Alignments, Topologies, Convex Geometries and Higgs Spaces

Aligned spaces generalize topological spaces and generate Higgs spaces. We give a necessary and sufficient condition for a finite aligned space to be a topological space, we prove the existence of two kinds of convex geometries, and we compare several concepts and results for arbitrary （that is, not necessarily finite） aligned, topological and Higgs spaces.

A Short Note on Compactness in Aligned Spaces and Higgs Spaces

We generalize to aligned spaces and to Higgs spaces the concept of compact topological spaces.

On Boolean Functions Associated to Finite Aligned Spaces

Boolean or switching functions can be associated to finite aligned spaces in a way similar to the way they can be associated to finite topological spaces. We prove a characterization of switching functions associated to aligned spaces which is similar to the one we have given for switching functions associated to finite topological spaces.

Feature Extraction of Kernel Regress Reconstruction for Fault Diagnosis Based on Self-organizing Manifold Learning

The feature space extracted from vibration signals with various faults is often nonlinear and of high dimension.Currently,nonlinear dimensionality reduction methods are available for extracting low-dimensional embeddings,such as manifold learning.However,these methods are all based on manual intervention,which have some shortages in stability,and suppressing the disturbance noise.To extract features automatically,a manifold learning method with self-organization mapping is introduced for the first time.Under the non-uniform sample distribution reconstructed by the phase space,the expectation maximization(EM) iteration algorithm is used to divide the local neighborhoods adaptively without manual intervention.After that,the local tangent space alignment(LTSA) algorithm is adopted to compress the high-dimensional phase space into a more truthful low-dimensional representation.Finally,the signal is reconstructed by the kernel regression.Several typical states include the Lorenz system,engine fault with piston pin defect,and bearing fault with outer-race defect are analyzed.Compared with the LTSA and continuous wavelet transform,the results show that the background noise can be fully restrained and the entire periodic repetition of impact components is well separated and identified.A new way to automatically and precisely extract the impulsive components from mechanical signals is proposed.

Orthogonal Discriminant Improved Local Tangent Space Alignment Based Feature Fusion for Face Recognition

Improved local tangent space alignment (ILTSA) is a recent nonlinear dimensionality reduction method which can efficiently recover the geometrical structure of sparse or non-uniformly distributed data manifold. In this paper, based on combination of modified maximum margin criterion and ILTSA, a novel feature extraction method named orthogonal discriminant improved local tangent space alignment (ODILTSA) is proposed. ODILTSA can preserve local geometry structure and maximize the margin between different classes simultaneously. Based on ODILTSA, a novel face recognition method which combines augmented complex wavelet features and original image features is developed. Experimental results on Yale, AR and PIE face databases demonstrate the effectiveness of ODILTSA and the feature fusion method.

High dimension feature extraction based visualized SOM fault diagnosis method and its application in p-xylene oxidation process

Purified terephthalic acid(PTA) is an important chemical raw material. P-xylene(PX) is transformed to terephthalic acid(TA) through oxidation process and TA is refined to produce PTA. The PX oxidation reaction is a complex process involving three-phase reaction of gas, liquid and solid. To monitor the process and to improve the product quality, as well as to visualize the fault type clearly, a fault diagnosis method based on selforganizing map(SOM) and high dimensional feature extraction method, local tangent space alignment(LTSA),is proposed. In this method, LTSA can reduce the dimension and keep the topology information simultaneously,and SOM distinguishes various states on the output map. Monitoring results of PX oxidation reaction process indicate that the LTSA–SOM can well detect and visualize the fault type.

Interference cancellation method based on space-time code for MIMO interference channel

We investigate how to cancel interference by using space time code and codeword space alignment for multiple-input multiple-output （MIMO） Y channel consisting of three users and a relay. All the nodes adopt Alamouti code. During the multiple access （MA） stage, two codewords within each reciprocal codeword pair are aligned through pre-coding. The relay decodes the elements of each codeword pair using the orthogonal property of effective channel matrix of Alamouti codeword. During the broadcast （BC） stage, the interference between codeword pairs at each user is eliminated by the orthogonal property of effective channel matrix of Alamouti codeword, instead of the interference alignment （IA） pre-coding. Thus, channel state information （CSI） is not required during the BC stage, which greatly reduce the amount of feedback.

Blind false data injection attacks in smart grids subject to measurement outliers

False data injection attacks(FDIAs)can manipulate measurement data from Supervisory Control and Data Acquisition(SCADA)system and threat state estimation in smart grids.Blind FDIAs(BFDIAs)enhance traditional FDIAs,which eliminate the limitation of grasping measurement Jacobian matrix H in advance,but when there are outliers in measurement data,attack performance is degraded.In this paper,improved BFDIAs are proposed.In off-line phase,lowdimensional measurement matrix without outliers calculated by Linear Local Tangent Space Alignment algorithm(LLTSA)is sent into Continuous Deep Belief Network(CDBN)as training data to learn their probability distribution.In on-line phase,real-time low-dimensional measurement matrix with outliers are sent into the trained model as inputs,and outputs are reconstructed by the probability distribution in off-line phase,which eliminates the influence of outliers indirectly.Simulations are implemented on PJM 5-bus and IEEE 14-bus systems to verify the performance of proposed strategy compared with PCA-based BFDIAs.