Performance Evaluation of Some Clustering Algorithms and Validity Indices

Ujjwal MaulikSanghamitra Bandyopadhyay

article2002TPAMI1,422 citations

Establishes theoretical lower bounds for the I cluster validity index while evaluating its ability, alongside traditional metrics and simulated annealing, to determine the optimal number of clusters across synthetic and real-world datasets.

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In modern data analysis and machine learning, discovering natural groupings within unlabeled data is a critical capability across many industries, from market segmentation to medical diagnostics. A persistent challenge in this area is determining exactly how many distinct groups exist within a dataset and verifying how reliably an algorithm has partitioned them. Choosing the wrong number of clusters or an ineffective grouping technique can lead to incorrect insights and flawed operational decisions.

The article aims to evaluate how accurately different cluster evaluation metrics and grouping algorithms identify the true underlying structure across various datasets. It also establishes a formal theoretical foundation for a newer cluster evaluation metric, known as Index I, to guarantee reliable identification of well-separated groupings.

To conduct this evaluation, the analysis assessed three distinct grouping algorithms—standard iterative centroid clustering, hierarchical linking, and an advanced probabilistic optimization technique based on simulated annealing. These algorithms were paired with four validation metrics across five benchmark datasets, spanning both synthetic tests and real-world cases such as crude oil classification and breast cancer diagnosis. The datasets varied in dimensionality from two to ten features and contained between two and ten target clusters.

The findings show that Index I consistently outperformed established traditional validation measures, achieving a 100% success rate in identifying the correct number of clusters across all tested datasets, regardless of the underlying algorithm used. In contrast, standard metrics like the Davies-Bouldin, Dunn, and Calinski-Harabasz indices frequently failed on complex or overlapping datasets. Furthermore, the simulated annealing optimization method consistently avoided poor, suboptimal groupings, providing superior final partitions compared to standard centroid approaches when the correct cluster count was supplied.

These results demonstrate that adopting more balanced evaluation metrics and optimization-based grouping algorithms significantly reduces the risk of misidentifying underlying data patterns. For organizations relying on automated classification, using robust metrics minimizes misclassification errors and prevents poor strategic choices caused by flawed data segmentation.

Organizations and practitioners are encouraged to integrate Index I as a standard validation benchmark when evaluating unlabeled data structures, paired with global optimization algorithms when high partition accuracy is required. Future work should focus on extending these evaluation frameworks to fuzzy grouping models where data points can belong to multiple categories simultaneously, as well as testing non-standard distance measures and algorithmic computational speeds on larger-scale data.

Indian Statistical Institute University of Texas at Arlington annealing cluster validity indices k-means algorithm cluster validity indices clustering algorithms Davies-Bouldin index

Maulik et al (2002).pdf

Paper: X-means: Extending K-means with Efficient Estimation of the Number of Clusters, Dan Pelleg et al. (2000). This paper establishes the foundational problem of estimating the true number of clusters in K-means clustering using information-theoretic model selection criteria.
Paper: Mean Shift, Mode Seeking, and Clustering, Yizong Cheng (1995). This work introduces mode-seeking and density-based clustering foundations that underlie non-parametric cluster discovery and partitioning comparisons.
Paper: The Infinite Gaussian Mixture Model, Carl Edward Rasmussen (1999). This paper provides core principles for determining the appropriate number of clusters automatically via statistical mixture modeling without fixing cluster counts in advance.
Paper: On Spectral Clustering: Analysis and an algorithm, Andrew Y. Ng et al. (2001). This seminal paper analyzes the limitations of standard K-means on complex geometries and establishes spectral partitioning alternatives.
Paper: A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise, Martin Ester et al. (1996). This paper introduces foundational density-based spatial clustering to address the limitations of standard partitioning methods when discovering clusters of arbitrary shape.

