Norm Multiple Kernel Learning Research Articles

ℓ q -Norm Sample-Adaptive Multiple Kernel Learning

Existing multiple kernel learning (MKL) algorithms indiscriminately apply the same set of kernel combination weights to all samples by pre-specifying a group of base kernels. Sample-adaptive MKL learning (SAMKL) overcomes this limitation by adaptively switching on/off the base kernels with respect to each sample. However, it restricts to solving MKL problems with pre-specified kernels. And, the formulation of existing SAMKL falls to an $\ell _{1}$ -norm MKL which is not flexible. To allow for robust kernel mixtures that generalize well in practical applications, we extend SAMKL to the arbitrary norm and apply it to image classification. In this paper, we formulate a closed-form solution for optimizing the kernel weights based on the equivalence between group-lasso and MKL, and derive an efficient $\ell _{q}$ -norm ( $q\geq 1$ and denoting the $\ell _{q}$ -norm of kernel weights) SAMKL algorithm. The cutting plane method is used to solve this margin maximization problem. Besides, we propose a framework for solving MKL problems in image classification. Experimental results on multiple data sets show the promising performance of the proposed solution compared with other competitive methods.

Fusion of heterogeneous bands and kernels in hyperspectral image processing

Hyperspectral imaging is a powerful technology that is plagued by large dimensionality. Herein, we explore a way to combat that hindrance via non-contiguous and contiguous (simpler to realize sensor) band grouping for dimensionality reduction. Our approach is different in the respect that it is flexible and it follows a well-studied process of visual clustering in high-dimensional spaces. Specifically, we extend the improved visual assessment of cluster tendency and clustering in ordered dissimilarity data unsupervised clustering algorithms for supervised hyperspectral learning. In addition, we propose a way to extract diverse features via the use of different proximity metrics (ways to measure the similarity between bands) and kernel functions. The discovered features are fused with $l_{\infty}$-norm multiple kernel learning. Experiments are conducted on two benchmark datasets and our results are compared to related work. These datasets indicate that contiguous or not is application specific, but heterogeneous features and kernels usually lead to performance gain.

Combining visual and textual features for medical image modality classification with ℓp−norm multiple kernel learning

Abstract Automatic modality classification of medical images is an important tool for medical image retrieval. In this paper, we combine visual and textual information for modality classification. The visual features used are SIFT feature, LBP feature, Gabor texture feature and Tamura texture feature. And the textual feature is a tf–idf feature vector drawn from image description text. We combine these features by l p - norm multiple kernel learning ( l p - norm MKL), and use One-vs-All approach for this multi-class problem. l p - norm MKL is explored with different norm value ( p ≥ 1 ). These MKL based methods are compared with several other feature combination methods and evaluated on the dataset of modality classification task in ImageCLEFmed 2010. The experimental results indicate that multiple kernel learning is a promising approach to combine visual and textual features for modality classification, and outperforms other simple kernel combination methods and the traditional early fusion method.

Image classification with densely sampled image windows and generalized adaptive multiple kernel learning.

We present a framework for image classification that extends beyond the window sampling of fixed spatial pyramids and is supported by a new learning algorithm. Based on the observation that fixed spatial pyramids sample a rather limited subset of the possible image windows, we propose a method that accounts for a comprehensive set of windows densely sampled over location, size, and aspect ratio. A concise high-level image feature is derived to effectively deal with this large set of windows, and this higher level of abstraction offers both efficient handling of the dense samples and reduced sensitivity to misalignment. In addition to dense window sampling, we introduce generalized adaptive l(p)-norm multiple kernel learning (GA-MKL) to learn a robust classifier based on multiple base kernels constructed from the new image features and multiple sets of prelearned classifiers from other classes. With GA-MKL, multiple levels of image features are effectively fused, and information is shared among different classifiers. Extensive evaluation on benchmark datasets for object recognition (Caltech256 and Caltech101) and scene recognition (15Scenes) demonstrate that the proposed method outperforms the state-of-the-art under a broad range of settings.

Training Lp norm multiple kernel learning in the primal

Some multiple kernel learning (MKL) models are usually solved by utilizing the alternating optimization method where one alternately solves SVMs in the dual and updates kernel weights. Since the dual and primal optimization can achieve the same aim, it is valuable in exploring how to perform Lp norm MKL in the primal. In this paper, we propose an Lp norm multiple kernel learning algorithm in the primal where we resort to the alternating optimization method: one cycle for solving SVMs in the primal by using the preconditioned conjugate gradient method and other cycle for learning the kernel weights. It is interesting to note that the kernel weights in our method can obtain analytical solutions. Most importantly, the proposed method is well suited for the manifold regularization framework in the primal since solving LapSVMs in the primal is much more effective than solving LapSVMs in the dual. In addition, we also carry out theoretical analysis for multiple kernel learning in the primal in terms of the empirical Rademacher complexity. It is found that optimizing the empirical Rademacher complexity may obtain a type of kernel weights. The experiments on some datasets are carried out to demonstrate the feasibility and effectiveness of the proposed method.

Error Bounds for lp‐Norm Multiple Kernel Learning with Least Square Loss

The problem of learning the kernel function with linear combinations of multiple kernels has attracted considerable attention recently in machine learning. Specially, by imposing an lp‐norm penalty on the kernel combination coefficient, multiple kernel learning (MKL) was proved useful and effective for theoretical analysis and practical applications (Kloft et al., 2009, 2011). In this paper, we present a theoretical analysis on the approximation error and learning ability of the lp‐norm MKL. Our analysis shows explicit learning rates for lp‐norm MKL and demonstrates some notable advantages compared with traditional kernel‐based learning algorithms where the kernel is fixed.

L p -Norm Multiple Kernel Learning

Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and scalability. Unfortunately, this l1-norm MKL is rarely observed to outperform trivial baselines in practical applications. To allow for robust kernel mixtures that generalize well, we extend MKL to arbitrary norms. We devise new insights on the connection between several existing MKL formulations and develop two efficient interleaved optimization strategies for arbitrary norms, that is lp-norms with p ≥ 1. This interleaved optimization is much faster than the commonly used wrapper approaches, as demonstrated on several data sets. A theoretical analysis and an experiment on controlled artificial data shed light on the appropriateness of sparse, non-sparse and l∞-norm MKL in various scenarios. Importantly, empirical applications of lp-norm MKL to three real-world problems from computational biology show that non-sparse MKL achieves accuracies that surpass the state-of-the-art. Data sets, source code to reproduce the experiments, implementations of the algorithms, and further information are available at http://doc.ml.tu-berlin.de/nonsparse_mkl/.