Jiangzhong Cao

Local information-based fast approximate spectral clustering

Spectral clustering has become one of the most popular clustering approaches in recent years. However, its high computational complexity prevents its application to large-scale datasets. To address this complexity, approximate spectral clustering methods have been proposed. In these methods, computational costs are reduced by using approximation techniques, such as the Nystrom method, or by constructing a smaller representative dataset on which spectral clustering is performed. However, the computational efficiency of these approximation methods is achieved at the cost of performance degradation. In this paper, we propose an efficient approximate spectral clustering method in which clustering performance is improved by utilizing local information among the data, while the scalability to the large-scale datasets is retained. Specifically, we improve the approximate spectral clustering method in two aspects. First, a sparse affinity graph is adopted to improve the performance of spectral clustering on the small representative dataset. Second, local interpolation is utilized to improve the extension of the clustering result. Experiments are conducted on several real-world datasets, showing that the proposed method is efficient and outperforms the state-of-the-art approximate spectral clustering algorithms.

Optimal Design of Cosine Modulated Nonuniform Linear Phase FIR Filter Bank via Both Stretching and Shifting Frequency Response of Single Prototype Filter

This paper designs an optimal cosine modulated nonuniform linear phase finite impulse response (FIR) filter bank. The frequency responses of all the analysis filters and the synthesis filters of the filter bank are derived based on both stretching and shifting the frequency response of a single prototype filter. The total aliasing error of the filter bank is minimized subject to specifications on the maximum magnitude distortion of the filter bank and the maximum ripple magnitudes of the prototype filter over both the passband and the stopband. This paper proposes a joint constraint transcription and modified filled function method for solving the optimization problem. In particular, the functional inequality constraints are converted to discrete constraints via the constraint transcription method. The globally optimal solution of the nonconvex optimization problem can be found efficiently via the modified filled function method. Computer numerical simulation results show that our design outperforms existing designs.

Optimal design of Hermitian transform and vectors of both mask and window coefficients for denoising applications with both unknown noise characteristics and distortions

This paper proposes an optimal design of a Hermitian transform and vectors of both mask and window coefficients for denoising signals with both unknown noise characteristics and distortions. The signals are represented in the vector form. Then, they are transformed to a new domain via multiplying these vectors to a Hermitian matrix. A vector of mask coefficients is point by point multiplied to the transformed vectors. The processed vectors are transformed back to the time domain. A vector of window coefficients is point by point multiplied to the processed vectors. An optimal design of the Hermitian matrix and the vectors of both mask and window coefficients is formulated as a quadratically constrained programming problem subject to a Hermitian constraint. By initializing the window coefficients, the Hermitian matrix and the vector of mask coefficients are derived via an orthogonal Procrustes approach. Based on the obtained Hermitian matrix and the vector of mask coefficients, the vector of window coefficients is derived. By iterating these two procedures, the final Hermitian matrix and the vectors of both mask and window coefficients are obtained. The convergence of the algorithm is guaranteed. The proposed method is applied to denoise both clinical electrocardiograms and electromyograms as well as speech signals with both unknown noise characteristics and distortions. Experimental results show that the proposed method outperforms existing denoising methods.

Optimal joint design of orthonormal real valued short time block code and linear transceiver

The main contribution of this paper is to propose an optimal joint design of an orthonormal real valued short time block code and a linear transceiver for multi-input multi-output (MIMO) wireless digital communication systems in next generation home. Firstly, a relaxed zero forcing condition governing the relationship between the short time block code and the linear transceiver is imposed via a Karhunen Loève transform (KLT) approach. The relaxed zero forcing condition guarantees that there is no transmission error under a noise free environment. Secondly, the linear transceiver is optimally designed via the orthogonal Procrustes approach. In particular, the transmission power gain is minimised subject to a specification on the ratio of the signal gain to the noise gain as well as to the relaxed zero forcing condition. Computer numerical simulation results show that our proposed optimal joint design of the orthonormal real valued short time block code and the linear transceiver can significantly improve the performances of MIMO wireless digital communication systems in next generation home.

Image Retrieval Based on Discrete Fractional Fourier Transform Via Fisher Discriminant

Discrete fractional Fourier transform (DFrFT) is a powerful signal processing tool. This paper proposes a method for DFrFT-based image retrieval via Fisher discriminant and 1-NN classification rule. First, this paper proposes to extend the conventional discrete Fourier transform (DFT) descriptors to the DFrFT descriptors to be used for representing the edges of images. The DFrFT descriptors extracted from the training images are employed to construct a dictionary, for which the corresponding optimal rotational angles of the DFrFTs are required to be determined. This dictionary design problem is formulated as an optimization problem, where the Fisher discriminant is the objective function to be minimized. This optimization problem is nonconvex (Guan et al. in IEEE Trans Image Process 20(7):2030–2048, 2011; Ho et al. in IEEE Trans Signal Process 58(8):4436–4441, 2010). Furthermore, both the intraclass separation and interclass separation of the DFrFT descriptors are independent of the rotational angles if these separations are defined in terms of the 2-norm operator. To tackle these difficulties, the 1-norm operator is employed. However, this reformulated optimization problem is nonsmooth. To solve this problem, the nondifferentiable points of the objective function are found. Then, the stationary points between any two consecutive nondifferentiable points are identified. The objective function values are evaluated at these nondifferentiable points and these stationary points. The smallest L objective function values are picked up and the corresponding rotational angles are determined, which are then used to construct the dictionary. Here, L is the total number of the rotational angles of the DFrFTs used to construct the dictionary. Finally, an 1-NN classification rule is applied to perform the image retrieval. Application examples and experimental results show that our proposed method outperforms the conventional DFT approach.