Paper: Information Theoretic Measures for Clusterings Comparison: Variants, Properties, Normalization and Correction for Chance, X. Nguyen et al. (2010). This work extends the evaluation of clustering quality by establishing rigorous information-theoretic criteria and chance-adjusted metrics for comparing clusterings.
Paper: V-Measure: A Conditional Entropy-Based External Cluster Evaluation Measure, Andrew Rosenberg et al. (2007). This paper introduces an entropy-based external evaluation measure (V-Measure) that addresses limitations in assessing cluster validity and completeness across varying cluster counts.
Paper: Consensus Clustering: A Resampling-Based Method for Class Discovery and Visualization of Gene Expression Microarray Data, Stefano Monti et al. (2003). This study advances cluster validation methodologies by introducing consensus clustering and resampling to assess stability and discover the number of clusters.
Paper: Clustering with Bregman Divergences, Arindam Banerjee et al. (2005). This work generalizes centroid-based partitioning algorithms like K-means to arbitrary Bregman divergences, unifying parametric clustering.
Paper: Kernel k-means: spectral clustering and normalized cuts, Inderjit S. Dhillon et al. (2004). This paper bridges iterative K-means partitioning with graph spectral clustering and normalized cut optimization.
Paper: K-means clustering via principal component analysis, C. Ding et al. (2004). This research provides a formal theoretical analysis showing the direct mathematical relationship between K-means clustering objectives and principal component analysis.
Paper: Self-Tuning Spectral Clustering, Lihi Zelnik-Manor et al. (2004). This paper introduces a self-tuning framework that automatically determines the number of clusters and scale parameters in spectral clustering.

Cover for Performance Evaluation of Some Clustering Algorithms and Validity Indices

Abstract

In this article, we evaluate the performance of three clustering algorithms, hard K-Means, single linkage, and a simulated annealing (SA) based technique, in conjunction with four cluster validity indices, namely Davies-Bouldin index, Dunn's index, Calinski-Harabasz index, and a recently developed index I. Based on a relation between the index I and the Dunn's index, a lower bound of the value of the former is theoretically estimated in order to get unique hard K-partition when the data set has distinct substructures. The effectiveness of the different validity indices and clustering methods in automatically evolving the appropriate number of clusters is demonstrated experimentally for both artificial and real-life data sets with the number of clusters varying from two to ten. Once the appropriate number of clusters is determined, the SA-based clustering technique is used for proper partitioning of the data into the said number of clusters.

Topics

annealing cluster validity indices k-means algorithm linkage analysis hierarchical clustering algorithms

Keywords

cluster validity indices clustering algorithms Davies-Bouldin index simulated annealing-based clustering linkage algorithms Euclidean distance partition matrix

1 INTRODUCTION
2 CLUSTERING ALGORITHMS
3 CLUSTER VALIDITY INDICES
4 EXPERIMENTAL RESULTS
4.1 Data Sets and Implementation Parameters
4.2 Determining the Number of Clusters
4.3 Determining the Appropriate Clustering
5 DISCUSSION AND CONCLUSIONS
ACKNOWLEDGMENTS
REFERENCES

Knowls

Knowl 1 — Index I Cluster Validity Measure
definition
The cluster validity index $I(K)$ evaluates the quality of a partition of a dataset $X = \{x_1, x_2, \dots, x_n\} \subset \mathbb{R}^N$ into $K$ clusters with cluster centers $z_1, z_2, \dots, z_K$ . It is defined as:

$I(K) = \left( \frac{1}{K} \times \frac{E_1}{E_K} \times D_K \right)^p$

where:
- $E_K = \sum_{k=1}^K \sum_{j=1}^n u_{kj} \|x_j - z_k\|$ is the total intra-cluster distance for $K$ clusters, where $u_{kj} \in \{0, 1\}$ represents the membership of data point $x_j$ in cluster $C_k$ .
- $E_1 = \sum_{j=1}^n \|x_j - z_1\|$ is the total scatter of the dataset computed with respect to the overall dataset centroid $z_1 = \frac{1}{n} \sum_{j=1}^n x_j$ . $E_1$ is constant for a given dataset.
- $D_K = \max_{i, j = 1}^K \|z_i - z_j\|$ measures the maximum Euclidean separation between any pair of cluster centers.
- $p$ is a power exponent used to control the contrast between different cluster configurations (chosen as $p = 2$ ).
The index balances three competing factors:
1. $\frac{1}{K}$ penalizes over-partitioning by decreasing monotonically with $K$ .
2. $\frac{E_1}{E_K}$ rewards cluster compactness, increasing as within-cluster scatter $E_K$ decreases.
3. $D_K$ rewards cluster separation, increasing with $K$ up to the maximum pairwise distance between points in the dataset.
The optimal number of clusters $K^*$ corresponds to the global maximum of the index:

