scholarly journals k-MACE Clustering for Gaussian Clusters

2021 ◽  
Author(s):  
Edward Wyndel Nidoy
Keyword(s):  
Objective Function ◽  
Covariance Structure ◽  
Cluster Center ◽  
Second Step ◽  
Clustering Methods ◽  
Correct Number ◽  
Validity Indices ◽  
Structure Simulation ◽  
Simulation Results ◽  
Single Objective

Conventional clustering approaches require a preprocessing step that estimates the correct number of cluster prior to the cluster center allocation step. In these approaches, the preprocessing step minimizes one objective function while the second step concentrates on optimization of another objective function. Inspired by MACE-means, we use a single objective function to simultaneously estimate the Correct Number of Cluster (CNC) and acquire the cluster centers. Similarly, we use the Average Central Error (ACE) as ourcost function. The proposed method, denoted by k-minimum ACE (k-MACE), improves MACE-means by rigorous calculation of probabilistic estimate of ACE. While MACE-means (Minimum ACE) only concentrates on Independent Indentically Distributed (IID) clusters, k 􀀀 MACE is a solution for Gaussian clusters with any covariance structure. Simulation results show superiority of k 􀀀 MACE over MACE means and over conven- tional clustering methods such as G-means, DBSCAN, and validity indices methods such as Calinkski Harabaz, Silhoutte, and gap index. Performance is evaluated in terms of

scholarly journals k-MACE Clustering for Gaussian Clusters

2021 ◽  
Author(s):  
Edward Wyndel Nidoy
Keyword(s):  
Objective Function ◽  
Covariance Structure ◽  
Cluster Center ◽  
Second Step ◽  
Clustering Methods ◽  
Correct Number ◽  
Validity Indices ◽  
Structure Simulation ◽  
Simulation Results ◽  
Single Objective

Conventional clustering approaches require a preprocessing step that estimates the correct number of cluster prior to the cluster center allocation step. In these approaches, the preprocessing step minimizes one objective function while the second step concentrates on optimization of another objective function. Inspired by MACE-means, we use a single objective function to simultaneously estimate the Correct Number of Cluster (CNC) and acquire the cluster centers. Similarly, we use the Average Central Error (ACE) as ourcost function. The proposed method, denoted by k-minimum ACE (k-MACE), improves MACE-means by rigorous calculation of probabilistic estimate of ACE. While MACE-means (Minimum ACE) only concentrates on Independent Indentically Distributed (IID) clusters, k 􀀀 MACE is a solution for Gaussian clusters with any covariance structure. Simulation results show superiority of k 􀀀 MACE over MACE means and over conven- tional clustering methods such as G-means, DBSCAN, and validity indices methods such as Calinkski Harabaz, Silhoutte, and gap index. Performance is evaluated in terms of

Based on GIS Spatial Clustering Algorithm Research

2014 ◽  
Vol 971-973 ◽  
pp. 1565-1568
Author(s):  
Zhi Yong Wang
Keyword(s):  
Objective Function ◽  
Spatial Data ◽  
Clustering Algorithm ◽  
Spatial Clustering ◽  
Direct Access ◽  
Cluster Center ◽  
Clustering Methods ◽  
Concept Clustering ◽  
Spatial Data Management ◽  
Calculated Distance

Facing the particularity of the current limitations and spatial clustering clustering methods, the objective function from concept clustering starting to GIS spatial data management and spatial analysis for technical support, explores the space between the sample direct access to the distance calculated distance and indirect reach up costs. K samples randomly selected as the cluster center, with space for the sample to reach the center of each cluster sample is divided according to the distance, the sum of the spatial clustering center of the sample to reach its cost objective function for clustering, introduction of genetic algorithm, a spatial clustering algorithm based on GIS. Finally, the algorithm is tested by examples.

scholarly journals Proton Exchange Membrane Fuel Cells Modeling Using Chaos Game Optimization Technique

2021 ◽  
Vol 13 (14) ◽  
pp. 7911
Author(s):  
Ibrahim Alsaidan ◽  
Mohamed A. M. Shaheen ◽  
Hany M. Hasanien ◽  
Muhannad Alaraj ◽  
Abrar S. Alnafisah
Keyword(s):  
Fuel Cell ◽  
Objective Function ◽  
Proton Exchange Membrane ◽  
Optimization Technique ◽  
Proton Exchange ◽  
Simulation Performance ◽  
Terminal Voltage ◽  
Chaos Game ◽  
Simulation Results ◽  
Exchange Membrane

