Heuristic Approaches in Clustering Problems

2018 ◽  
pp. 107-124 ◽  
Author(s):  
Onur Doğan
Keyword(s):  
Local Minimum ◽  
Heuristic Algorithms ◽  
Minimum Point ◽  
Optimization Approach ◽  
Similar Data ◽  
Heuristic Approaches ◽  
Clustering Problem ◽  
Local Minimum Point ◽  
Np Hard Problem ◽  
Short Time

Clustering is an approach used in data mining to classify objects in parallel with similarities or separate according to dissimilarities. The aim of clustering is to decrease the amount of data by grouping similar data items together. There are different methods to cluster. One of the most popular techniques is K-means algorithm and widely used in literature to solve clustering problem is discussed. Although it is a simple and fast algorithm, there are two main drawbacks. One of them is that, in minimizing problems, solution may trap into local minimum point since objective function is not convex. Since the clustering is an NP-hard problem and to avoid converging to a local minimum point, several heuristic algorithms applied to clustering analysis. The heuristic approaches are a good way to reach solution in a short time. Five approaches are mentioned briefly in the chapter and given some directions for details. For an example, particle swarm optimization approach was used for clustering problem. In example, iris dataset including 3 clusters and 150 data was used.

On the number of interior peaks of solutions to a non-autonomous singularly perturbed Neumann problem

2009 ◽  
Vol 139 (2) ◽  
pp. 427-448 ◽  
Author(s):  
Chunyi Zhao
Keyword(s):  
Positive Integer ◽  
Neumann Problem ◽  
Smooth Function ◽  
Local Minimum ◽  
Singularly Perturbed ◽  
Minimum Point ◽  
Local Minimum Point ◽  
Image Position

We study the following non-autonomous singularly perturbed Neumann problem:where the index p is subcritical and a(x) is a positive smooth function in . We show that, given ε small enough, there exists a K(ε) such that, for any positive integer K ≤ K(ε), there always exists a solution with K interior peaks concentrating at a strict sth-order local minimum point of a.

Health indicator construction for roller bearing based on an unsupervised deep belief network with a novel sigmoid zero local minimum point model

2020 ◽  
pp. 147592172096395
Author(s):  
Fan Xu ◽  
Xin Shu ◽  
Xin Li ◽  
Ruoli Tang
Keyword(s):  
Local Minimum ◽  
Roller Bearing ◽  
Main Idea ◽  
Deep Belief Network ◽  
Remaining Useful Life ◽  
Minimum Point ◽  
Sigmoid Function ◽  
Health Indicator ◽  
Belief Network ◽  
Local Minimum Point

Extracting bearing degradation curves with good smoothness and monotonicity as a health indicator lays a solid foundation for predicting the bearing’s remaining useful life. Traditional bearing health indicator construction methods generally have the following problems: (1) they require manual experience, such as manual labeling of data is burdensome when the amount of collected data is large, for feature extraction, selection, and fusion with other indicators and models because the methods rely on substantial expert experience and signal-processing technology; (2) deep belief networks in deep learning require engineering experts with rich experience to label the data, and because the degradation state of a bearing is constantly changing, it is difficult to rely on manual experience to distinguish and label it accurately; (3) owing to the noise in the data collected during the study, the extracted health indicator curve shows obvious oscillation and poor smoothness. In response to the above problems, this study proposes a model based on an unsupervised deep belief network and a new sigmoid zero local minimum point to eliminate health indicator curve oscillation and improve monotonicity. The main idea is that a deep belief network without a label output layer is used to extract the preliminary health indicator curve directly from the original signal, whereas the sigmoid zero local minimum point uses the average value based on a sigmoid function to reduce the weight of the current health indicator value to eliminate concussion, and then it uses the zero and local minimum points to further improve the monotonicity of the extracted health indicator without parameters. Finally, the superiority of the model proposed in this study (deep belief network–sigmoid zero local minimum point) is verified through a comparison of multiple bearing datasets and other models.

Study on Improved APF Algorithm for Autonomous Mobile Robot

2014 ◽  
Vol 519-520 ◽  
pp. 1337-1341 ◽  
Author(s):  
Xiao Meng Shu ◽  
Da Ming Jiang ◽  
Lian Dai
Keyword(s):  
Mobile Robot ◽  
Mobile Robots ◽  
Real Time ◽  
Obstacle Avoidance ◽  
Local Minimum ◽  
Minimum Point ◽  
Autonomous Mobile Robot ◽  
Simulation Environment ◽  
Local Minimum Point

In algorithms of obstacle avoidance for autonomous mobile robot, APF algorithm is simple, real-time and smooth, but has some limitations for solving problems. For example, the local minimum point may trap mobile robots before reaching its goal. Even though many improved APF algorithms have been put forward, few articles describe the process in detail to show how these algorithms are applied. Considering above factors, this paper focuses on embodiment of abstract improved theory for APF algorithm by showing some changes with formulas and parameters. The whole work has been done in simulation environment. According to the results this paper draws a conclusion.