$K^* = \arg\max_{K} I(K)$
Knowl 2 — Theoretical Lower Bound on Index I for Well-Separated Clusters
theoretical result
Let $X = \{x_1, x_2, \dots, x_n\} \subset \mathbb{R}^N$ be partitioned into $K$ clusters $C_1, C_2, \dots, C_K$ with centers $z_1, z_2, \dots, z_K$ and cluster cardinalities $n_1, n_2, \dots, n_K$ such that $\sum_{k=1}^K n_k = n$ . Define the cluster-wise mean squared error for cluster $k$ as:

$\tau_k = \frac{1}{n_k} \sum_{i=1}^{n_k} \|x_i - z_k\|^2$

and let $\tau_{\min} = \min_{1 \le k \le K} \tau_k$ .

Under the assumption $K \le \sqrt{n}$ , Index $I(K)$ (with $p = 2$ ) and Dunn's cluster validity index $\nu_D$ satisfy the relationship:

$I(K) \cdot \frac{1}{\nu_D^2} \ge \frac{\tau_{\min}}{n}$

When the dataset contains well-separated substructures such that Dunn's index satisfies $\nu_D > 1$ (the theoretical condition guaranteeing a unique hard $K$ -partition), Index $I(K)$ is bounded from below by:

$I(K) \ge \frac{\tau_{\min}}{n}$

As clusters become increasingly compact and separated, $\nu_D \to \infty$ and Index $I(K)$ grows without bound.
Knowl 3 — Simulated Annealing-Based Clustering with Probabilistic Redistribution
algorithm
The simulated annealing (SA) clustering algorithm finds a crisp $K$ -partition of $n$ points by minimizing the total squared error energy $E = \sum_{k=1}^K \sum_{x \in C_k} \|x - z_k\|^2$ , using probabilistic redistribution of data points to escape local minima.
Input: Dataset $X = \{x_1, x_2, \dots, x_n\} \subset \mathbb{R}^N$ , number of clusters $K$ , initial temperature $T_{\max} = 100$ , minimum temperature $T_{\min} = 0.001$ , cooling factor $\alpha = 0.05$ , iterations per temperature $N_T = 100$ .
Output: Final cluster centers $Z = \{z_1, z_2, \dots, z_K\}$ and crisp partition $\{C_1, C_2, \dots, C_K\}$ .
1. Initialize cluster centers $Z = \{z_1, z_2, \dots, z_K\}$ as $K$ randomly chosen points from $X$ .
2. Assign each point $x_j \in X$ to cluster $C_k$ where $k = \arg\min_{l=1,\dots,K} \|x_j - z_l\|^2$ .
3. Compute initial energy $E = \sum_{k=1}^K \sum_{x \in C_k} \|x - z_k\|^2$ .
4. Set temperature $T \leftarrow T_{\max}$ .
5. while $T > T_{\min}$ do:
     for iter $\leftarrow 1$ to $N_T$ do:
       Create candidate partition $\{C_1', \dots, C_K'\}$ :
       for each cluster $C_j$ ( $j = 1, \dots, K$ ) and each point $x_i \in C_j$ do:
         for each cluster $C_k$ ( $k \ne j$ ) do:
           Let $D_{ij} = \|x_i - z_j\|$ and $D_{ik} = \|x_i - z_k\|$ .
           Reassign $x_i$ to $C_k$ with probability $\exp\left( - \frac{\max(0, D_{ik} - D_{ij})}{T} \right)$ .
       Update centers $Z' = \{z_1', \dots, z_K'\}$ to the means of points in $\{C_1', \dots, C_K'\}$ .
       Compute candidate energy $E' = \sum_{k=1}^K \sum_{x \in C_k'} \|x - z_k'\|^2$ .
       Compute acceptance probability $P_{\text{accept}} = \frac{1}{1 + \exp\left( - \frac{E - E'}{T} \right)}$ .
       Draw random number $r \sim \text{Uniform}(0, 1)$ .
       if $r < P_{\text{accept}}$ then:
          $Z \leftarrow Z'$ , $E \leftarrow E'$ , $\{C_1, \dots, C_K\} \leftarrow \{C_1', \dots, C_K'\}$ .
     Cool temperature: $T \leftarrow T \times (1 - \alpha)$ .
6. return $Z$ and $\{C_1, C_2, \dots, C_K\}$ .
The computational complexity of distance evaluation per iteration is $O(K n N)$ , scaling linearly with cluster count $K$ , dataset size $n$ , and feature dimensionality $N$ .

