Search results for "kernel"
showing 10 items of 357 documents
Model selection based product kernel learning for regression on graphs
2013
The choice of a suitable graph kernel is intrinsically hard and often cannot be made in an informed manner for a given dataset. Methods for multiple kernel learning offer a possible remedy, as they combine and weight kernels on the basis of a labeled training set of molecules to define a new kernel. Whereas most methods for multiple kernel learning focus on learning convex linear combinations of kernels, we propose to combine kernels in products, which theoretically enables higher expressiveness. In experiments on ten publicly available chemical QSAR datasets we show that product kernel learning is on no dataset significantly worse than any of the competing kernel methods and on average the…
A structural cluster kernel for learning on graphs
2012
In recent years, graph kernels have received considerable interest within the machine learning and data mining community. Here, we introduce a novel approach enabling kernel methods to utilize additional information hidden in the structural neighborhood of the graphs under consideration. Our novel structural cluster kernel (SCK) incorporates similarities induced by a structural clustering algorithm to improve state-of-the-art graph kernels. The approach taken is based on the idea that graph similarity can not only be described by the similarity between the graphs themselves, but also by the similarity they possess with respect to their structural neighborhood. We applied our novel kernel in…
Optimal selection of touristic packages based on user preferences during sports mega-events
2022
Sport mega-events, such as the Soccer World Cup or Olympic Games, attract many visitors from all over the world. Most of these visitors are also interested in, besides attending the sports events, visiting the host nation and the neighboring countries. In this paper, we focus on the upcoming FIFA World Cup Qatar 2022. As per the schedule of the tournament, a national team can play 7 matches at most. Therefore, a supporter will have six short breaks (of three to five days) between consecutive matches in addition to two longer ones, immediately before and after the tournament, during which they can plan some touris- tic trips. We study the problem faced by a touristic trip provider who wants …
A more distinctive representation for 3D shape descriptors using principal component analysis
2015
Many researchers have used the Heat Kernel Signature (or HKS) for characterizing points on non-rigid three-dimensional shapes and Classical Multidimensional Scaling (Classical MDS) method in object classification which we quote, in particular, the example of Jian Sun et al. (2009) [1]. However, in this paper, the main focuses on classification that we propose a concise and provably factorial method by invoking Principal Component Analysis (PCA) as a classifier to improve the scheme of 3D shape classification. To avoid losing or disordering information after extracting features from the mesh, PCA is used instead of the Classical MDS to discriminate-as much as possible-feature points for each…
Gravity, Non-Commutative Geometry and the Wodzicki Residue
1993
We derive an action for gravity in the framework of non-commutative geometry by using the Wodzicki residue. We prove that for a Dirac operator $D$ on an $n$ dimensional compact Riemannian manifold with $n\geq 4$, $n$ even, the Wodzicki residue Res$(D^{-n+2})$ is the integral of the second coefficient of the heat kernel expansion of $D^{2}$. We use this result to derive a gravity action for commutative geometry which is the usual Einstein Hilbert action and we also apply our results to a non-commutative extension which, is given by the tensor product of the algebra of smooth functions on a manifold and a finite dimensional matrix algebra. In this case we obtain gravity with a cosmological co…
Quark–hadron duality: Pinched kernel approach
2016
Hadronic spectral functions measured by the ALEPH collaboration in the vector and axial-vector channels are used to study potential quark-hadron duality violations (DV). This is done entirely in the framework of pinched kernel finite energy sum rules (FESR), i.e. in a model independent fashion. The kinematical range of the ALEPH data is effectively extended up to $s = 10\; {\mbox{GeV}^2}$ by using an appropriate kernel, and assuming that in this region the spectral functions are given by perturbative QCD. Support for this assumption is obtained by using $e^+ e^-$ annihilation data in the vector channel. Results in both channels show a good saturation of the pinched FESR, without further nee…
Passive millimeter wave image classification with large scale Gaussian processes
2017
Passive Millimeter Wave Images (PMMWIs) are being increasingly used to identify and localize objects concealed under clothing. Taking into account the quality of these images and the unknown position, shape, and size of the hidden objects, large data sets are required to build successful classification/detection systems. Kernel methods, in particular Gaussian Processes (GPs), are sound, flexible, and popular techniques to address supervised learning problems. Unfortunately, their computational cost is known to be prohibitive for large scale applications. In this work, we present a novel approach to PMMWI classification based on the use of Gaussian Processes for large data sets. The proposed…
A Novel System for Multi-level Crohn’s Disease Classification and Grading Based on a Multiclass Support Vector Machine
2020
Crohn’s disease (CD) is a chronic inflammatory condition of the gastrointestinal tract that can highly alter patient’s quality of life. Diagnostic imaging, such as Enterography Magnetic Resonance Imaging (E-MRI), provides crucial information for CD activity assessment. Automatic learning methods play a fundamental role in the classification of CD and allow to avoid the long and expensive manual classification process by radiologists. This paper presents a novel classification method that uses a multiclass Support Vector Machine (SVM) based on a Radial Basis Function (RBF) kernel for the grading of CD inflammatory activity. To validate the system, we have used a dataset composed of 800 E-MRI…
Biophysical parameter estimation with adaptive Gaussian Processes
2009
We evaluate Gaussian Processes (GPs) for the estimation of biophysical parameters from acquired multispectral data. The standard GP formulation is used, and all hyperparameters (kernel parameters and noise variance) are optimized by maximizing the marginal likelihood. This gives rise to a fully-adaptive GP to data characteristics, both in terms of signal and noise properties. The good numerical results in the estimation of oceanic chlorophyll concentration and leaf membrane state confirm GPs as adequate, alternative non-parametric methods for biophysical parameter estimation. GPs are also analyzed by scrutinizing the predictive variance, the estimated noise variance, and the relevance of ea…
On identification of separable kernel systems
1979
An identification procedure for special separable kernel systems is presented. The suitable definition of adequateness of a signal leads to a systematic treatment of the choice of inputs for identification.