Graph signal processing (GSP) is an emerging field in the signal processing community. Novel GSP-based transforms, such as graph Fourier transform and graph wavelet filter banks, have been successfully utilized in image processing and pattern recognition. As a rapidly developing research area, graph signal processing aims to extend classical signal processing techniques to signals with irregular underlying structures. One of the hot topics in GSP is to develop multi-scale transforms such that novel GSP-based techniques can be applied in image processing or other related areas. For designing graph signal multi-scale frameworks, downsampling operations that ensuring multi-level downsampling should be specifically constructed. Among the existing downsampling methods in graph signal processing, the state-of-the-art method was constructed based on the maximum spanning tree (MST). However, when using this method for multi-level downsampling of graph signals defined on unweighted densely connected graphs, such as social network data, the sampling rates are not close to [Formula: see text]. This phenomenon is summarized as a new problem and called downsampling unbalance problem in this paper. Due to the unbalance, MST-based downsampling method cannot be applied to construct graph signal multi-scale transforms. In this paper, we propose a novel and efficient method to detect and reduce the downsampling unbalance generated by the MST-based method. For any given graph signal, we apply the graph density to construct a measurement of the downsampling unbalance generated by the MST-based method. If a graph signal has large unbalance possibility, the multi-level downsampling is conducted after the MST is improved. The experimental results on synthetic and real-world social network data show that downsampling unbalance can be efficiently detected and then reduced by our method.

Representation-based classification (RC) methods such as sparse RC (SRC) have attracted great interest in pattern recognition recently. Despite their empirical success, few theoretical results are reported to justify their effectiveness. In this paper, we establish the theoretical guarantees for a general unified framework termed as atomic representation-based classification (ARC), which includes most RC methods as special cases. We introduce a new condition called atomic classification condition (ACC), which reveals important geometric insights for the theory of ARC. We show that under such condition ARC is provably effective in correctly recognizing any new test sample, even corrupted with noise. Our theoretical analysis significantly broadens the range of conditions under which RC methods succeed for classification in the following two aspects: (1) prior theoretical advances of RC are mainly concerned with the single SRC method while our theory can apply to the general unified ARC framework, including SRC and many other RC methods; and (2) previous works are confined to the analysis of noiseless test data while we provide theoretical guarantees for ARC using both noiseless and noisy test data. Numerical results are provided to validate and complement our theoretical analysis of ARC and its important special cases for both noiseless and noisy test data.

A improved swarm optimization method based on particle swarm optimization (PSO) and simplified swarm optimization (SSO) is proposed to adjust the weight in artificial neural network. This method is a modification of traditional PSO and SSO, and combines them to a new optimization method (PSOSSO for short). The proposed method overcomes some of the drawbacks of SSO and improves its ability to train the weight of ANN. In the experiments, the PSOSSO is employed to train fuzzy wavelet neural network (FWNN) forecasting model to predict the prices of Hong Kong Hang Seng Index. The experimental results present that the PSOSSO is more efficient than traditional PSO and SSO methods.

This paper proposes an adaptive multiscale decomposition algorithm for graph signals. We develop two types of graph signal cost functions: α-sparsity functional and graph signal entropies, to capture the energy compaction of the signal components. The adaptive decomposition can then be constructed by applying a minimum cost constraint during the full subband decomposition. The proposed adaptive decomposition is shown to outperform graph wavelet decomposition in compressing nonpiecewise constant graph signals.

This paper presents a new method for texture analysis through Bidimensional Empirical Mode Decomposition (BEMD). Although there have been many filter based methods for texture analysis, problems of non-adaptively and redundancy are still hard to solve. The BEMD is a locally adaptive method and suitable for the analysis of nonlinear or nonstationary signals. The texture image can be decomposed to several IMFs (intrinsic mode functions) by BEMD, which present new characters of the images. But for the BEMD, the boundary interference is a main limit for its application. In this paper, we proposed a new BEMD method based on the self-similar extend method and the neighbor local extremes to reduce the boundary interference. This new method can get a lower orthogonality index (OI) of the IMF, which present more clearly features of the texture images. The experiment result shown the new method also reduced the computation complex compared to other surface interpolation based methods.

Hilbert-Huang transform (HHT) is a novel signal processing method which can efficiently handle non-stationary and nonlinear signals. Two key parts are included: Empirical Mode Decomposition (EMD) and Hilbert transform. EMD decomposes signals into a complete series of Intrinsic Mode Functions (IMFs), which capture the intrinsic frequency components of the original signals. Hilbert transform is adopted on the IMFs to get the analytical local features. Due to its efficiency in signal processing, the bidimensional version has been studied for the advanced image processing. EMD has been extended to bidimensional EMD (BEMD), and the corresponding monogenic signals are studied. Phase information is an important local feature of signals in frequency domain because it is robust to contrast, brightness, noise, shading in the image. The quantity Phase congruency (PC) is invariant to changes in image illumination. In this paper, we firstly proposed an improved BEMD method based on the novel evaluation of local mean, then the Riesz transform is applied to get the corresponding monogenic signals. Finally, PC was calculated based on the new phase information and it then has been adopted as facial features to classify faces under variant illumination conditions. The experimental results demonstrated the efficiency of the proposed approach.

Aiming for the problem of falling into local optimum when searching for the optimal threshold of the image using normal genetic algorithm, this paper presents a new method based on the maximal variance and improved genetic algorithm to segment the face image. This new method uses the maximal variance of the face gray image as the fitness and changes the problem of image segmentation into a problem of optimization. Adopting genetic algorithm which is characteristic of robustness and adaptability can increase efficiency. As a result, this new method can obtain the optimal segmentation result when applied to different face images. Experiments show that using this method to search for the global threshold can converge the optimal value and decrease the searching time

Research on the interference within the face aiming at face complexity when locating the face, this paper advances a new algorithm of multiple-step hiding genetic algorithm to locate the face. This algorithm searches for intermediate locating parameters through genetic algorithm and parameterized deformable ellipse template, locates a hiding region based on the parameter and hides this region. On the basis of the hided image, searching for the next hiding region until finding the optimal region, and locate the contour ultimately based on the processing region. This algorithm can solve the interference within the face effectively when searching the face edge adopting genetic algorithm. Experimental results show that this method can obtain a satisfied result in the interference killing feature and stability.