Knowl 4 — Empirical Identification of Optimal Cluster Number Across Validity Indices

data/table

The performance of four validity indices—Davies-Bouldin ( $DB$ ), Dunn's index ( $\nu_D$ ), Calinski-Harabasz ( $CH$ ), and Index $I$ —in detecting the true number of clusters $K^*$ was evaluated across three clustering algorithms: K-Means, Single Linkage (S-Link), and Simulated Annealing (SA).

Data Set	Algorithm	$DB$	$\nu_D$	$CH$	$I$
AD_10_2 (True $K=10$ )	K-means	8	18	2	10
	S-Link	8	4	2	10
	SA	8	5	2	10
AD_4_3N (True $K=4$ )	K-means	4	2	4	4
	S-Link	4	2	4	4
	SA	4	2	4	4
AD_2_10 (True $K=2$ )	K-means	30	14	2	2
	S-Link	30	14	2	2
	SA	30	14	2	2
Crude_Oil (True $K=3$ )	K-means	2	6/7	2	3
	S-Link	3/4	9–13	2	3
	SA	4	2	2	3
Cancer (True $K=2$ )	K-means	2	2	2	2
	S-Link	2	2	2	2
	SA	2	2	2	2

Index $I$ correctly identified the true number of clusters $K^*$ across all five datasets for all three clustering algorithms. In comparison:

$DB$ failed on AD_10_2 ( $K=8$ ), AD_2_10 ( $K=30$ ), and Crude_Oil (yielding $K=2, 3/4, 4$ ).
$\nu_D$ failed on AD_10_2, AD_4_3N, AD_2_10, and Crude_Oil across all algorithms.
$CH$ failed on AD_10_2 ( $K=2$ ) and Crude_Oil ( $K=2$ ).

Knowl 5 — Formulations of Baseline Cluster Validity Indices
definition
Three baseline cluster validity indices evaluated alongside Index $I$ are defined as follows:
1. Davies-Bouldin ( $DB$ ) Index: $DB = \frac{1}{K} \sum_{i=1}^K R_i, \quad R_i = \max_{j \ne i} \left\{ \frac{S_i + S_j}{d_{ij}} \right\}$ where $S_i = \frac{1}{|C_i|} \sum_{x \in C_i} \|x - z_i\|$ is within-cluster scatter and $d_{ij} = \|z_i - z_j\|$ is inter-cluster center distance. Lower values indicate better partitions; optimal $K^*$ minimizes $DB$ .
2. Dunn's ( $\nu_D$ ) Index: $\nu_D = \min_{1 \le i \le K} \left\{ \min_{1 \le j \le K, j \ne i} \left\{ \frac{\delta(C_i, C_j)}{\max_{1 \le k \le K} \Delta(C_k)} \right\} \right\}$ where cluster diameter $\Delta(C_k) = \max_{x, y \in C_k} \|x - y\|$ and set distance $\delta(C_i, C_j) = \min_{x \in C_i, y \in C_j} \|x - y\|$ . Larger values indicate better partitions; optimal $K^*$ maximizes $\nu_D$ .
3. Calinski-Harabasz ( $CH$ ) Index: $CH = \frac{\text{trace}(B) / (K - 1)}{\text{trace}(W) / (n - K)}$ where between-cluster scatter trace is $\text{trace}(B) = \sum_{k=1}^K n_k \|z_k - z\|^2$ , within-cluster scatter trace is $\text{trace}(W) = \sum_{k=1}^K \sum_{i=1}^{n_k} \|x_i - z_k\|^2$ , $n_k$ is the size of cluster $k$ , $n$ is total points, and $z$ is the dataset centroid. Larger values indicate better partitions; optimal $K^*$ maximizes $CH$ .

