corresponding transformations in the training data. The ASSOM system can act as a learning feature-extraction stage for pattern recognisers, being able to adapt to arbitrary sensory environments. We then show that the invariant Gabor features can be effectively used in face recognition, whereby the sets of Gabor filter outputs are coded with the SOM and a face is represented by the histogram over the SOM units.     

基于自组织特征映射的图像压缩技术

计算机人工神经网络技术提供了新的图像压缩方法。自组织特征映射人工神经网络就能够用于图像的有损压缩。通过将图像分成若干小块,然后使用神经网络进行训练达到特征向量自动聚类,从而将这若干个图像块分成不同的类,其类别个数远小于图像块的个数,最后使用一个映射表保存这些信息。该方式,将图像中相同或者非常相似的部分归为一类,降低了信息冗余度,从而可以进行图像的有损压缩。该方法采用了计算机神经网络,有比较好的适应性,能够方便的和其它压缩技术结合实现效果更好的混合压缩,具有良好的推广价值。     

Reclustering techniques improve early vision feature maps

We propose a recursive post-processing algorithm to improve feature-maps, like disparity- or motion-maps, computed by early vision modules. The statistical distribution of the features is computed from the original feature-map, and from this the most likely candidate for a correct feature is determined for every pixel. This process is performed automatically by a clustering algorithm which determines the feature candidates as the cluster centres in the distribution. After determining the feature candidates, a cost function is computed for every pixel, and a candidate will only replace the original feature if the cost is reduced. In this way, a new feature-map is generated which, in the next iteration, serves as the basis for the computation of the updated feature distribution. Iterations are stopped if the total cost reduction is less than a pre-defined threshold. In general, our technique is albe to reduce two of the most common problems that affect feature-maps, the sparseness, i.e. the presence of areas where the algorithm is not able to give meaningful measurements, and the blur. To show the efficacy of our approach, we apply the reclustering algorithm to several examples of increasing complexity, showing results for synthetic and natural images.     

Efficient synthesis of feature models

ContextVariability modeling, and in particular feature modeling, is a central element of model-driven software product line architectures. Such architectures often emerge from legacy code, but, creating feature models from large, legacy systems is a long and arduous task. We describe three synthesis scenarios that can benefit from the algorithms in this paper.ObjectiveThis paper addresses the problem of automatic synthesis of feature models from propositional constraints. We show that the decision version of the problem is NP-hard. We designed two efficient algorithms for synthesis of feature models from CNF and DNF formulas respectively.MethodWe performed an experimental evaluation of the algorithms against a binary decision diagram (BDD)-based approach and a formal concept analysis (FCA)-based approach using models derived from realistic models.ResultsOur evaluation shows a 10 to 1,000-fold performance improvement for our algorithms over the BDD-based approach. The performance of the DNF-based algorithm was similar to the FCA-based approach, with advantages for both techniques. We identified input properties that affect the runtimes of the CNF- and DNF-based algorithms.ConclusionsOur algorithms are the first known techniques that are efficient enough to be used on dependencies extracted from real systems, opening new possibilities of creating reverse engineering and model management tools for variability models.     

Efficient fastest-path computations for road maps

Computational Visual Media - In the age of real-time online traffic information and GPS-enabled devices, fastest-path computations between two points in a road network modeled as a directed graph,...