Efficient method for finding globally optimal solution of problem with weighted Lp norm and L 2 norm objective function

This study proposes an iterative method to approximate an N-dimensional optimisation problem with a weighted L p and L 2 norm objective function by a sequence of N independent one-dimensional optimisation problems. Inspired by the existing weighted L 1 and L 2 norm separable surrogate functional (SSF) iterative shrinkage algorithm, there are N independent one-dimensional optimisation problems with weighted L p and L 2 norm objective functions. However, these optimisation problems are non-convex. Hence, they may have more than one locally optimal solutions and it is very difficult to find their globally optimal solutions. This paper proposes to partition the feasible set of each approximated problem into various regions such that the sign of the convexity of the objective function in each region remains unchanged. Here, there is no more than one stationary point in each region. By finding the stationary point in each region, the globally optimal solution of each approximated optimisation problem can be found. Besides, this study also shows that the sequence of the globally optimal solutions of the approximated problems converge to the globally optimal solution of the original optimisation problem. Computer numerical simulation results show that the proposed method outperforms the existing weighted L 1 and L 2 norm SSF iterative shrinkage algorithm.

k-NN graph construction based on markov random walk

k-nearest-neighbors (k-NN) graphs are widely used in image retrieval, machine learning and other research fields. Selecting its neighbors is a core for constructing the k-NN graph. However, existing selection methods usually encounter some unreliable neighbors in the k-NN graph. This paper proposes an efficient Markov random walk (MRW) based method for selecting more reliable neighbors for constructing the k-NN graph. The MRW model is defined on the raw k-NN graph. The k-NN of a sample is determined by the probability of the MRW. Since the high order transition probabilities reflects complex relationships among data, the neighbors in the graph obtained by our proposed method are more reliable than those of existing methods. Also, our proposed method can improve the performances of some applications with k-NN graph. Experiments are performed on the synthetic and real datasets for comparison. The results show that the graph obtained by our proposed method better correspond to the structure of the data compared to those of the state-of-the-art methods.

Spectral Clustering with Sparse Graph Construction Based on Markov Random Walk

Spectral clustering has become one of the most popular clustering approaches in recent years. Similarity graph constructed on the data is one of the key factors that influence the performance of spectral clustering. However, the similarity graphs constructed by existing methods usually contain some unreliable edges. To construct reliable similarity graph for spectral clustering, an efficient method based on Markov random walk (MRW) is proposed in this paper. In the proposed method, theMRW model is defined on the raw k-NN graph and the neighbors of each sample are determined by the probability of the MRW. Since the high order transition probabilities carry complex relationships among data, the neighbors in the graph determined by our proposed method are more reliable than those of the existing methods. Experiments are performed on the synthetic and real-world datasets for performance evaluation and comparison. The results show that the graph obtained by our proposed method reflects the structure of the data better than those of the state-of-the-art methods and can effectively improve the performance of spectral clustering.

Efficient method for solving one norm equality constrained problem

The paper proposes an efficient method for solving a one norm equality constrained optimization problem. In fact, this kind of optimization problems is nonconvex. First, the problem is formulated as the least absolute shrinkage and selection operator (LASSO) optimization problem. Then, it is solved by iterative shrinkage algorithms such as the fast iterative shrinkage thresholding algorithm (FISTA). Next, the solution of the LASSO optimization problem is employed for formulating the constraint of the corresponding least squares constrained optimization problem. The solution of the least squares constrained optimization problem is taken as a near globally optimal solution of the one norm equality constrained optimization problem. Computer numerical simulation results show that our proposed method outperforms existing methods in terms of the accuracy of the obtained solution satisfying the one norm equality constraint.

Optimal joint design of orthonormal real valued short time block code and linear transceiver for next generation home

The main contribution of this paper is to propose an optimal joint design of an orthonormal real valued short time block code and a linear transceiver for multi-input multi-output (MIMO) wireless digital communication systems in next generation home. Firstly, a relaxed zero forcing condition governing the relationship between the short time block code and the linear transceiver is imposed via a Karhunen Loeve transform (KLT) approach. The relaxed zero forcing condition guarantees that there is no transmission error under a noise free environment. Secondly, the linear transceiver is optimally designed via the orthogonal Procrustes approach. In particular, the transmission power gain is minimised subject to a specification on the ratio of the signal gain to the noise gain as well as to the relaxed zero forcing condition. Computer numerical simulation results show that our proposed optimal joint design of the orthonormal real valued short time block code and the linear transceiver can significantly improve the performances of MIMO wireless digital communication systems in next generation home.