Knowl 6 — Benchmark Datasets for Cluster Validity Evaluation

data/table

The experimental evaluation was conducted on five benchmark datasets comprising three synthetic and two real-world datasets spanning 2 to 10 dimensions and 2 to 10 clusters:

Dataset Name	Number of Points ( $n$ )	Number of Clusters ( $K$ )	Dimensions ( $N$ )	Points per Cluster
AD_10_2	500	10	2	50 per cluster
AD_4_3N	402	4	3	101, 100, 101, 100
AD_2_10	1000	2	10	492, 508
Crude_Oil	56	3	5	7, 11, 38
Cancer	683	2	9	444 (Benign), 239 (Malignant)

AD_10_2 is a 2D synthetic dataset with 10 overlapping clusters.
AD_4_3N is a 3D synthetic dataset with 4 compact clusters.
AD_2_10 is a 10D synthetic dataset generated from triangular distributions over $[0, 2]^{10}$ for class 1 and $[1, 3] \times [0, 2]^9$ for class 2 with equal prior probabilities.
Crude_Oil is an overlapping real-world dataset with 5 chemical properties.
Cancer is the 9-dimensional Wisconsin Breast Cancer dataset with 2 classes.

Knowl 7 — Two-Stage Automated Clustering Framework
model/method
The unsupervised classification procedure resolves the cluster count and cluster assignment in two distinct stages:
1. Automated Cluster Number Selection:
  - Cluster counts are evaluated in the range $K \in [K_{\min}, K_{\max}]$ , where $K_{\min} = 2$ and $K_{\max} = \lfloor\sqrt{n}\rfloor$ .
  - Partitions $U_K$ are evolved using a candidate algorithm (K-Means, Single Linkage, or Simulated Annealing), and validity index values $V(K)$ are computed.
  - The optimal cluster number $K^*$ is identified by optimizing the validity index ( $K^* = \arg\max_K I(K)$ for Index $I$ ).
2. Partition Generation:
  - Given $K^*$ , the simulated annealing clustering technique with probabilistic point redistribution is executed with $K = K^*$ to produce the final crisp partition $U_{K^*}$ . This avoids suboptimal local minima inherent to iterative gradient-descent schemes like K-Means.
  - The resulting tuple $\langle U_{K^*}, K^* \rangle$ is output as the clustering solution.
Knowl 8 — Upper Bound on Cluster Search Space
assumption
In evaluating cluster validity indices and establishing theoretical bounds relating Index $I$ to Xie-Beni and Dunn's indices, the number of clusters $K$ for a dataset of size $n$ is assumed to be bounded by:

$K \le \sqrt{n}$

This constraint defines the maximum search limit $K_{\max} = \lfloor\sqrt{n}\rfloor$ for cluster validity search across all evaluated datasets.
Knowl 9 — Crisp and Euclidean Distance Limitations
limitation
The formulations of Index $I$ , the baseline indices, and the simulated annealing clustering algorithm possess several specific limitations:
1. Crisp Partition Restriction: The validity measures and clustering methods operate on crisp membership matrices where $u_{kj} \in \{0, 1\}$ ; fuzzy partition extensions where memberships lie continuously in $[0, 1]$ require separate formulation.
2. Metric Dependency: The formulations assume a Euclidean distance metric and hyperspheroidal cluster geometries, which may not be well suited for manifold or non-Euclidean data distributions.
3. Theoretical Convergence: Formal analytical comparisons regarding the relative convergence rates of the different validity indices remain uncharacterized.

Coverage note — None was omitted; all primary contributions including definitions, algorithms, theoretical bounds, experimental data, empirical results, assumptions, and limitations have been extracted.

