International Journal of Wavelets, Multiresolution and Information Processing

In this paper, we consider conditional quantile regression learning algorithms based on the pinball loss with data dependent hypothesis space and ℓ²-regularizer. Functions in this hypothesis space are linear combination of basis functions generated by a kernel function and sample data. The only conditions imposed on the kernel function are the continuity and boundedness which are pretty weak. Our main goal is to study the consistency of this regularized quantile regression learning. By concentration inequality with ℓ²-empirical covering numbers and operator decomposition techniques, satisfied error bounds and convergence rates are explicitly derived.

Graphs labeled with complex-valued Gabor jets are one of the important data formats for face recognition and the classification of facial images into medically relevant classes like genetic syndromes. We here present an interpolation rule and an iterative algorithm for the reconstruction of images from these graphs. This is especially important if graphs have been manipulated for information processing. One such manipulation is averaging the graphs of a single syndrome, another one building a composite face from the features of various individuals. In reconstructions of averaged graphs of genetic syndromes, the patients' identities are suppressed, while the properties of the syndromes are emphasized. These reconstructions from average graphs have a much better quality than averaged images.

Semi-supervised learning deals with learning with a small amount labeled sample and a large amount of unlabeled sample to improve the learning ability. The purpose of the semi-supervised gradient learning is to increase the smoothness of the solution using unlabeled gradient data. In this paper, we study the semi-supervised kernel-based regularization scheme involving function gradient value. We show that the learning rate can be bounded by a K-functional with gradients of the function, which verify how the unlabeled gradient data quantitatively influences the learning rate. Some approaches from convex analysis play a key role in our error analysis.

This paper proposes the fractal features for glycyrrhiza fingerprint of medicinal herbs, to obtain the intrinsic mode functions (IMFs) from high to low frequency by using empirical mode decomposition (EMD). The EMD fractal features are extracted through computing the fractal dimensions of each IMF. The novel approach is applied to the recognition of the three types of glycyrrhiza fingerprints. Experiments show that EMD fractal features have better recognition rate than that of the traditional ones in the case of concentration-change, i.e. the number of peak and peak drift of sample which has slight changes. An existing method to extract the fractal features for fingerprint of medicinal herbs based on wavelet transform, which is called fractal-wavelet features, was presented. This method has anti-jamming property against the change of samples concentration. However, the recognition rate based on fractal-wavelet features is not satisfactory when fingerprint of medicinal herbs has some slight concentrations changes, the number of peak and peak drift of samples are processed in the special situation.

The ordinary feature selection methods select only the explicit relevant attributes by filtering the irrelevant ones. They trade the selection accuracy for the execution time and complexity. In which, the hidden supportive information possessed by the irrelevant attributes may be lost, so that they may miss some good combinations. We believe that attributes are useless regarding the classification task by themselves, sometimes may provide potentially useful supportive information to other attributes and thus benefit the classification task. Such a strategy can minimize the information lost, therefore is able to maximize the classification accuracy. Especially for the dataset contains hidden interactions among attributes. This paper proposes a feature selection methodology from a new angle that selects not only the relevant features, but also targeting at the potentially useful false irrelevant attributes by measuring their supportive importance to other attributes. The empirical results validate the hypothesis by demonstrating that the proposed approach outperforms most of the state-of-the-art filter based feature selection methods.

Kernel canonical correlation analysis (CCA) is a nonlinear extension of CCA, which aims at extracting information shared by two random variables. In this paper, a new notion of conditional kernel CCA is introduced. Conditional kernel CCA aims at analyzing the effect of variable Z to the dependence between X and Y. Rates of convergence of an empirical normalized conditional cross-covariance operator (empirical NCCCO) to the normalized conditional cross-covariance operator (NCCCO) are also investigated in this paper. Elaborate error analysis of conditional kernel CCA is elegantly conducted under mild decay conditions. Our refined analysis leads to satisfactory learning rates in a more general setting.

