International Journal of Wavelets, Multiresolution and Information Processing

Tight wavelet frames and their promising features in applications have attracted a great deal of interest and effort in recent years. In this paper, we give an explicit construction of tight wavelet frames generated by the Walsh polynomials on positive half-line ℝ⁺ using the extension principles. Finally, we derive the wavelet frame decomposition and reconstruction formulas which are similar to those of orthonormal wavelets on positive half-line ℝ⁺.

We propose a snowing model to iteratively smoothe the various image noises while preserving the important image structures such as edges and lines. Considering the gray image as a digital terrain model, we develop an adaptive weighted least squares support vector machine (LS-SVM) to iteratively estimate the optimal gray surface underlying the noisy image. The LS-SVM works on Gaussian noise while the weighted LS-SVM works on the outliers and non-Gaussian noise. To improve its performance in preserving the directional signal while suppressing the noise, the dominant orientation information of the gradients is integrated into the weighting scheme. The contribution of each attribute to the final LS-SVM model is adaptively determined in a fitness modulated, elongated, elliptical contour spread along the direction of the local edge structure. The farther away from the hyperplane in kernel space the point is, the less weight it gets, while the point on the direction of the local structure gets more weight. With adaptive weighting scheme, the robust LS-SVM smoothes most strongly along the edges, rather than across them, while it minimizes the effects of outliers, and results in strong preservation of details in the final output. The iteratively adaptive reweighted LS-SVM simulated the snowing process. The investigation on real images contaminated by mixture Gaussian noise has demonstrated that the performance of the present method is stable and reliable under noise distributions varying from Gaussian to impulsive.

Solving the Saint-Venant equations by numerical methods like finite element and finite difference methods yields an unstable solution for a fairly large open channel. Multiple Knot B-Spline Wavelets (MKBSW) are in the class of semi-orthogonal wavelets that have compact support. Hence, these basis functions are suitable for solving the Saint-Venant equations. However, solving the Saint-Venant equations by MKBSW method requires a long CPU time. In this paper, we present an adaptive wavelet method to solve the Saint-Venant equation in a fairly short time. In fact, we first solve the problem in a few first moments and then by statistical methods of time series and regression, where the active wavelets are predicted in the next moments. Moreover, by this adaptive method, the cumulative errors (that are produced by solving the discretized system, numerically) are decreased for large open channels. Two numerical examples are given to support our results.

Recently, semi-supervised learning (SSL) has attracted significant attention in machine learning fields. While numerous experimental results have shown the effectiveness of SSL methods, the theoretical analysis in this area is still poorly understood. In this paper, we investigate the generalization performance of the recently proposed sparse graph-based semi-supervised classification algorithm. We use a computationally more simple way to solve the algorithm and present the excess misclassification error bounds. In detail, the Fenchel-Legendre conjugate is first employed to reform the algorithm to an inf-sup problem. Then, the covering number is used to estimate the excess misclassification error. Experiment results are given to demonstrate the effectiveness of the sparse SSL algorithm with new solving strategy.

Attribute reduction of formal context is a crucial reseach issue in formal concept analysis. In this paper, based on the meet-irreducible elements and join-irreducible elements of concept lattice, two kinds of attribute reductions of formal context are proposed, which are called MI-attribute reduction and JI-attribute reduction. Subsequently, we discuss the relationships among them and two existing attribute reductions of formal context, lattice-based attribute reduction and granular reduction. Consequently, we find that the MI-attribute reduction and lattice-based attribute reduction are identical. For JI-attribute reduction, the judgement theorems of JI-consistent attribute sets are obtained. Finally, by using the discernibility attribute sets, a method of computing all JI-attribute reducts of a formal context is presented.

Wavelet set wavelets were the first examples of wavelets that may not have associated multiresolution analyses. Furthermore, they provided examples of complete orthonormal wavelet systems in L²(ℝ^d) which only require a single generating wavelet. Although work had been done to smooth these wavelets, which are by definition discontinuous on the frequency domain, nothing had been explicitly done over ℝ^d, d > 1. This paper, along with another one cowritten by the author, finally addresses this issue. Smoothing does not work as expected in higher dimensions. For example, Bin Han's proof of existence of Schwartz class functions which are Parseval frame wavelets and approximate Parseval frame wavelet set wavelets does not easily generalize to higher dimensions. However, a construction of wavelet sets in which may be smoothed is presented. Finally, it is shown that a commonly used class of functions cannot be the result of convolutional smoothing of a wavelet set wavelet.