References

1.J.T. Tou and R.C. Gonzalez, Pattern Recognition Principles. Reading: Addison-Wesley, 1974.
2.A.K. Jain and R.C. Dubes, Algorithms for Clustering Data. Prentice Hall, 1988.
3.H. Frigui and R. Krishnapuram, "A Robust Competitive Clustering Algorithm with Application in Computer Vision," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 1, pp. 450-465, Jan. 1999.
4.B.S. Everitt, Cluster Analysis, Halsted Press, third ed., 1993.
5.U. Maulik and S. Bandyopadhyay, "Genetic Algorithm Based Clustering Technique," Pattern Recognition, vol. 33, pp. 1455-1465, 2000.
6.G.W. Milligan and C. Cooper, "An Examination of Procedures for Determining the Number of Clusters in a Data Set," Psychometrika, vol. 50, no. 2, pp. 159-179, 1985.
7.M. Meil a and D. Heckerman, "An Experimental Comparison of Several Clustering and Initialization Methods," Proc. 14th Conf. Uncertainty in Artificial Intelligence, pp. 386-395, 1998.
8.C. Fraley and A.E. Raftery, "How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis," The Computer J., vol. 41, no. 8, pp. 578-588, 1998.
9.L.O. Hall, I.B. Ozyurt, and J. C. Bezdek, "Clustering with a Genetically Optimized Approach," IEEE Trans. Evolutionary Computation, vol. 3, no. 2, pp. 103-112, 1999.
10.D.L. Davies and D.W. Bouldin, "A Cluster Separation Measure," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 1, pp. 224-227, 1979.
11.J.C. Dunn, "A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters," J. Cybernetics, vol. 3, pp. 32-57, 1973.
12.R.B. Calinski and J. Harabasz, "A Dendrite Method for Cluster Analysis," Comm. in Statistics, vol. 3, pp. 1-27, 1974.
13.S. Kirkpatrik, C. Gelatt, and M. Vecchi, "Optimization by Simulated Annealing," Science, vol. 220, pp. 671-680, 1983.
14.S. Bandyopadhyay, U. Maulik, and M.K. Pakhira, "Clustering Using Simulated Annealing with Probabilistic Redistribution," Int'l J. Pattern Recognition and Artificial Intelligence, vol. 15, no. 2, pp. 269-285, 2001.
15.X.L. Xie and G. Beni, "A Validity Measure for Fuzzy Clustering," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 841-847, 1991.
16.J.C. Dunn, "Well Separated Clusters and Optimal Fuzzy Partitions," J. Cybernetics, vol. 4, pp. 95-104, 1974.
17.R.A. Johnson and D.W. Wichern, Applied Multivariate Statistical Analysis. Prentice Hall, 1982.

Citation

MLA

Maulik, U., and S. Bandyopadhyay. “Performance Evaluation of Some Clustering Algorithms and Validity Indices”. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 12, 2002, pp. 1650–54, https://doi.org/10.1109/TPAMI.2002.1114856.

APA

Maulik, U., & Bandyopadhyay, S. (2002). Performance evaluation of some clustering algorithms and validity indices. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(12), 1650–1654. https://doi.org/10.1109/TPAMI.2002.1114856

Chicago

Maulik, U., and S. Bandyopadhyay. 2002. “Performance Evaluation of Some Clustering Algorithms and Validity Indices”. IEEE Transactions on Pattern Analysis and Machine Intelligence 24 (12): 1650–54. https://doi.org/10.1109/TPAMI.2002.1114856.

Harvard

Maulik, U. and Bandyopadhyay, S. (2002) “Performance evaluation of some clustering algorithms and validity indices”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(12), pp. 1650–1654. Available at: https://doi.org/10.1109/TPAMI.2002.1114856.

Vancouver

1. Maulik U, Bandyopadhyay S (2002) Performance evaluation of some clustering algorithms and validity indices. IEEE Transactions on Pattern Analysis and Machine Intelligence 24:1650–1654

BibTeX

@article{Maulik_2002, title={Performance evaluation of some clustering algorithms and validity indices}, volume={24}, ISSN={0162-8828}, url={http://dx.doi.org/10.1109/TPAMI.2002.1114856}, DOI={10.1109/tpami.2002.1114856}, number={12}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Maulik, U. and Bandyopadhyay, S.}, year={2002}, month=Dec, pages={1650–1654} }

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Performance Evaluation of Some Clustering Algorithms and Validity Indices

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — Index I Cluster Validity Measure

Knowl 2 — Theoretical Lower Bound on Index I for Well-Separated Clusters

Knowl 3 — Simulated Annealing-Based Clustering with Probabilistic Redistribution

Knowl 4 — Empirical Identification of Optimal Cluster Number Across Validity Indices

Knowl 5 — Formulations of Baseline Cluster Validity Indices

Knowl 6 — Benchmark Datasets for Cluster Validity Evaluation

Knowl 7 — Two-Stage Automated Clustering Framework

Knowl 8 — Upper Bound on Cluster Search Space

Knowl 9 — Crisp and Euclidean Distance Limitations

References

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