For the precise simulation performance, the accuracy of fuel cell modeling is important. Therefore, this paper presents a developed optimization method called Chaos Game Optimization Algorithm (CGO). The developed method provides the ability to accurately model the proton exchange membrane fuel cell (PEMFC). The accuracy of the model is tested by comparing the simulation results with the practical measurements of several standard PEMFCs such as Ballard Mark V, AVISTA SR-12.5 kW, and 6 kW of the Nedstack PS6 stacks. The complexity of the studied problem stems from the nonlinearity of the PEMFC polarization curve that leads to a nonlinear optimization problem, which must be solved to determine the seven PEMFC design variables. The objective function is formulated mathematically as the total error squared between the laboratory measured terminal voltage of PEMFC and the estimated terminal voltage yields from the simulation results using the developed model. The CGO is used to find the best way to fulfill the preset requirements of the objective function. The results of the simulation are tested under different temperature and pressure conditions. Moreover, the results of the proposed CGO simulations are compared with alternative optimization methods showing higher accuracy.

Development of a Stepped Calibration Approach for XAJ Hydrological Model

2013 ◽  
Vol 405-408 ◽  
pp. 2222-2225
Author(s):  
Qian Li ◽  
Wei Min Bao ◽  
Jing Lin Qian
Keyword(s):  
Root Mean Square Error ◽  
Objective Function ◽  
Traditional Method ◽  
Hydrological Model ◽  
Model Performance ◽  
Layer By Layer ◽  
Mean Square ◽  
Objective Functions ◽  
Single Objective ◽  
Calibration Approach

This paper discusses the conceptual stepped calibration approach (SCA) which has been developed for the Xinanjiang (XAJ) model. Multi-layer and multi-objective functions which can make optimization work simpler and more effective are introduced in this procedure. In all eight parameters were considered, they were divided into four layers according to the structure of XAJ model, and then calibrated layer by layer. The SCA procedure tends to improve the performance of the traditional method of calibration (thus, using a single objective function, such as root mean square error RMSE). The compared results demonstrate that the SCA yield better model performance than RMSE.

A Two Step Damage Prognosis Method for Beam-Like Truss Structures

2014 ◽  
Vol 578-579 ◽  
pp. 1092-1095
Author(s):  
Hao Kai Jia ◽  
Ling Yu
Keyword(s):  
Finite Element Method ◽  
Strain Energy ◽  
Truss Structure ◽  
Truss Structures ◽  
Second Step ◽  
The Finite Element Method ◽  
Modal Strain Energy ◽  
Damage Prognosis ◽  
Modal Curvature ◽  
Simulation Results

In this study, a two step damage prognosis method is proposed for beam-like truss structures via combining modal curvature change (MCC) with modal strain energy change ratio (MSECR). Changes in the modal curvature and the elemental strain energy are selected as the indicator of damage prognosis. Different damage elements with different damage degrees are simulated. In the first step, the finite element method is used to model a beam-like truss structure and the displacement modes are got. The damage region is estimated by the MCC of top and bottom chords of a beam-like truss structure. In the second step, the elemental MSECR in the damage region is calculated and the maximum MSECR element is deemed as the damage element. The simulation results show that this method can accurately locate the damage in the beam-like truss structure.

scholarly journals Order Selection in Unsupervised Learning and Clustering for Arbitrary and Non-Arbitrary Shaped Data

2021 ◽  
Author(s):  
Mahdi Shahbaba
Keyword(s):  
Objective Function ◽  
Unsupervised Learning ◽  
Minimum Spanning Tree ◽  
Statistical Testing ◽  
Adjusted Rand Index ◽  
Order Selection ◽  
Clustering Methods ◽  
Conventional Methods ◽  
Anderson Darling ◽  
Statistical Testing Method

