Empirical evaluation of five algorithms for the initialization phase of the k-Means algorithm

do Carmo Nicoletti Maria; de Oliveira Anderson Francisco

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Empirical evaluation of five algorithms for the initialization phase of the k-Means algorithm

机译：k均值算法初始化阶段的五种算法的经验评价

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A recurring problem in a wide variety of research areas such as pattern recognition, machine learning, data mining and statistics, among others, is characterized as a clustering problem. Such a problem can be described in a simplistic way as: given a set of data (observations, objects, points, etc.), group similar data into clusters (groups). A clustering of a given data set is then characterized as a set of clusters, in which elements belonging to a cluster are similar to each other and elements belonging to distinct clusters are not similar. Clustering algorithms are non-supervised algorithms and, among the many available in the literature, the k-Means, that uses a random initizalization process, can be considered one of the most popular and successful. The performance of the k-Means, however, is highly dependent on a ‘good’ initialization of the k cluster centers (centroids), as well as on the value assigned to the number (k ) of clusters the final clustering should have. This paper addresses experiments using five initialization algorithms available in the literature namely, the Method1, the k-Means++, the CCIA, the Maedeh and Suresh and the SPSS algorithms, to empirically evaluate their contribution for improving the k-Means performance.

机译：在各种研究领域的重复问题，如模式识别，机器学习，数据挖掘和统计数据，等特征在于聚类问题。可以以简单化方式描述这样的问题：给定一组数据（观察，对象，点等），将类似的数据分组到群集中（组）。然后，给定数据集的群集被表征为一组簇，其中属于群集的元素彼此相似，并且属于不同群集的元素是不相似的。聚类算法是非监督算法，并且在文献中的许多可用中，使用随机发电过程的K-means，可以被视为最受欢迎和成功的一个。然而，k均值的性能高度依赖于“良好”初始化K集群中心（质心），以及最终聚类应该具有的群集的数量（k）。本文通过文献中可用的五种初始化算法来解决实验，即方法1，K-Means ++，CCIA，Maedeh和Suresh和SPSS算法，以凭经验评估它们对提高K-Means性能的贡献。

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来源
《International Journal of Hybrid Intelligent Systems》 |2020年第1期|35-53|共19页
作者
do Carmo Nicoletti Maria; de Oliveira Anderson Francisco;
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Centro Universitário C. Limpo Paulista C. L. Paulista SP|b Universidade Federal de S. Carlos S. Carlos SP;

Centro Universitário C. Limpo Paulista C. L. Paulista SP;

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正文语种 eng
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Unsupervised learning; k-Means; initialization algorithms;

机译：无监督的学习;K-means;初始化算法;

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专利

1. An empirical comparison of four initialization methods for the K-Means algorithm [J] . J.M.Pena, J.A.Lozano, P.Larranaga Pattern Recognition Letters . 1999,第10期

机译：K-Means算法的四种初始化方法的经验比较
2. Evaluation Of Fuzzy K-Means And K-Means Clustering Algorithms In Intrusion Detection Systems [J] . Farhad Soleimanian Gharehchopogh, Neda Jabbari, Zeinab Ghaffari Azar International Journal of Scientific & Technology Research . 2012,第11期

机译：入侵检测系统中模糊K-均值和K-均值聚类算法的评估
3. Does Determination of Initial Cluster Centroids Improve the Performance of K-Means Clustering Algorithm? Comparison of Three Hybrid Methods by Genetic Algorithm, Minimum Spanning Tree, and Hierarchical Clustering in an Applied Study [J] . Saeedeh Pourahmad, Atefeh Basirat, Amir Rahimi, Computational and mathematical methods in medicine . 2020,第1期

机译：初始簇质心的确定是否提高了K-Means聚类算法的性能？应用研究中遗传算法，最小生成树和分层聚类的三种混合方法的比较
4. Empirical evaluation of K-Means, Bisecting K-Means, Fuzzy C-Means and Genetic K-Means clustering algorithms [C] . Shreya Banerjee, Ankit Choudhary, Somnath Pal IEEE International WIE Conference on Electrical and Computer Engineering . 2015