A singularly perturbed elliptic problem involving supercritical Sobolev exponent

1998 ◽  
Vol 128 (4) ◽  
pp. 809-819 ◽  
Author(s):  
Yaotian Shen ◽  
Shusen Yan
Keyword(s):  
Elliptic Problem ◽  
Local Minimum ◽  
Global Minimum ◽  
Singularly Perturbed ◽  
Minimum Point ◽  
Regular Part ◽  
Local Minimum Point ◽  
Minimisation Problem ◽  
Sobolev Exponent ◽  
Global Minimum Point

This paper deals with −Δu + εuq−1 = u2*−1, , where q > 2*, ε > 0. We first show that the minimiser of the associated minimisation problem blows up at the global minimum point of H(x, x), where H(y, x) is the regular part of the Green's function. We then prove that for each strictly local minimum point x0 of H(x, x), this problem has a solution concentrating at x0 as ε→0.

scholarly journals A chain rule for nonsmooth composite functions via minimisation

1994 ◽  
Vol 49 (1) ◽  
pp. 129-137 ◽  
Author(s):  
D. Ralph
Keyword(s):  
Local Minimum ◽  
Chain Rule ◽  
Minimum Point ◽  
Composite Functions ◽  
Nonsmooth Calculus ◽  
Local Minimum Point ◽  
Approximate Subdifferential ◽  
A Chain ◽  
Vector Valued

Nonsmooth calculus using the approximate subdifferential of Mordukhovich and loffe admits a sharper chain rule, hence sharper applications in optimisation, than does the generalised gradient of Clarke. We observe, however, that at a local minimum point of the composition of nonsmooth vector valued and real valued functions, the generalised gradient admits a special, relatively sharp chain rule, that yields sharper results than have been seen before in the context of the generalised gradient.

scholarly journals Modified projected Newton scheme for non-convex function with simple constraints

2021 ◽  
pp. 2-2
Author(s):  
Suvra Chakraborty ◽  
Geetanjali Panda
Keyword(s):  
Convex Optimization ◽  
Local Minimum ◽  
Optimization Problem ◽  
Saddle Points ◽  
Hessian Matrix ◽  
Minimum Point ◽  
Numerical Illustration ◽  
Convex Optimization Problem ◽  
Indefinite Matrix ◽  
Local Minimum Point

In this paper, a descent line search scheme is proposed to find a local minimum point of a non-convex optimization problem with simple constraints. The idea ensures that the scheme escapes the saddle points and finally settles for a local minimum point of the non-convex optimization problem. A positive definite scaling matrix for the proposed scheme is formed through symmetric indefinite matrix factorization of the Hessian matrix of the objective function at each iteration. A numerical illustration is provided, and the global convergence of the scheme is also justified.

An Algorithm of License Plate Recognition Based on Improved PSO-BP Network

2013 ◽  
Vol 427-429 ◽  
pp. 1714-1717
Author(s):  
Zuo Jun Liu ◽  
Li Hong Li
Keyword(s):  
Local Minimum ◽  
Recognition Algorithm ◽  
Minimum Point ◽  
License Plate ◽  
License Plate Recognition ◽  
Bp Network ◽  
Generalization Ability ◽  
Local Minimum Point ◽  
Network Algorithm ◽  
Improved Pso

Aiming at the problems of BP network algorithm easily falling into local minimum point, slow converging and the problem that generalization ability can not be guaranteed, a method to improve the PSO is proposed. This method of improved PSO can strengthen the parameters of BP network. Based on this, a license plate recognition algorithm is designed. Some conclusions can be drawn from the experiments: (1) the improved PSO-BP network is stable and robust which can avoid falling into flat areas and local minimum point. (2) the performance and efficiency of license plate recognition based on the improved PSO-BP network is pretty good.

scholarly journals Fast Ant Colony Optimization for Clustering

2018 ◽  
Vol 12 (1) ◽  
pp. 78
Author(s):  
Abba Suganda Girsang ◽  
Tjeng Wawan Cenggoro ◽  
Ko-Wei Huang
Keyword(s):  
Ant Colony Optimization ◽  
Data Clustering ◽  
Heuristic Algorithms ◽  
Computation Time ◽  
Ant Colony ◽  
Experimental Result ◽  
Cluster Problem ◽  
Swarm Optimization ◽  
Clustering Problem ◽  
Np Hard Problem

<p>Data clustering is popular data analysis approaches, which used to organizing data into sensible clusters based on similarity measure, where data within a cluster are similar to each other but dissimilar to that of another cluster. In the recently, the cluster problem has been proven as NP-hard problem, thus, it can be solved with meta-heuristic algorithms, such as the particle swarm optimization (PSO), genetic algorithm (GA), and ant colony optimization (ACO), respectively. This paper proposes an algorithm called Fast Ant Colony Optimization for Clustering (FACOC) to reduce the computation time of Ant Colony Optimization (ACO) in clustering problem. FACOC is developed by the motivation that a redundant computation is occurred in ACO for clustering. This redundant computation can be cut in order to reduce the computation time of ACO for clustering. The proposed FACOC algorithm was verified on 5 well-known benchmarks. Experimental result shows that by cutting this redundant computation, the computation time can be reduced about 28% while only suffering a small quality degradation.</p>

An Optimization Path Planning Method Based on Evolutionary Artificial Potential Field

2013 ◽  
Vol 380-384 ◽  
pp. 1414-1417
Author(s):  
Fei Long Li
Keyword(s):  
Path Planning ◽  
Potential Field ◽  
Local Minimum ◽  
Minimum Point ◽  
Artificial Potential Field ◽  
Minimum Problem ◽  
Field Approach ◽  
Local Minimum Point ◽  
The Matrix ◽  
Local Minimum Problem

This paper presents an evolutionary way for the robot to plan path. The way is based on the Evolutionary Artificial Potential Field approach. APF is an efficient way for a robot to plan its path, and the evolutionary APF can help the robot to jump out of the local minimum point. A matrix is integrated in the new algorithm. The matrix can modify the direction of a robot when the robot is trapped in a local minimum point. The force which has been changed will prompt the robot to escape from the local minimum point. Simulation result shows that the optimized algorithm is an effective way to solve the local minimum problem.

Sign in / Sign up

Export Citation Format

Share Document