This thesis focuses on clustering for the purpose of unsupervised learning. One topic of our interest is on estimating the correct number of clusters (CNC). In conventional clustering approaches, such as X-means, G-means, PG-means and Dip-means, estimating the CNC is a preprocessing step prior to finding the centers and clusters. In another word, the first step estimates the CNC and the second step finds the clusters. Each step having different objective function to minimize. Here, we propose minimum averaged central error (MACE)-means clustering and use one objective function to simultaneously estimate the CNC and provide the cluster centers. We have shown superiority of MACEmeans over the conventional methods in term of estimating the CNC with comparable complexity. In addition, on average MACE-means results in better values for adjusted rand index (ARI) and variation of information (VI). Next topic of our interest is order selection step of the conventional methods which is usually a statistical testing method such as Kolmogrov-Smrinov test, Anderson-Darling test, and Hartigan's Dip test. We propose a new statistical test denoted by Sigtest (signature testing). The conventional statistical testing approaches rely on a particular assumption on the probability distribution of each cluster. Sigtest on the other hand can be used with any prior distribution assumption on the clusters. By replacing the statistical testing of the mentioned conventional approaches with Sigtest, we have shown that the clustering methods are improved in terms of having more accurate CNC as well as ARI and VI. Conventional clustering approaches fail in arbitrary shaped clustering. Our last contribution of the thesis is in arbitrary shaped clustering. The proposed method denoted by minimum Pathways is Arbitrary Shaped (minPAS) clustering is proposed based on a unique minimum spanning tree structure of the data. Our simulation results show advantage of minPAS over the state-of-the-art arbitrary shaped clustering methods such as DBSCAN and Affinity Propagation in terms of accuracy, ARI and VI indexes.

scholarly journals FLUCTUATIONS OF THE CARGO TRANSPORTED BY LIFTING CRANE: SIMULATION AND ANALYSIS

2019 ◽  
Vol 16 (5) ◽  
pp. 526-533
Author(s):  
M. S. Korytov ◽  
V. S. Shcherbakov ◽  
V. E. Belyakov
Keyword(s):  
Objective Function ◽  
Arbitrary Order ◽  
Deflection Angle ◽  
Suspension Point ◽  
Program Code ◽  
First Derivative ◽  
Urgent Task ◽  
Acceleration And Deceleration ◽  
The Deflection Angle ◽  
Simulation Results

Introduction. Reducing fluctuations in the load transported by hoisting cranes with a flexible rope suspension of the load is an urgent task since it can significantly reduce the time taken to complete the operation of moving the load. A promising direction for reducing load fluctuations is to optimize the trajectory of movement of the load suspension upper point.Materials and methods. The paper discussed the method of mathematical simulation of plane vibrations of a load moved by a crane with a horizontally moving suspension point, using the software of the MATLAB system. For modeling, the authors used the function of the MATLAB ode45 system, intended for the numerical solution of systems of non-stationary differential equations of arbitrary order.The second-order differential equation used to describe the fluctuations of the transported load and its implementation in the form of program code was presented. Moreover, the authors demonstrated the elements of program code for the analysis and visualization of simulation results.Results. The authors obtained and presented the series of graphs in the inclination angle’s changing of the cargo rope, the acceleration of the suspension point and the value of the objective function with the sinusoidal nature of the acceleration. The objective function was the sum of the absolute values of the deflection angle of the rope and the first derivative at the final moment of the suspension point’s movement with acceleration.Discussion and conclusions. As a result, the paper shows that the system with energy dissipation does not reach the zero value of the objective function even by a symmetrical nature of acceleration and deceleration of the suspension point. Therefore, it is necessary to give asymmetry to the acceleration and deceleration periods of the suspension point in order to completely absorb the residual fluctuations of the load.

scholarly journals Glowworm Swarm Optimization and Its Application to Blind Signal Separation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Zhucheng Li ◽  
Xianglin Huang
Keyword(s):  
Objective Function ◽  
Global Optimum ◽  
Convergence Speed ◽  
Signal Separation ◽  
Blind Signal Separation ◽  
Swarm Optimization ◽  
Blind Signal ◽  
Glowworm Swarm Optimization ◽  
Simulation Results ◽  
Speed And Accuracy

Traditional optimization algorithms for blind signal separation (BSS) are mainly based on the gradient, which requires the objective function to be continuous and differentiable, so the applications of these algorithms are very limited. Moreover, these algorithms have problems with the convergence speed and accuracy. To overcome these drawbacks, this paper presents a modified glowworm swarm optimization (MGSO) algorithm based on a novel step adjustment rule and then applies MGSO to BSS. Taking kurtosis of the mixed signals as the objective function of BSS, MGSO-BSS succeeds in separating the mixed signals in Matlab environment. The simulation results prove that MGSO is more effective in capturing the global optimum of the objective function of the BSS algorithm and has faster convergence speed and higher accuracy, compared with particle swarm optimization (PSO) and GSO.