In order to obtain higher small target detection accuracy, this paper presents an effective algorithm inspired by the local contrast mechanism. The proposed method can enhance target signal and suppress background clutter simultaneously. In the first stage, a enhanced image is obtained using the proposed Weighted Laplacian of Gaussian. In the second stage, an adaptive threshold is adopted to segment the target. Experimental results on two challenging image sequences show that the proposed method can detect the bright and dark targets simultaneously, and is not sensitive to sea–sky line of the infrared (IR) image. So it is fit for small IR target detection.

In this paper, we present new Bayesian estimators for adaptive generalized Gaussian (GG) random vectors in additive white Gaussian noise (AWGN). The derivations are an extension of existing results for Pearson type VII random vectors in AWGN. Pearson type VII random vectors is one of the distribution that successfully use for image denoising. However, Pearson type VII distribution have higher-order moment in statistical parameter for fitted the data such as mean, variance and kurtosis. In our literature, where high-order statistics were used, better performance can be obtained but with much higher computational complexity. In fact, adaptive GG random vectors is similar to Pearson type VII random vectors. However, the special case of adaptive GG random vectors has only first few statistical moments such as adaptive parameter. So, the proposed method can be calculated very fast, without any complex step. In fact, the adaptive parameter of adaptive GG density is the function of standard deviation. Here, we employ minimum mean square error (MMSE) estimation to calculate local observed variances with gamma density prior for local observed variances and Gaussian distribution for noisy wavelet coefficients. In our experiments, our proposed method gives promising denoising results with moderate complexity.

For the smooth surface M, the explicit construction of local flattening map p is given, where the bijection projection p is the local flattening map from a smooth surface M to a plane. By virtue of the inverse projection p^-1, the local wavelet transform on M can be generated from wavelet transform on a plane. Take the torus T² for example, by using the local flattening map p of torus, the construction of the local dilation on the torus is systematically studied, the local wavelet transform formula on the torus is offered and the inverse transform formula of the local wavelet transform, that is, the reconstruction formula is also offered. Finally, we show the graphical representation of the local wavelet on the torus.

Most of the existing privacy preserving clustering (PPC) algorithms do not consider the worst case privacy guarantees and are based on heuristic notions. In addition, these algorithms do not run efficiently in the case of high dimensionality of data. In this paper, to alleviate these challenges, we propose a new PPC algorithm, which is based on Daubechies-2 wavelet transform (D2WT) and preserves the differential privacy notion. Differential privacy is the strong notion of privacy, which provides the worst case privacy guarantees. On the other hand, most of the existing differential-based PPC algorithms generate data with poor utility. If we apply differential privacy properties over the original raw data, the resulting data will offer lower quality of clustering (QOC) during the clustering analysis. Therefore, we use D2WT for the preprocessing of the original data before adding noise to the data. By applying D2WT to the original data, the resulting data not only contains lower dimension compared to the original data, but also can provide differential privacy guarantee with high QOC due to less noise addition. The proposed algorithm has been implemented and experimented over some well-known datasets. We also compare the proposed algorithm with some recently introduced algorithms based on utility and privacy degrees.

A multiresolution analysis (MRA) on local fields of positive characteristic was defined by Shah and Abdullah for which the translation set is a discrete set which is not a group. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis (VNUMRA) where the associated subspace V₀ of L²(K, ℂ^M) has an orthonormal basis of the form {Φ (x - λ)}_λ∈Λ where Λ = {0, r/N} + 𝒵, N ≥ 1 is an integer and r is an odd integer such that r and N are relatively prime and 𝒵 = {u(n) : n ∈ ℕ₀}. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of VNUMRA on local fields starting from a vector refinement mask G(ξ) with appropriate conditions. Further, these results also hold for Cantor and Vilenkin groups.

This paper discusses generalization bounds for complex data learning which serve as a theoretical foundation for complex support vector machine (SVM). Drawn on the generalization bounds, a complex SVM approach based on the Szegő kernel of the Hardy space H²(𝔻) is formulated. It is applied to the frequency-domain identification problem of discrete linear time-invariant system (LTIS). Experiments show that the proposed algorithm is effective in applications.