Search results for "kernel"
showing 10 items of 357 documents
Residual 𝑝 properties of mapping class groups and surface groups
2008
Let M ( Σ , P ) \mathcal {M}(\Sigma , \mathcal {P}) be the mapping class group of a punctured oriented surface ( Σ , P ) (\Sigma ,\mathcal {P}) (where P \mathcal {P} may be empty), and let T p ( Σ , P ) \mathcal {T}_p(\Sigma ,\mathcal {P}) be the kernel of the action of M ( Σ , P ) \mathcal {M} (\Sigma , \mathcal {P}) on H 1 ( Σ ∖ P , F p ) H_1(\Sigma \setminus \mathcal {P}, \mathbb {F}_p) . We prove that T p ( Σ , P ) \mathcal {T}_p( \Sigma ,\mathcal {P}) is residually p p . In particular, this shows that M ( Σ , P ) \mathcal {M} (\Sigma ,\mathcal {P}) is virtually residually p p . For a group G G we denote by I p ( G ) \mathcal {I}_p(G) the kernel of the natural action of Out ( G ) \ope…
S_Kernel: A New Symmetry Measure
2005
Symmetry is an important feature in vision. Several detectors or transforms have been proposed. In this paper we concentrate on a measure of symmetry. Given a transform S, the kernel SK of a pattern is defined as the maximal included symmetric sub-set of this pattern. It is easily proven that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its flipped version. For the measure we compute a modified difference between respective surfaces of a pattern and its kernel. That founds an efficient algorithm to attention focusing on symmetric patterns.
Performance of power control in inter-cell interference coordination for frequency reuse
2010
To mitigate inter-cell interference in 3G evolution systems, a novel inter-cell interference coordination scheme called soft fractional frequency reuse is proposed in this article, which enables to improve the data rate in cell-edge. On this basis, an inter-cell power control is presented for the inter-cell interference coordination, and the inter-cell balanced signal to interference plus noise ratio (SINR) among users is established for power allocation, which enables mitigation of inter-cell interference. Especially, the power control is based on a novel exponential kernel equation at higher convergence speed than the traditional arithmetic kernel equations. Numerical results show that th…
The shape of small sample biases in pricing kernel estimations
2016
AbstractNumerous empirical studies find pricing kernels that are not-monotonically decreasing; the findings are at odds with the pricing kernel being marginal utility of a risk-averse, so-called representative agent. We study in detail the common procedure which estimates the pricing kernel as the ratio of two separate density estimations. In the first step, we analyse theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader regarding potential computational issues coupled with statistical techniques. In the second step, we study this quantitatively; we show that small sample biases shape the estimated pricing kernel, and that est…
Support vector machines in engineering: an overview
2014
This paper provides an overview of the support vector machine SVM methodology and its applicability to real-world engineering problems. Specifically, the aim of this study is to review the current state of the SVM technique, and to show some of its latest successful results in real-world problems present in different engineering fields. The paper starts by reviewing the main basic concepts of SVMs and kernel methods. Kernel theory, SVMs, support vector regression SVR, and SVM in signal processing and hybridization of SVMs with meta-heuristics are fully described in the first part of this paper. The adoption of SVMs in engineering is nowadays a fact. As we illustrate in this paper, SVMs can …
Support Vector Machine and Kernel Classification Algorithms
2018
This chapter introduces the basics of support vector machine (SVM) and other kernel classifiers for pattern recognition and detection. It also introduces the main elements and concept underlying the successful binary SVM. The chapter starts by introducing the main elements and concept underlying the successful binary SVM. Next, it introduces more advanced topics in SVM for classification, including large margin filtering (LMF), SSL, active learning, and large‐scale classification using SVMs. The LMF method performs both signal filtering and classification simultaneously by learning the most appropriate filters. SSL with SVMs exploits the information contained in both labeled and unlabeled e…
Upport vector machines for nonlinear kernel ARMA system identification.
2006
Nonlinear system identification based on support vector machines (SVM) has been usually addressed by means of the standard SVM regression (SVR), which can be seen as an implicit nonlinear autoregressive and moving average (ARMA) model in some reproducing kernel Hilbert space (RKHS). The proposal of this letter is twofold. First, the explicit consideration of an ARMA model in an RKHS (SVM-ARMA 2k) is proposed. We show that stating the ARMA equations in an RKHS leads to solving the regularized normal equations in that RKHS, in terms of the autocorrelation and cross correlation of the (nonlinearly) transformed input and output discrete time processes. Second, a general class of SVM-based syste…
Kernel manifold alignment for domain adaptation
2016
The wealth of sensory data coming from different modalities has opened numerous opportu- nities for data analysis. The data are of increasing volume, complexity and dimensionality, thus calling for new methodological innovations towards multimodal data processing. How- ever, multimodal architectures must rely on models able to adapt to changes in the data dis- tribution. Differences in the density functions can be due to changes in acquisition conditions (pose, illumination), sensors characteristics (number of channels, resolution) or different views (e.g. street level vs. aerial views of a same building). We call these different acquisition modes domains, and refer to the adaptation proble…
Optimizing Kernel Ridge Regression for Remote Sensing Problems
2018
Kernel methods have been very successful in remote sensing problems because of their ability to deal with high dimensional non-linear data. However, they are computationally expensive to train when a large amount of samples are used. In this context, while the amount of available remote sensing data has constantly increased, the size of training sets in kernel methods is usually restricted to few thousand samples. In this work, we modified the kernel ridge regression (KRR) training procedure to deal with large scale datasets. In addition, the basis functions in the reproducing kernel Hilbert space are defined as parameters to be also optimized during the training process. This extends the n…
Large-scale random features for kernel regression
2015
Kernel methods constitute a family of powerful machine learning algorithms, which have found wide use in remote sensing and geosciences. However, kernel methods are still not widely adopted because of the high computational cost when dealing with large scale problems, such as the inversion of radiative transfer models. This paper introduces the method of random kitchen sinks (RKS) for fast statistical retrieval of bio-geo-physical parameters. The RKS method allows to approximate a kernel matrix with a set of random bases sampled from the Fourier domain. We extend their use to other bases, such as wavelets, stumps, and Walsh expansions. We show that kernel regression is now possible for data…