机译：K均值，平分K均值，模糊C均值和遗传K均值聚类算法的经验评估
5. Hardware Implementation and Performance Evaluation of K-Means and K-Means++ Clustering Algorithms [D] . Singh, Manisha . 2019

机译：K-Means和K-Means ++聚类算法的硬件实现和性能评估
6. Does Determination of Initial Cluster Centroids Improve the Performance of K-Means Clustering Algorithm? Comparison of Three Hybrid Methods by Genetic Algorithm Minimum Spanning Tree and Hierarchical Clustering in an Applied Study [O] . Saeedeh Pourahmad, Atefeh Basirat, Amir Rahimi, 2020

机译：初始簇质心的确定是否提高了K-Means聚类算法的性能？应用研究中遗传算法最小生成树和分层聚类的三种混合方法的比较
7. MODERATED EPOSTERS1385Longitudinal strain assessment in dilated cardiomyopathy patients using a novel accelerated DENSE sequence1407Simultaneous T1 and T2 cardiac quantification with CABIRIA: initial clinical experience1423Head-to-head comparison of acceleration algorithms in 4-dimensional flow CMR1502Left ventricular function and size evaluated by hybrid cardiac positron emission tomography-magnetic resonance: Intraindividual comparison of left ventricular ejection fraction and ventricular volumes derived by two modalities1510Left Atrium assessed by Cardiovascular Magnetic Resonance at 1.5 and 3 Tesla – age and gender effects1514Comparison of Free Breathing Cardiac MRI Radial technique to the Standard Multi breath-hold cine SSFP CMR technique for the assessment of LV Volumes and Function1536Self-navigated free-breathing isotropic 3D whole heart phase sensitive inversion recovery magnetic resonance without navigator for detection of myocardial infarction1547Assessment of Right Ventricular Strain Using Myocardial Deformation Recovery Semi Automated Technique: Initial Experience and Normal Values1586Tissue tracking myocardial deformation analysis and prediction of left ventricular remodeling in acute myocardial infarction1589Investigating strategies for optimal 31P MRS clinical cardiac at 3T: Initial Results1620Quantitative Criteria for the Diagnosis of the Congenital Absence of Pericardium by Cardiac Magnetic Resonance1632Widespread tissue injury during acute myocardial infarction: evidence from advanced CMR relaxometry1322Computed tomography coronary angiography verSus sTRess cArdiac magneTic rEsonance for the manaGement of sYmptomatic revascularized patients: a cost effectiveness study (STRATEGY study)1339Comparison of low- versus high-dose of gadobutrol for late gadolinium enhancement imaging at 1.5 Tesla: a clinical feasibility study1347Multi-parametric Cardiac Magnetic Resonance for Prediction of Cardiac Complications in Thalassemia Intermedia: a Prospective Multicenter Study1461Prognostic value of Cardiovascular Magnetic Resonance derived indexes of myocardial fibrosis in heart transplant recipients1523The role of CMR in the acute phase of hospitalization: changing paradigms1542Preoperative CMR-based score predict ventricular response after surgical left ventricular reconstruction in ischemic heart failure patients1555Excellent response rate to cardiac resynchronization therapy guided with magnetic resonance imaging1626The ECG as a predictor of arrhythmogenic substrate on Cardiac Magnetic Resonance Imaging in patients undergoing ablation for premature ventricular contractions1649Comparison of T1-mapping at 3.0T CMR and angiographic APPROACH score for area at risk assessment in ST-segment elevation myocardial infarction1340Pathological correlates of left bundle branch disease in patients with non-ischemic cardiomyopathy: a cardiovascular magnetic resonance study1342Myocardial remodelling and fibrosis in nonischaemic dilated cardiomyopathy: insights from cardiovascular magnetic resonance1411The association between fibrosis and contractile dysfunction in hypertrophic cardiomyopathy assessed by cardiovascular magnetic resonance1622Persistent myocardial inflammation due to intramyocardial haemorrhage in reperfused STEMI as a precursor to adverse LV remodelling - insights from multi-parametric mapping1566Semiquantitative analysis of low and high b value DWI for detecting myocardial edema in acute myocarditis1567Value of Cardiac MRI In Detecting Coronary Artery Disease In Newly Diagnosed Systolic Dysfunction1570Usefulness of cardiac magnetic resonance in tuberous sclerosis complex1578Papillary muscles offer further insight into hypertrophied hearts: a cardiovascular magnetic resonance study1627Diagnostic and clinical implications of CMR timing (early versus late) in patients with troponin positive acute coronary syndromes and unobstructed coronary arteries: Table 1. [O] . Upasana Tayal, Alexandros Kallifatidis, P. Garg, 2016