This paper proposes a hybrid learning method to speed up the classification procedure of Support Vector Machines (SVM). Comparing most algorithms trying to decrease the support vectors in an SVM classifier, we focus on reducing the data points that need SVM for classification, and reduce the number of support vectors for each SVM classification. The system uses a Nearest Neighbor Classifier (NNC) to treat data points attentively. In the training phase, the NNC selects data near partial decision boundary, and then trains sub SVM for each Voronoi pair. For classification, most non-boundary data points are classified by NNC directly, while remaining boundary data points are passed to a corresponding local expert SVM. We also propose a data selection method for training reliable expert SVM. Experimental results on several generated and public machine learning data sets show that the proposed method significantly accelerates the testing speed.

Nowadays, in pattern recognition and classification, does not exist a dominant classifier for all data distributions. Also, data distribution of the task at hand is usually unknown, i.e. there is no algorithm achieving the best accuracy for all situations. An answer and a challenge to this problem is to build ensembles of classifiers working together, i.e. Multiple Classifier Systems, instead of building and running different classifiers separately: Multiple Classifier Systems can show better performance than a single classifier, provided a careful choice of the individual classifiers composing it. Furthermore, diversity among single classifiers, measured by some diversity metrics, is known to be a necessary condition to improve the ensemble performance. In this paper we extend the use of one of the most used diversity metrics, that is the Q diversity metric, from an oracle output to a soft output for the choice of the best classifier ensemble. We introduce the Q^t diversity metric, i.e. an extension of the Q metric to multi-label and multi-ranking Multiple Classifier Systems. A field evaluation of this metric is presented in a text categorization case study, using as a test set the standard document corpus Reuters 21578 ModApte 10. Our results strengthen the use of the extended metric in multi-label and multi-ranking Multiple Classifier Systems.

SenseCam is an effective memory-aid device that can automatically record images and other data from the wearer's whole day. The main issue is that, while SenseCam produces a sizeable collection of images over the time period, the vast quantity of captured data contains a large percentage of routine events, which are of little interest to review. In this article, the aim is to detect "Significant Events" for the wearers. We use several time series analysis methods such as Detrended Fluctuation Analysis (DFA), Eigenvalue dynamics and Wavelet Correlations to analyse the multiple time series generated by the SenseCam. We show that Detrended Fluctuation Analysis exposes a strong long-range correlation relationship in SenseCam collections. Maximum Overlap Discrete Wavelet Transform (MODWT) was used to calculate equal-time Correlation Matrices over different time scales and then explore the granularity of the largest eigenvalue and changes of the ratio of the sub-dominant eigenvalue spectrum dynamics over sliding time windows. By examination of the eigenspectrum, we show that these approaches enable detection of major events in the time SenseCam recording, with MODWT also providing useful insight on details of major events. We suggest that some wavelet scales (e.g., 8 minutes–16 minutes) have the potential to identify distinct events or activities.

A new algorithm named dynamic graph merging (DGM) for automatic image segmentation is explored. Firstly a novel variational model for multi-section cut is introduced by decomposing the traditional cut into two parts, the harmonic cut and the elastic energy of the boundary. The new energy is called the continuous combined cut. Secondly a new algorithm that removes those edges with higher energy and synchronously merges their starting and ending vertices in an ordered manner is proposed. The continual merging process would iteratively contract the graph, merge those homogeneous vertices into bigger and bigger super-pixels, and fuse the remainder edges into longer and longer boundaries. So we call this algorithm dynamic graph merging. Merging criterions based on the continuous combined cut model are also discussed, which will be used to determine whether a given edge should collapse. Since the merging condition should be highly related to the image content, we present different predicates for structure images and texture images respectively. This algorithm whose efficiency is showed by experiments has a linear time/space complexity, and can efficiently segment gray/color and 2D/3D images.