A Comparative Study: L1-Norm Vs. L2-Norm; Point-to-Point Vs. Point-to-Line Metric; Evolutionary Computation Vs. Gradient Search

2015 ◽  
Vol 29 (2) ◽  
pp. 164-210 ◽  
Author(s):  
J. Moravec
Keyword(s):  
Comparative Study ◽  
Evolutionary Computation ◽  
Gradient Search ◽  
L1 Norm ◽  
L2 Norm ◽  
Point To Point

scholarly journals Kernel Sparse Representation with Hybrid Regularization for On-Road Traffic Sensor Data Imputation

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 2884 ◽  
Author(s):  
Xiaobo Chen ◽  
Cheng Chen ◽  
Yingfeng Cai ◽  
Hai Wang ◽  
Qiaolin Ye
Keyword(s):  
Data Analysis ◽  
Sparse Representation ◽  
Intelligent Transportation Systems ◽  
Missing Values ◽  
Road Traffic ◽  
Linear Representation ◽  
Transportation Systems ◽  
Sensor Data ◽  
L1 Norm ◽  
L2 Norm

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.

scholarly journals Gradient Projection with Approximate L0 Norm Minimization for Sparse Reconstruction in Compressed Sensing

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3373 ◽  
Author(s):  
Ziran Wei ◽  
Jianlin Zhang ◽  
Zhiyong Xu ◽  
Yongmei Huang ◽  
Yong Liu ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Objective Function ◽  
Signal Reconstruction ◽  
Reconstruction Error ◽  
Sparse Signal ◽  
Reconstruction Accuracy ◽  
L1 Norm ◽  
Function Model ◽  
L2 Norm

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.

scholarly journals Cardiac Activation Maps Reconstruction: A Comparative Study Between Data-Driven and Physics-Based Methods

2021 ◽  
Vol 12 ◽  
Author(s):  
Amel Karoui ◽  
Mostafa Bendahmane ◽  
Nejib Zemzemi
Keyword(s):  
Neural Networks ◽  
Comparative Study ◽  
Body Surface ◽  
Data Driven ◽  
Diagnostic Tools ◽  
L1 Norm ◽  
Surface Potentials ◽  
Body Surface Potential ◽  
Data Driven Approach ◽  
Classic Technique

One of the essential diagnostic tools of cardiac arrhythmia is activation mapping. Noninvasive current mapping procedures include electrocardiographic imaging. It allows reconstructing heart surface potentials from measured body surface potentials. Then, activation maps are generated using the heart surface potentials. Recently, a study suggests to deploy artificial neural networks to estimate activation maps directly from body surface potential measurements. Here we carry out a comparative study between the data-driven approach DirectMap and noninvasive classic technique based on reconstructed heart surface potentials using both Finite element method combined with L1-norm regularization (FEM-L1) and the spatial adaptation of Time-delay neural networks (SATDNN-AT). In this work, we assess the performance of the three approaches using a synthetic single paced-rhythm dataset generated on the atria surface. The results show that data-driven approach DirectMap quantitatively outperforms the two other methods. In fact, we observe an absolute activation time error and a correlation coefficient, respectively, equal to 7.20 ms, 93.2% using DirectMap, 14.60 ms, 76.2% using FEM-L1 and 13.58 ms, 79.6% using SATDNN-AT. In addition, results show that data-driven approaches (DirectMap and SATDNN-AT) are strongly robust against additive gaussian noise compared to FEM-L1.

scholarly journals Comparative Study of the L1 Norm Regression Algorithms

2019 ◽  
Vol 1 (1) ◽  
pp. 31-40
Author(s):  
Bijan Bidabad
Keyword(s):  
Comparative Study ◽  
Comparative Studies ◽  
L1 Norm ◽  
Comparative Efficiency ◽  
Regression Algorithms

This paper tries to compare more accurate and efficient L1 norm regression algorithms. Other comparative studies are mentioned, and their conclusions are discussed. Many experiments have been performed to evaluate the comparative efficiency and accuracy of the selected algorithms.  

scholarly journals A comparative study of particle swarm optimization and genetic algorithm

2019 ◽  
Vol 8 (2) ◽  
pp. 40
Author(s):  
Saman M. Almufti ◽  
Amar Yahya Zebari ◽  
Herman Khalid Omer
Keyword(s):  
Genetic Algorithm ◽  
Particle Swarm Optimization ◽  
Comparative Study ◽  
Evolutionary Computation ◽  
Particle Swarm ◽  
Swarm Optimization ◽  
Computation Algorithms ◽  
Crossover And Mutation

This paper provides an introduction and a comparison of two widely used evolutionary computation algorithms: Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) based on the previous studies and researches. It describes Genetic Algorithm basic functionalities including various steps such as selection, crossover, and mutation.  

Quantile and Expectile Smoothing based on L1-norm and L2-norm F-transforms

2018 ◽  
Author(s):  
Maria Letizia Guerra ◽  
Luciano Stefanini ◽  
Laerte Sorini
Keyword(s):  
L1 Norm ◽  
L2 Norm
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