International Journal of Wavelets, Multiresolution and Information Processing

In recent years, data mining has raised some issues related to the privacy of individuals. Due to these issues, data owners abstain to share their sensitive information with data miners. Thus, privacy preserving data mining (PPDM) techniques have been introduced. One of these techniques is for data hiding purpose, which depending on the type of privacy problems can be categorized as follows: (1) Perturbation of the original sensitive data before delivering to the data miners and (2) anonymization of the entities before publishing the data. In this paper, we propose a new technique for privacy preserving clustering (PPC) over centralized databases that belongs to the first category. The proposed technique uses Haar wavelet transform and scaling data perturbation to provide both data hiding and data reduction to protect the underlying numerical attributes subjected to clustering analysis. We present extensive experimental results for the proposed technique. Our experimental evaluations demonstrated that the proposed technique is effective and find a good tradeoff between clustering quality, data privacy, and data reduction. We will present the results of the comparison of the proposed technique with other existing PPC techniques. We will also present a formal description of the proposed technique and its privacy analysis, which proves its security.

Translation and convolution associated with the discrete wavelet transform are investigated using properties of Calderón–Zygmund operator and Riesz fractional integral operator. Dual convolution is also studied. The wavelet convolution is applied to approximate functions belonging to certain L^p-spaces.

This paper presents a new approach of face recognition based on wavelet network using 2D fast wavelet transform and multiresolution analysis. This approach is divided in two stages: the training stage and the recognition stage. The first consists to approximate every training face image by a wavelet network. The second consists in recognition of a new test image by comparing it to all the training faces, the distances between this test face and all images from the training set are calculated in order to identify the searched person. The usual training algorithms presents some disadvantages when the weights of the wavelet network are computed by applying the back-propagation algorithm or by direct solution which requires computing an inversion of matrix, this computation may be intensive when the learning data is too large. We present in this paper our solutions to overcome these limitations. We propose a novel learning algorithm based on the 2D Fast Wavelet Transform. Furthermore, we have increased the performances of our algorithm by introducing the Levenberg–Marquardt method to optimize the learning functions and using the Beta wavelet which has at both an analytical expression and wavelet filter bank. Extensive empirical experiments are performed to compare the proposed method with other approaches as PCA, LDA, EBGM and RBF neural network using the ORL and FERET benchmarks.

In this paper, we introduce dual g-frames for a closed subspace in a separable Hilbert space and also give a characterization. Generally dual g-frames for a closed subspace are non-commutative. Therefore, we construct dual g-frames for closed subspaces from two aspects and give the corresponding formulas, respectively. Finally, we give a necessary and sufficient condition for commutative dual g-frame pairs for closed subspaces under certain conditions.

In this paper, a multifractal analysis of some non-self-similar functions based on the superposition of finite number of weighted quasi-self-similar ones ∑_iω_iF_i is developed. In general, such superpositions do not yield neither a self-similar nor a quasi-self-similar outcome. Furthermore, there are two main problems that appear. Firstly, a phenomenon of regularity compensation may exist. Secondly, the computation of the spectrum of singularities and therefore the validity of the multifractal formalism based on the possibility of constructing Gibbs measures fail. In this paper, we propose to study such problems by conducting a multifractal analysis of such combinations and to check the validity of the multifractal formalism in the case where there is no compensation of regularity. Furthermore, we compute the box dimension of the associated graphs and provide some examples. The paper in its full subject re-considers the results of Ref. 3 in the quasi-self-similar case.

In this paper, we construct a nonlinear wavelet estimator of conditional density function for a left truncation model. We provide an asymptotic expression for the mean integrated squared error (MISE) of the estimator. It is assumed that the lifetime observations form a stationary α-mixing sequence. Unlike for kernel estimator, the MISE expression of the nonlinear wavelet estimator is not affected by the presence of discontinuities in the curves.

This paper proposes a novel method for classification using rank-1 tensor projection via regularized regression to directly map tensor example to its corresponding label, which is different from the general procedure of classification on the compact representation of the original data. Action can be naturally considered as a third-order tensor, where the first two dimensions represent the space and the third one is temporal. By applying this method to multi-label action classification based on problem transformation and subset embedding technique, we obtain the comparable results to the state-of-the-art approaches on the popular action datasets Weizmann and KTH. Our experimental results are also considerably robust to the viewpoint changes, the partial occlusion and the irregularities in the motion styles.