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About 697 papers for “kernel trick”

Nonlinear Projection Trick in Kernel Methods: An Alternative to the Kernel Trick

Nojun Kwak · IEEE Transactions on Neural Networks and Learning Systems · 2013

In kernel methods such as kernel principal component analysis (PCA) and support vector machines, the so called kernel trick is used to avoid direct calculations in a high (virtually infinite) dimensional kernel space. In this brief, based on the fact that the effective dimensionality of a kernel space is less than the number of training samples, we propose an alternative to the kernel trick that explicitly maps the input data into a reduced dimensional kernel space. This is easily obtained by the eigenvalue decomposition of the kernel matrix. The proposed method is named as the nonlinear projection trick in contrast to the kernel trick. With this technique, the applicability of the kernel methods is widened to arbitrary algorithms that do not use the dot product. The equivalence between the kernel trick and the nonlinear projection trick is shown for several conventional kernel methods. In addition, we extend PCA-L1, which uses L1-norm instead of L2-norm (or dot product), into a kernel version and show the effectiveness of the proposed approach.

Cited by 56

Exploiting the kernel trick to . . .

Yan Fu, et al. · 2004

Motivation: The correlation among fragment ions in a tandem mass spectrum is crucial in reducing stochastic mismatches for peptide identification by database searching. Until now, an efficient scoring algorithm that considers the correlative information in a tunable and comprehensive manner has been lacking. Results: This paper provides a promising approach to utilizing the correlative information for improving the peptide identification accuracy.The kernel trick, rooted in the statistical learning theory, is exploited to address this issue with low computational effort. The common scoring method, the tandem mass spectral dot product (SDP), is extended to the kernel SDP (KSDP). Experiments on a dataset reported previously demonstrate the effectiveness of the KSDP.The implementation on consecutive fragments shows a decrease of 10 % in the error rate compared with the SDP. Our software tool, pFind, using a simple scoring function based on the KSDP, outperforms two SDPbased software tools, SEQUEST and Sonar MS/MS, in terms of identification accuracy.

Cited by 0

Recursive kernel trick for network segmentation

Sun‐Yuan Kung, Yuhui Luo · International Journal of Robust and Nonlinear Control · 2011

SUMMARY Kernel K‐means has been a powerful unsupervised machine learning tool for cluster discovery. This paper explores its application towards network segmentation, a type of cluster discovery. Very commonly we encounter networks of extremely large size, making computational complexity a major issue in the algorithmic development. In this regard, the sparse structure of kernel matrices can be an invaluable asset. For partitioning nonvectorial data such as network graphs, we need to use a vector‐free clustering criterion for K‐means. The kernel matrix constructed from nonvectorial data usually needs to be preprocessed to assure Mercer's condition, which is required to guarantee monotonic convergence of the kernel K ‐means algorithm. This paper describes a centroid‐free criterion for K‐means so that it can be applied to nonvectorial data such as network segmentation. Such a criterion leads to our introduction of pattern‐centroid similarity which ultimately leads to a kernel trick algorithm based on updating of the pattern‐centroid similarity. Furthermore, by adopting a recursive updating scheme, the recursive kernel‐trick allows a computational saving from O ( N 2 / K ) to O ( N ). For networks with high sparsity structure, the amount of computation required can be further reduced from O ( N ) to O ( N s ), where N s is the average number of nonzero elements per column in the kernel matrix. Copyright © 2011 John Wiley & Sons, Ltd.

Cited by 3

Schematic digamma of the kernel trick.

Pramod S. Kathmore (20410298), Bhanudas D. Bachchhav (20410301), Duran Kaya (20410304) et al. · Figshare · 2024

<div><p>This study aimed to investigate the impact of a lubricant derived from trimethylolpropane trioleate on power consumption and surface roughness during high-speed drilling of Al-6061, with the goal of developing an environmentally friendly cutting fluid. The study investigated the impact of additive concentration, spindle speed, and feed rate on energy consumption and surface roughness using a Taguchi L27 orthogonal array. Through analysis of the Taguchi experimental outcomes and single-to-noise ratios, the parameters were ranked accordingly. The results of the ANOVA analysis reveal that spindle speed has the greatest impact on Power (87.89%), followed by followed feed rate (6.96%) and additive concentration (2.98%). However, feed rate (43.51%) has the most significant influence on surface roughness, followed by speed (38.48%) and additive concentration (11.90%). Varying additive concentration affects more on surface quality rather than power consumption. Furthermore, a machine learning algorithm was developed to forecast and compare various key aspects of high-speed drilling machinability, including power and surface roughness. Three different measures of accuracy were used to evaluate the performance of the projected values: coefficient of determination (R2), mean absolute percentage error, and mean square error. The decision tree performed better than other models in accurately predicting power and surface roughness. This research introduces an innovative method for assessing the most effective biodegradable cutting fluid and forecasting power and surface quality by developing an optimal combination.</p></div>

