scholarly journals RobOMP: Robust variants of Orthogonal Matching Pursuit for sparse representations

2019 ◽  
Vol 5 ◽  
pp. e192 ◽  
Author(s):  
Carlos A. Loza
Keyword(s):  
Mean Squared Error ◽  
Matching Pursuit ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Parameter Tuning ◽  
Weight Vector ◽  
Orthogonal Matching Pursuit ◽  
Main Mode ◽  
Observation Matrix ◽  
And Performance

Sparse coding aims to find a parsimonious representation of an example given an observation matrix or dictionary. In this regard, Orthogonal Matching Pursuit (OMP) provides an intuitive, simple and fast approximation of the optimal solution. However, its main building block is anchored on the minimization of the Mean Squared Error cost function (MSE). This approach is only optimal if the errors are distributed according to a Gaussian distribution without samples that strongly deviate from the main mode, i.e. outliers. If such assumption is violated, the sparse code will likely be biased and performance will degrade accordingly. In this paper, we introduce five robust variants of OMP (RobOMP) fully based on the theory of M-Estimators under a linear model. The proposed framework exploits efficient Iteratively Reweighted Least Squares (IRLS) techniques to mitigate the effect of outliers and emphasize the samples corresponding to the main mode of the data. This is done adaptively via a learned weight vector that models the distribution of the data in a robust manner. Experiments on synthetic data under several noise distributions and image recognition under different combinations of occlusion and missing pixels thoroughly detail the superiority of RobOMP over MSE-based approaches and similar robust alternatives. We also introduce a denoising framework based on robust, sparse and redundant representations that open the door to potential further applications of the proposed techniques. The five different variants of RobOMP do not require parameter tuning from the user and, hence, constitute principled alternatives to OMP.

scholarly journals RobOMP: Robust variants of Orthogonal Matching Pursuit for sparse representations

2019 ◽  
Author(s):  
Carlos A Loza
Keyword(s):  
Mean Squared Error ◽  
Matching Pursuit ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Parameter Tuning ◽  
Weight Vector ◽  
Orthogonal Matching Pursuit ◽  
Main Mode ◽  
Observation Matrix ◽  
And Performance

Sparse coding aims to find a parsimonious representation of an example given an observation matrix or dictionary. In this regard, Orthogonal Matching Pursuit (OMP) provides an intuitive, simple and fast approximation of the optimal solution. However, its main building block is anchored on the minimization of the Mean Squared Error cost function (MSE). This approach is only optimal if the errors are distributed according to a Gaussian distribution without samples that strongly deviate from the main mode, i.e. outliers. If such assumption is violated, the sparse code will likely be biased and performance will degrade accordingly. In this paper, we introduce five robust variants of OMP (RobOMP) fully based on the theory of M-Estimators under a linear model. The proposed framework exploits efficient Iteratively Reweighted Least Squares (IRLS) techniques to mitigate the effect of outliers and emphasize the samples corresponding to the main mode of the data. This is done adaptively via a learned weight vector that models the distribution of the data in a robust manner. Experiments on synthetic data under several noise distributions and image recognition under different combinations of occlusion and missing pixels thoroughly detail the superiority of RobOMP over MSE-based approaches and similar robust alternatives. We also introduce a denoising framework based on robust, sparse and redundant representations that open the door to potential further applications of the proposed techniques. The five different variants of RobOMP do not require parameter tuning from the user and, hence, constitute principled alternatives to OMP.

scholarly journals RobOMP: Robust variants of Orthogonal Matching Pursuit for sparse representations

2019 ◽  
Author(s):  
Carlos A Loza
Keyword(s):  
Mean Squared Error ◽  
Matching Pursuit ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Parameter Tuning ◽  
Weight Vector ◽  
Orthogonal Matching Pursuit ◽  
Main Mode ◽  
Observation Matrix ◽  
And Performance

Sparse coding aims to find a parsimonious representation of an example given an observation matrix or dictionary. In this regard, Orthogonal Matching Pursuit (OMP) provides an intuitive, simple and fast approximation of the optimal solution. However, its main building block is anchored on the minimization of the Mean Squared Error cost function (MSE). This approach is only optimal if the errors are distributed according to a Gaussian distribution without samples that strongly deviate from the main mode, i.e. outliers. If such assumption is violated, the sparse code will likely be biased and performance will degrade accordingly. In this paper, we introduce five robust variants of OMP (RobOMP) fully based on the theory of M-Estimators under a linear model. The proposed framework exploits efficient Iteratively Reweighted Least Squares (IRLS) techniques to mitigate the effect of outliers and emphasize the samples corresponding to the main mode of the data. This is done adaptively via a learned weight vector that models the distribution of the data in a robust manner. Experiments on synthetic data under several noise distributions and image recognition under different combinations of occlusion and missing pixels thoroughly detail the superiority of RobOMP over MSE-based approaches and similar robust alternatives. We also introduce a denoising framework based on robust, sparse and redundant representations that open the door to potential further applications of the proposed techniques. The five different variants of RobOMP do not require parameter tuning from the user and, hence, constitute principled alternatives to OMP.

