hold. The facts above are well-known as the classical Shannon sampling theorem initially proved by Ogura [10]. Ashino and Mandai [1] generalized the sampling theorem in Lebesgue spaces L0(R) for 1 < p0 < ∞. Their generalized sampling theorem is the following. Theorem 1.1 ([1]). Let r > 0 and 1 < p0 < ∞. Then for all f ∈ L 0(R) with supp f̂ ⊂ [−rπ, rπ], we have the norm inequality C p r ‖f‖Lp0(Rn...

In this paper, we propose a novel method based on support vector machine (SVM) for microarray classification and gene (feature) selection. The proposed method, called similaritybased SVM (SSVM), incorporates the prior knowledge of gene similarity into the standard SVM by combining the standard l2 norm and the similarity penalty of all the genes. The preliminary experiments show that our method ...

We develop the theory and practical implementation of p-adic sparse coding of data. Rather than the standard, sparsifying criterion that uses the L0 pseudo-norm, we use the p-adic norm. We require that the hierarchy or tree be node-ranked, as is standard practice in agglomerative and other hierarchical clustering, but not necessarily with decision trees. In order to structure the data, all comp...

In this paper, we propose a novel sparse coding and counting method under Bayesian framework for visual tracking. In contrast to existing methods, the proposed method employs the combination of L0 and L1 norm to regularize the linear coefficients of incrementally updated linear basis. The sparsity constraint enables the tracker to effectively handle difficult challenges, such as occlusion or im...

Maximum hands-off control aims to maximize the length of time over which zero actuator values are applied to a system when executing specified control tasks. To tackle such problems, recent literature has investigated optimal control problems which penalize the size of the support of the control function and thereby lead to desired sparsity properties. This article gives the exact set of necess...

We develop a method to carry out MAP estimation for a class of Bayesian regression models in which coefficients are assigned with Gaussian-based spike and slab priors. The objective function in the corresponding optimization problem has a Lagrangian form in that regression coefficients are regularized by a mixture of squared l2 and l0 norms. A tight approximation to the l0 norm using majorizati...

The theory of (tight) wavelet frames has been extensively studied in the past twenty years and they are currently widely used for image restoration and other image processing and analysis problems. The success of wavelet frame based models, including balanced approach [18, 7] and analysis based approach [11, 31, 50], is due to their capability of sparsely approximating piecewise smooth function...

Unsupervised feature selection is a useful tool for reducing the complexity and improving the generalization performance of data mining tasks. In this paper, we propose an Adaptive Unsupervised Feature Selection (AUFS) algorithm with explicit l2/l0-norm minimization. We use a joint adaptive loss for data fitting and a l2/l0 minimization for feature selection. We solve the optimization problem w...