机译：在使用新的扩张型心肌病的患者缓和EPOSTERS1385Longitudinal应变评估加速DENSE sequence1407Simultaneous T1和T2与CABIRIA心脏定量：在4维流动的加速算法初始临床experience1423Head对头比较CMR1502Left心室功能和尺寸由混合心脏正电子发射断层摄影术评价 - 磁性共振：由两个modalities1510Left庭派生左室射血分数和心室体积的个体间的比较，在1.5和3特斯拉评估心血管磁共振 - 免费的年龄和性别effects1514Comparison呼吸心脏MRI径向技术标准的多屏气电影SSFP CMR技术的LV卷和Function1536Self-导航自由呼吸各向同性3D整个心脏相位敏感反转恢复磁共振导航仪没有检测右Ventricu心肌infarction1547Assessment的评估拉尔菌株使用心肌变形恢复半自动技术：初步经验和正常Values1586Tissue跟踪心肌变形分析和预测左室重构急性心肌infarction1589Investigating策略优化31P MRS临床心脏在3T：初始Results1620Quantitative标准的先天缺失的诊断心包心脏磁Resonance1632Widespread组织损伤急性心肌梗死时：证据先进CMR relaxometry1322Computed CT冠状动脉成像与压力心脏磁共振对症的管理吻合血管患者：成本效益研究（战略研究）1339Comparison低与高剂量钆布醇在1.5特斯拉晚钆增强成像的临床可行性，在中间型地贫心脏并发症的预测study1347Multi参数心脏核磁共振的前瞻性德穆尔心血管磁共振的ticenter Study1461Prognostic价值衍生心肌纤维化指标在住院的急性期CMR的心脏移植recipients1523The作用：改变基于CMR-paradigms1542Preoperative比分预测缺血性心脏衰竭patients1555Excellent响应速度外科左心室重建心脏再同步化后心室反应治疗与磁共振imaging1626The ECG导引作为心脏磁共振成像致心律失常性基板的在ST段抬高心肌infarction1340Pathological在风险评估经历在3.0T CMR T1映射的室性早搏contractions1649Comparison和血管造影APPROACH分数区域消融患者的预测左束支传导疾病的患者与非缺血性心肌病相关因素：心血管磁共振study1342Myocardial重塑和纤维化nonischaemic扩张型心肌病：在从在由心血管磁性resonance1622Persistent心肌炎症评估肥厚型心肌病的纤维化和收缩功能障碍之间心血管磁性resonance1411The协会由于心肌内出血景点在再灌注STEMI为先导，以不利的LV重塑 - 从低的多参数mapping1566Semiquantitative分析和高的b值DWI的见解为在心脏MRI检测冠状动脉疾病急性myocarditis1567Value在结节性硬化症complex1578Papillary肌肉初诊收缩期Dysfunction1570Usefulness心脏磁共振检测心肌水肿提供进一步的深入了解肥大心脏：心血管磁共振study1627Diagnostic和CMR定时的临床意义（早期与晚）患者肌钙蛋白阳性的急性冠脉综合征和通畅的冠状动脉：表1。

Empirical evaluation of five algorithms for the initialization phase of the k-Means algorithm

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