scholarly journals Enhanced Orthogonal Matching Pursuit Algorithm and Its Application in Mechanical Equipment Fault Diagnosis

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Yong Lv ◽  
Jie Luo ◽  
Cancan Yi
Keyword(s):  
Fault Diagnosis ◽  
Matching Pursuit ◽  
Optimal Solution ◽  
Computation Time ◽  
Vibration Signal ◽  
Orthogonal Matching Pursuit ◽  
Complex Signal ◽  
Mechanical Equipment ◽  
Real World Data ◽  
Fault Characteristic

The vibration signal measured from the mechanical equipment is associated with the operation of key structure, such as the rolling bearing and gear. The effective signal processing method for early weak fault has attracted much attention and it is of vital importance in mechanical fault monitoring and diagnosis. The recently proposed atomic sparse decomposition algorithm is performed around overcomplete dictionary instead of the traditional signal analysis method using orthogonal basis operator. This algorithm has been proved to be effective in extracting useful components from complex signal by reducing influence of background noises. In this paper, an improved linear frequency-modulated (Ilfm) function as an atom is employed in the proposed enhanced orthogonal matching pursuit (EOMP) algorithm. Then, quantum genetic algorithm (QGA) with the OMP algorithm is integrated since the QGA can quickly obtain the global optimal solution of multiple parameters for rapidly and accurately extracting fault characteristic information from the vibration signal. The proposed method in this paper is superior to the traditional OMP algorithm in terms of accuracy and reducing the computation time through analyzing the simulation data and real world data. The experimental results based on the application of gear and bearing fault diagnosis indicate that it is more effective than traditional method in extracting fault characteristic information.

Pareto domain: an invaluable source of process information

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Geraldine Cáceres Sepúlveda ◽  
Silvia Ochoa ◽  
Jules Thibault
Keyword(s):  
Case Studies ◽  
Optimal Solution ◽  
Pareto Optimal ◽  
Process Variables ◽  
Optimal Point ◽  
Decision Variables ◽  
Visualization Tools ◽  
Pareto Domain ◽  
And Performance ◽  
Typical Process

AbstractDue to the highly competitive market and increasingly stringent environmental regulations, it is paramount to operate chemical processes at their optimal point. In a typical process, there are usually many process variables (decision variables) that need to be selected in order to achieve a set of optimal objectives for which the process will be considered to operate optimally. Because some of the objectives are often contradictory, Multi-objective optimization (MOO) can be used to find a suitable trade-off among all objectives that will satisfy the decision maker. The first step is to circumscribe a well-defined Pareto domain, corresponding to the portion of the solution domain comprised of a large number of non-dominated solutions. The second step is to rank all Pareto-optimal solutions based on some preferences of an expert of the process, this step being performed using visualization tools and/or a ranking algorithm. The last step is to implement the best solution to operate the process optimally. In this paper, after reviewing the main methods to solve MOO problems and to select the best Pareto-optimal solution, four simple MOO problems will be solved to clearly demonstrate the wealth of information on a given process that can be obtained from the MOO instead of a single aggregate objective. The four optimization case studies are the design of a PI controller, an SO2 to SO3 reactor, a distillation column and an acrolein reactor. Results of these optimization case studies show the benefit of generating and using the Pareto domain to gain a deeper understanding of the underlying relationships between the various process variables and performance objectives.

scholarly journals Effects of 3D Printing-Line Directions for Stretchable Sensor Performances

Materials ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1791
Author(s):  
Chi Cuong Vu ◽  
Thanh Tai Nguyen ◽  
Sangun Kim ◽  
Jooyong Kim
Keyword(s):  
3D Printing ◽  
Thermoplastic Polyurethane ◽  
Three Dimensional ◽  
Optimal Solution ◽  
Human Motion ◽  
Repeated Measurements ◽  
Fused Filament Fabrication ◽  
And Performance ◽  
The Times ◽  
Stretchable Sensors

Health monitoring sensors that are attached to clothing are a new trend of the times, especially stretchable sensors for human motion measurements or biological markers. However, price, durability, and performance always are major problems to be addressed and three-dimensional (3D) printing combined with conductive flexible materials (thermoplastic polyurethane) can be an optimal solution. Herein, we evaluate the effects of 3D printing-line directions (45°, 90°, 180°) on the sensor performances. Using fused filament fabrication (FDM) technology, the sensors are created with different print styles for specific purposes. We also discuss some main issues of the stretch sensors from Carbon Nanotube/Thermoplastic Polyurethane (CNT/TPU) and FDM. Our sensor achieves outstanding stability (10,000 cycles) and reliability, which are verified through repeated measurements. Its capability is demonstrated in a real application when detecting finger motion by a sensor-integrated into gloves. This paper is expected to bring contribution to the development of flexible conductive materials—based on 3D printing.

Sign in / Sign up

Export Citation Format

Share Document