Investigating cluster validation metrics for optimal number of clusters determination

2021 ◽  
pp. 1-16
Author(s):  
Aikaterini Karanikola ◽  
Charalampos M. Liapis ◽  
Sotiris Kotsiantis
Keyword(s):  
Real World ◽  
Optimal Number ◽  
Cluster Validation ◽  
Clustering Methods ◽  
Number Of Clusters ◽  
Validity Indices ◽  
Selection Of ◽  
Specific Distance ◽  
Optimal Number Of Clusters

In short, clustering is the process of partitioning a given set of objects into groups containing highly related instances. This relation is determined by a specific distance metric with which the intra-cluster similarity is estimated. Finding an optimal number of such partitions is usually the key step in the entire process, yet a rather difficult one. Selecting an unsuitable number of clusters might lead to incorrect conclusions and, consequently, to wrong decisions: the term “optimal” is quite ambiguous. Furthermore, various inherent characteristics of the datasets, such as clusters that overlap or clusters containing subclusters, will most often increase the level of difficulty of the task. Thus, the methods used to detect similarities and the parameter selection of the partition algorithm have a major impact on the quality of the groups and the identification of their optimal number. Given that each dataset constitutes a rather distinct case, validity indices are indicators introduced to address the problem of selecting such an optimal number of clusters. In this work, an extensive set of well-known validity indices, based on the approach of the so-called relative criteria, are examined comparatively. A total of 26 cluster validation measures were investigated in two distinct case studies: one in real-world and one in artificially generated data. To ensure a certain degree of difficulty, both real-world and generated data were selected to exhibit variations and inhomogeneity. Each of the indices is being deployed under the schemes of 9 different clustering methods, which incorporate 5 different distance metrics. All results are presented in various explanatory forms.

scholarly journals Robust multi-objective calibration strategies – possibilities for improving flood forecasting

2012 ◽  
Vol 16 (10) ◽  
pp. 3579-3606 ◽  
Author(s):  
T. Krauße ◽  
J. Cullmann ◽  
P. Saile ◽  
G. H. Schmitz
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Model Performance ◽  
Data Depth ◽  
Automatic Calibration ◽  
Multi Objective ◽  
Robust Model ◽  
Robust Parameter ◽  
Robust Parameter Estimation ◽  
Single Objective

Abstract. Process-oriented rainfall-runoff models are designed to approximate the complex hydrologic processes within a specific catchment and in particular to simulate the discharge at the catchment outlet. Most of these models exhibit a high degree of complexity and require the determination of various parameters by calibration. Recently, automatic calibration methods became popular in order to identify parameter vectors with high corresponding model performance. The model performance is often assessed by a purpose-oriented objective function. Practical experience suggests that in many situations one single objective function cannot adequately describe the model's ability to represent any aspect of the catchment's behaviour. This is regardless of whether the objective is aggregated of several criteria that measure different (possibly opposite) aspects of the system behaviour. One strategy to circumvent this problem is to define multiple objective functions and to apply a multi-objective optimisation algorithm to identify the set of Pareto optimal or non-dominated solutions. Nonetheless, there is a major disadvantage of automatic calibration procedures that understand the problem of model calibration just as the solution of an optimisation problem: due to the complex-shaped response surface, the estimated solution of the optimisation problem can result in different near-optimum parameter vectors that can lead to a very different performance on the validation data. Bárdossy and Singh (2008) studied this problem for single-objective calibration problems using the example of hydrological models and proposed a geometrical sampling approach called Robust Parameter Estimation (ROPE). This approach applies the concept of data depth in order to overcome the shortcomings of automatic calibration procedures and find a set of robust parameter vectors. Recent studies confirmed the effectivity of this method. However, all ROPE approaches published so far just identify robust model parameter vectors with respect to one single objective. The consideration of multiple objectives is just possible by aggregation. In this paper, we present an approach that combines the principles of multi-objective optimisation and depth-based sampling, entitled Multi-Objective Robust Parameter Estimation (MOROPE). It applies a multi-objective optimisation algorithm in order to identify non-dominated robust model parameter vectors. Subsequently, it samples parameter vectors with high data depth using a further developed sampling algorithm presented in Krauße and Cullmann (2012a). We study the effectivity of the proposed method using synthetical test functions and for the calibration of a distributed hydrologic model with focus on flood events in a small, pre-alpine, and fast responding catchment in Switzerland.

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