L1-Norm Distance Discriminant Analysis with Multiple Adaptive Graphs and Sample Reconstruction

Linear discriminant analysis (LDA) is sensitive to noise and its performance may decline greatly. Recursive discriminative subspace learning method with an L1-norm distance constraint (RDSL) formulates LDA with the maximum margin criterion and becomes robust to noise by applying L1-norm and slack variables. However, the method only considers inter-class separation and intra-class compactness and ignores the intra-class manifold structure and the global structure of data. In this paper, we present L1-norm distance discriminant analysis with multiple adaptive graphs and sample reconstruction (L1-DDA) to deal with the problem. We use multiple adaptive graphs to preserve intra-class manifold structure and simultaneously apply the sample reconstruction technique to preserve the global structure of data. Moreover, we use an alternating iterative technique to obtain projection vectors. Experimental results on three real databases demonstrate that our method obtains better classification performance than RDSL.

Cutting L1-Norm Distance Discriminant Analysis with Sample Reconstruction

Dimensionality reduction plays an important role in the fields of pattern recognition and computer vision. Recursive discriminative subspace learning with an L1-norm distance constraint (RDSL) is proposed to robustly extract features from contaminated data and L1-norm and slack variables are utilized for accomplishing the goal. However, its performance may decline when too many outliers are available. Moreover, the method ignores the global structure of the data. In this paper, we propose cutting L1-norm distance discriminant analysis with sample reconstruction (C-L1-DDA) to solve the two problems. We apply cutting L1-norm to measure within-class and between-class distances and thus outliers may be strongly suppressed. Moreover, we use cutting squared L2-norm to measure reconstruction errors. In this way, outliers may be constrained and the global structure of data may be approximately preserved. Finally, we give an alternating iterative algorithm to extract feature vectors. Experimental results on two publicly available real databases verify the feasibility and effectiveness of the proposed method.

Prediction Model of Collapse Risk Based on Information Entropy and Distance Discriminant Analysis Method

The prediction and risk classification of collapse is an important issue in the process of highway construction in mountainous regions. Based on the principles of information entropy and Mahalanobis distance discriminant analysis, we have produced a collapse hazard prediction model. We used the entropy measure method to reduce the influence indexes of the collapse activity and extracted the nine main indexes affecting collapse activity as the discriminant factors of the distance discriminant analysis model (i.e., slope shape, aspect, gradient, and height, along with exposure of the structural face, stratum lithology, relationship between weakness face and free face, vegetation cover rate, and degree of rock weathering). We employ postearthquake collapse data in relation to construction of the Yingxiu-Wolong highway, Hanchuan County, China, as training samples for analysis. The results were analyzed using the back substitution estimation method, showing high accuracy and no errors, and were the same as the prediction result of uncertainty measure. Results show that the classification model based on information entropy and distance discriminant analysis achieves the purpose of index optimization and has excellent performance, high prediction accuracy, and a zero false-positive rate. The model can be used as a tool for future evaluation of collapse risk.

DFT-Based on Mahalanobis Distance Discriminant Analysis Method Channel Estimation Algorithm for OFDM Systems

An enhanced discrete Fourier transform DFT-based channel estimation for OFDM systems is proposed. Conventional DFT-based channel estimations improve the performance by suppressing time domain noise. However, they potentially require information on channel impulse responses and may also result in mean-square error (MSE) floor due to incorrect channel information such as channel delay spread. In order to overcome the disadvantage, our proposed channel estimation can improve the performance by deciding significant channel taps adaptively. Significant channel taps are detected on the basis of Mahalanobis distance discriminant analysis. Simulation results demonstrate that the proposed algorithm outperforms the conventional DFT-based estimation in terms of BER and MSE performance.

Instability Identification of Goaf Risky in Mines Based on Distance Discriminant Analysis Method

The instability identification of goaf risky is an important work in the mine engineering. Based on distance discriminant analysis, a method to identify the instability of goaf risky in mines was presented in this paper. Nine factors influencing the stability of goaf risky, including uniaxial compressive strength of rock, elastic modulus of rock, rock quality designation (RQD), area ration of pillar, ratio of width to height of pillar, depth of ore body, volume of goaf, dip of ore body and area of goaf, were selected as discriminant indexes in the stability analysis of goaf. The actual data of 40 goafs were used as training samples to establish a discriminant analysis model to identify the stability of goaf. The results show that this discriminant analysis model has high precision and misdiscriminant ratio is 0.025 in re-substitution process. The instability identification of a metal mine was discriminanted by using this model and the identification result is identical with that of practical situation.