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Multi-kernel Regression For Graph Signal Processing

arXiv.org Machine Learning

We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective kernel function by appropriate regularization based on graph smoothness. We show that the resulting optimization problem is shown to be convex and pro- pose an accelerated projected gradient descent based solution. Simulation results using real-world graph signals show efficiency of the multi-kernel based approach over a standard kernel based approach.


Zhang

AAAI Conferences

Opioid (e.g., heroin and morphine) addiction has become one of the largest and deadliest epidemics in the United States. To combat such deadly epidemic, in this paper, we propose a novel framework named AutoOPU to automatically detect the opioid users from Twitter, which will assist in sharpening our understanding toward the behavioral process of opioid addiction and treatment. In AutoOPU, to model the users and posted tweets as well as their rich relationships, we first introduce a heterogeneous information network (HIN) for representation. Then we use meta-structure based approach to characterize the semantic relatedness over users. Afterwards, we integrate content-based similarity and relatedness depicted by each meta-structure to formulate a similarity measure over users. Further, we aggregate different similarities using multi-kernel learning, each of which is automatically weighted by the learning algorithm to make predictions. To the best of our knowledge, this is the first work to use multi-kernel learning based on meta-structures over HIN for biomedical knowledge mining, especially in drug-addiction domain. Comprehensive experiments on real sample collections from Twitter are conducted to validate the effectiveness of our developed system AutoOPU in opioid user detection by comparisons with other alternative methods.


Sparse Kernel Principal Component Analysis

Neural Information Processing Systems

'Kernel' principal component analysis (PCA) is an elegant nonlinear generalisationof the popular linear data analysis method, where a kernel function implicitly defines a nonlinear transformation intoa feature space wherein standard PCA is performed. Unfortunately, thetechnique is not'sparse', since the components thus obtained are expressed in terms of kernels associated with every trainingvector. This paper shows that by approximating the covariance matrix in feature space by a reduced number of example vectors,using a maximum-likelihood approach, we may obtain a highly sparse form of kernel PCA without loss of effectiveness. 1 Introduction Principal component analysis (PCA) is a well-established technique for dimensionality reduction,and examples of its many applications include data compression, image processing, visualisation, exploratory data analysis, pattern recognition and time series prediction.


Sparse Kernel Principal Component Analysis

Neural Information Processing Systems

'Kernel' principal component analysis (PCA) is an elegant nonlinear generalisation of the popular linear data analysis method, where a kernel function implicitly defines a nonlinear transformation into a feature space wherein standard PCA is performed. Unfortunately, the technique is not'sparse', since the components thus obtained are expressed in terms of kernels associated with every training vector. This paper shows that by approximating the covariance matrix in feature space by a reduced number of example vectors, using a maximum-likelihood approach, we may obtain a highly sparse form of kernel PCA without loss of effectiveness. 1 Introduction Principal component analysis (PCA) is a well-established technique for dimensionality reduction, and examples of its many applications include data compression, image processing, visualisation, exploratory data analysis, pattern recognition and time series prediction.


Sparse Kernel Principal Component Analysis

Neural Information Processing Systems

'Kernel' principal component analysis (PCA) is an elegant nonlinear generalisation of the popular linear data analysis method, where a kernel function implicitly defines a nonlinear transformation into a feature space wherein standard PCA is performed. Unfortunately, the technique is not'sparse', since the components thus obtained are expressed in terms of kernels associated with every training vector. This paper shows that by approximating the covariance matrix in feature space by a reduced number of example vectors, using a maximum-likelihood approach, we may obtain a highly sparse form of kernel PCA without loss of effectiveness. 1 Introduction Principal component analysis (PCA) is a well-established technique for dimensionality reduction, and examples of its many applications include data compression, image processing, visualisation, exploratory data analysis, pattern recognition and time series prediction.