Cited by 0Open access

Formulating distance functions via the kernel trick

Gang Wu, Edward Yi Chang, Navneet Panda · 2005

Tasks of data mining and information retrieval depend on a good distance function for measuring similarity between data instances. The most effective distance function must be formulated in a context-dependent (also application-, data-, and user-dependent) way. In this paper, we propose to learn a distance function by capturing the nonlinear relationships among contextual information provided by the application, data, or user. We show that through a process called the "kernel trick," such nonlinear relationships can be learned efficiently in a projected space. Theoretically, we substantiate that our method is both sound and optimal. Empirically, using several datasets and applications, we demonstrate that our method is effective and useful.

Cited by 36

Urychlení výpočtu gramatické evoluce pomocí metody "Kernel trick"

Anna Kučerová · Brno University of Technology Digital Library (Brno University of Technology) · 2020

Tato práce se zabývá popisem evolučních algoritmů, konkrétně pak gramatické evoluce, která je implementována do optimalizačního programu PonyGE2. Dále popisuje princip jádrové metody.

Cited by 0Open access

Learning with Algebraic Invariances, and the Invariant Kernel Trick

Franz J. Király, Andreas Ziehe, Klaus‐Robert Müller · arXiv (Cornell University) · 2014

When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we show that algebraic properties such as sign symmetries in data, phase independence, scaling etc. can be included easily by essentially performing the kernel trick twice. We demonstrate the usefulness of our theory in simulations on selected applications such as sign-invariant spectral clustering and underdetermined ICA.

Cited by 1Open access

Learning with Algebraic Invariances, and the Invariant Kernel Trick

Franz J. Király, Andreas Ziehe, Klaus-robert Müller · 2014

When solving data analysis problems it is important to integrate prior knowl-edge and/or structural invariances. This paper contributes by a novel frame-work for incorporating algebraic invariance structure into kernels. In particular, we show that algebraic properties such as sign symmetries in data, phase in-dependence, scaling etc. can be included easily by essentially performing the kernel trick twice. We demonstrate the usefulness of our theory in simulations on selected applications such as sign-invariant spectral clustering and underde-termined ICA. 1.

Cited by 0

Robotic Tracking Control with Kernel Trick-based Reinforcement Learning

Hu YZ(胡亚洲), Wang WX(王文学), Liu, Hao et al. · SIA OpenIR (Chinese Academy of Sciences) · 2019

In recent years, reinforcement learning has been developed dramatically and is widely used to solve control problems, e.g., playing games. However, there are still some problems for reinforcement learning to perform robotic control tasks. Fortunately, the kernel trick-based methods provide a chance to deal with those challenges. This work aims at developing a kernel trick-based learning control method to carry out robotic tracking control tasks. A reward system, in this work, is presented in order to speed up the learning processes. And then, a kernel trick-based reinforcement learning tracking controller is presented to perform tracking control tasks on a robotic manipulator system. To evaluate the policy and assist the reward system to accelerate the speed of finding the optimal control policy, a critic system is introduced. Finally, from the comparison with the benchmark, the simulation results illustrate that our algorithm has faster convergence rate and can execute tracking control tasks effectively, the reward function and the critic system proposed in this work is efficient.

Cited by 0

Robotic Tracking Control with Kernel Trick-based Reinforcement Learning

Yazhou Hu, Wenxue Wang, Hao Liu et al. · 2019

In recent years, reinforcement learning has been developed dramatically and is widely used to solve control problems, e.g., playing games. However, there are still some problems for reinforcement learning to perform robotic control tasks. Fortunately, the kernel trick-based methods provide a chance to deal with those challenges. This work aims at developing a kernel trick-based learning control method to carry out robotic tracking control tasks. A reward system, in this work, is presented in order to speed up the learning processes. And then, a kernel trick-based reinforcement learning tracking controller is presented to perform tracking control tasks on a robotic manipulator system. To evaluate the policy and assist the reward system to accelerate the speed of finding the optimal control policy, a critic system is introduced. Finally, from the comparison with the benchmark, the simulation results illustrate that our algorithm has faster convergence rate and can execute tracking control tasks effectively, the reward function and the critic system proposed in this work is efficient.

