scholarly journals Cutting L1-Norm Distance Discriminant Analysis with Sample Reconstruction

2021 ◽  
Author(s):  
Guowan Shao ◽  
Chunjiang Peng ◽  
Wenchu Ou ◽  
Kai Duan

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.

2021 ◽  
Author(s):  
Guowan Shao ◽  
Chunjiang Peng ◽  
Wenchu Ou ◽  
Kai Duan

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.


2020 ◽  
Vol 50 (5) ◽  
pp. 2138-2151 ◽  
Author(s):  
Dong Zhang ◽  
Yunlian Sun ◽  
Qiaolin Ye ◽  
Jinhui Tang

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 2884 ◽  
Author(s):  
Xiaobo Chen ◽  
Cheng Chen ◽  
Yingfeng Cai ◽  
Hai Wang ◽  
Qiaolin Ye

The problem of missing values (MVs) in traffic sensor data analysis is universal in current intelligent transportation systems because of various reasons, such as sensor malfunction, transmission failure, etc. Accurate imputation of MVs is the foundation of subsequent data analysis tasks since most analysis algorithms need complete data as input. In this work, a novel MVs imputation approach termed as kernel sparse representation with elastic net regularization (KSR-EN) is developed for reconstructing MVs to facilitate analysis with traffic sensor data. The idea is to represent each sample as a linear combination of other samples due to inherent spatiotemporal correlation, as well as periodicity of daily traffic flow. To discover few yet correlated samples and make full use of the valuable information, a combination of l1-norm and l2-norm is employed to penalize the combination coefficients. Moreover, the linear representation among samples is extended to nonlinear representation by mapping input data space into high-dimensional feature space, which further enhances the recovery performance of our proposed approach. An efficient iterative algorithm is developed for solving KSR-EN model. The proposed method is verified on both an artificially simulated dataset and a public road network traffic sensor data. The results demonstrate the effectiveness of the proposed approach in terms of MVs imputation.


Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3373 ◽  
Author(s):  
Ziran Wei ◽  
Jianlin Zhang ◽  
Zhiyong Xu ◽  
Yongmei Huang ◽  
Yong Liu ◽  
...  

In the reconstruction of sparse signals in compressed sensing, the reconstruction algorithm is required to reconstruct the sparsest form of signal. In order to minimize the objective function, minimal norm algorithm and greedy pursuit algorithm are most commonly used. The minimum L1 norm algorithm has very high reconstruction accuracy, but this convex optimization algorithm cannot get the sparsest signal like the minimum L0 norm algorithm. However, because the L0 norm method is a non-convex problem, it is difficult to get the global optimal solution and the amount of calculation required is huge. In this paper, a new algorithm is proposed to approximate the smooth L0 norm from the approximate L2 norm. First we set up an approximation function model of the sparse term, then the minimum value of the objective function is solved by the gradient projection, and the weight of the function model of the sparse term in the objective function is adjusted adaptively by the reconstruction error value to reconstruct the sparse signal more accurately. Compared with the pseudo inverse of L2 norm and the L1 norm algorithm, this new algorithm has a lower reconstruction error in one-dimensional sparse signal reconstruction. In simulation experiments of two-dimensional image signal reconstruction, the new algorithm has shorter image reconstruction time and higher image reconstruction accuracy compared with the usually used greedy algorithm and the minimum norm algorithm.


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