Cited by 2

A uniform kernel trick for high-dimensional two-sample problems

Javier Cárcamo, Antonio Cuevas, Luis-Alberto Rodríguez · arXiv (Cornell University) · 2022

We use a suitable version of the so-called "kernel trick" to devise two-sample (homogeneity) tests, especially focussed on high-dimensional and functional data. Our proposal entails a simplification related to the important practical problem of selecting an appropriate kernel function. Specifically, we apply a uniform variant of the kernel trick which involves the supremum within a class of kernel-based distances. We obtain the asymptotic distribution (under the null and alternative hypotheses) of the test statistic. The proofs rely on empirical processes theory, combined with the delta method and Hadamard (directional) differentiability techniques, and functional Karhunen-Loève-type expansions of the underlying processes. This methodology has some advantages over other standard approaches in the literature. We also give some experimental insight into the performance of our proposal compared to the original kernel-based approach \cite{Gretton2007} and the test based on energy distances \cite{Szekely-Rizzo-2017}.

Cited by 0Open access

Research Track Poster Formulating Distance Functions via the Kernel Trick

Gang Wu, Edward Y. Chang, Navneet Panda · 2013

Tasks of data mining and information retrieval depend on a good distance function for measuring similarity between data instances. The most effective distance function must be formulated in a contextdependent (also application-, data-, and user-dependent) way. In this paper, we propose to learn a distance function by capturing the nonlinear relationships among contextual information provided by the application, data, or user. We show that through a process called the “kernel trick, ” such nonlinear relationships can be learned efficiently in a projected space. Theoretically, we substantiate that our method is both sound and optimal. Empirically, using several datasets and applications, we demonstrate that our method is effective and useful.

Cited by 0

Generalized vec trick for fast learning of pairwise kernel models

Markus Viljanen, Antti Airola, Tapio Pahikkala · Machine Learning · 2022

Abstract Pairwise learning corresponds to the supervised learning setting where the goal is to make predictions for pairs of objects. Prominent applications include predicting drug-target or protein-protein interactions, or customer-product preferences. In this work, we present a comprehensive review of pairwise kernels, that have been proposed for incorporating prior knowledge about the relationship between the objects. Specifically, we consider the standard, symmetric and anti-symmetric Kronecker product kernels, metric-learning, Cartesian, ranking, as well as linear, polynomial and Gaussian kernels. Recently, a $$O(nm+nq)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mi>n</mml:mi><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> time generalized vec trick algorithm, where $$n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math> , $$m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>m</mml:mi></mml:math> , and $$q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math> denote the number of pairs, drugs and targets, was introduced for training kernel methods with the Kronecker product kernel. This was a significant improvement over previous $$O(n^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math> training methods, since in most real-world applications $$m,q&lt;&lt; n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>&lt;</mml:mo><mml:mo>&lt;</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math> . In this work we show how all the reviewed kernels can be expressed as sums of Kronecker products, allowing the use of generalized vec trick for speeding up their computation. In the experiments, we demonstrate how the introduced approach allows scaling pairwise kernels to much larger data sets than previously feasible, and provide an extensive comparison of the kernels on a number of biological interaction prediction tasks.

Cited by 9Open access

Experimental quantum kernel trick with nuclear spins in a solid

Takeru Kusumoto, Kosuke Mitarai, Keisuke Fujii et al. · npj Quantum Information · 2021

Abstract The kernel trick allows us to employ high-dimensional feature space for a machine learning task without explicitly storing features. Recently, the idea of utilizing quantum systems for computing kernel functions using interference has been demonstrated experimentally. However, the dimension of feature spaces in those experiments have been smaller than the number of data, which makes them lose their computational advantage over explicit method. Here we show the first experimental demonstration of a quantum kernel machine that achieves a scheme where the dimension of feature space greatly exceeds the number of data using 1 H nuclear spins in solid. The use of NMR allows us to obtain the kernel values with single-shot experiment. We employ engineered dynamics correlating 25 spins which is equivalent to using a feature space with a dimension over 10 15 . This work presents a quantum machine learning using one of the largest quantum systems to date.

Cited by 52Open access