V-Measure: A Conditional Entropy-Based External Cluster Evaluation Measure

article2007EMNLP1,904 citations

Introduces V-measure, an entropy-based external evaluation metric that transparently balances clustering homogeneity and completeness without depending on dataset size or cluster counts.

Listen

Automated data clustering is widely used across technology applications to group information without manual labeling, but evaluating the true quality of these groupings against known benchmarks has historically been flawed. Many existing evaluation metrics suffer from key structural weaknesses: they often require matching clusters to specific target classes (which ignores unmatched data points and distorts performance scores), depend heavily on dataset size and cluster count, or assess only whether clusters contain single classes while ignoring whether classes are split across multiple groups. The article introduces V-Measure, an external entropy-based cluster evaluation metric designed to resolve these limitations by explicitly measuring and combining two core properties: homogeneity (ensuring each cluster contains only data points from a single class) and completeness (ensuring all data points from a given class are grouped together).

The researchers assessed the validity of V-Measure using a two-part evaluation framework. First, they used parametric synthetic simulations to test V-Measure alongside eight existing measures (including Rand Index, Variation of Information, and F-Measure) against seven formal criteria for cluster quality. Second, they applied V-Measure, Variation of Information, and the Q0/Q2 metric to real-world tasks involving document clustering on news corpora (1,884 documents across 12 topics) and speech pitch accent categorization.

The findings show that V-Measure, Variation of Information, and Q0/Q2 were the only metrics to satisfy all seven formal clustering quality criteria across all experimental conditions, whereas traditional metrics like the Rand Index and standard F-Measure failed when handling noise clusters or noise classes. Unlike pair-matching and mapping-based metrics, V-Measure avoids distortion by assessing the full distribution of every data point. Furthermore, in contrast to distance-based metrics like Variation of Information, which vary drastically with cluster size and count, V-Measure remains fully invariant to dataset size and cluster counts, scaling neatly between 0 and 1. Finally, unlike Q2, which penalizes larger numbers of clusters regardless of performance, V-Measure correctly reflects performance gains when adding clusters improves homogeneity without sacrificing completeness.

These results provide organizations and data science teams with a reliable, standardized metric for benchmarking unsupervised machine learning systems. Adopting V-Measure mitigates the risk of selecting inferior clustering algorithms caused by skewed evaluation metrics, and its modular design allows practitioners to assign custom weights to homogeneity or completeness depending on operational requirements. The article demonstrates high confidence in the metric's theoretical grounding and practical utility across diverse domains, suggesting that teams evaluating external clustering should implement V-Measure as a general-purpose metric while using its separate homogeneity and completeness scores as direct diagnostic tools.

Columbia University clustering methods data points document clustering external cluster evaluation measure conditional entropy document clustering

Rosenberg et al (2007).pdf

Paper: Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions, Alexander Strehl et al. (2002). This work introduces normalized mutual information for comparing clusterings, establishing foundational concepts of information-theoretic clustering comparison that V-measure directly refines.
Paper: An Information-Theoretic Definition of Similarity, Dekang Lin (1998). This paper establishes formal information-theoretic principles for measuring similarity, providing theoretical grounding for entropy-based evaluation metrics like V-measure.

Paper: Information Theoretic Measures for Clusterings Comparison: Variants, Properties, Normalization and Correction for Chance, X. Nguyen et al. (2010). This paper provides a comprehensive study of information-theoretic clustering evaluation measures, systematically analyzing properties, normalizations, and chance adjustments for metrics such as V-measure.
Paper: Unsupervised Deep Embedding for Clustering Analysis, Junyuan Xie et al. (2015). This work develops deep embedded clustering and relies on external clustering evaluation metrics introduced in earlier literature to validate deep unsupervised representations.
Paper: Defining and evaluating network communities based on ground-truth, Jaewon Yang et al. (2012). This paper investigates ground-truth community evaluation in complex networks, applying external clustering and partition validation methodologies to network structures.

Cover for V-Measure: A Conditional Entropy-Based External Cluster Evaluation Measure

Abstract

We present V-measure, an external entropy-based cluster evaluation measure. V-measure provides an elegant solution to many problems that affect previously defined cluster evaluation measures including 1) dependence on clustering algorithm or data set, 2) the “problem of matching”, where the clustering of only a portion of data points are evaluated and 3) accurate evaluation and combination of two desirable aspects of clustering, homogeneity and completeness. We compare V-measure to a number of popular cluster evaluation measures and demonstrate that it satisfies several desirable properties of clustering solutions, using simulated clustering results. Finally, we use V-measure to evaluate two clustering tasks: document clustering and pitch accent type clustering.

Topics

clustering methods data points document clustering

Keywords

external cluster evaluation measure conditional entropy document clustering Rand index cluster assignments target partition

1 Introduction
2 V-Measure and Its Calculation
3 Existing Evaluation Measures
4 Comparing Evaluation Measures
5 Applying V-measure
5.1 Document Clustering
5.2 Pitch Accent Clustering
6 Conclusion
Acknowledgments
References

Knowls

Knowl 1 — Definition of Clustering Homogeneity
definition
Let $N$ be the total number of data points, $C = \{c_1, \dots, c_n\}$ be the partition of ground-truth classes, and $K = \{k_1, \dots, k_m\}$ be the partition of hypothesized clusters. Let $A = (a_{ck})$ be the contingency table where $a_{ck}$ is the number of data points in class $c \in C$ assigned to cluster $k \in K$ .

A clustering satisfies homogeneity if every cluster contains only data points that are members of a single class. Homogeneity $h$ is defined as:

$h = \begin{cases} 1 & \text{if } H(C, K) = 0 \\ 1 - \frac{H(C|K)}{H(C)} & \text{otherwise} \end{cases}$

where the conditional entropy of the class distribution given the cluster assignments $H(C|K)$ is:

$H(C|K) = - \sum_{k=1}^{|K|} \sum_{c=1}^{|C|} \frac{a_{ck}}{N} \log \left( \frac{a_{ck}}{\sum_{c'=1}^{|C|} a_{c'k}} \right)$

and the class entropy $H(C)$ is:

$H(C) = - \sum_{c=1}^{|C|} \frac{\sum_{k=1}^{|K|} a_{ck}}{N} \log \left( \frac{\sum_{k=1}^{|K|} a_{ck}}{N} \right)$

When each cluster contains only data points belonging to a single class, $H(C|K) = 0$ and $h = 1$ . When the clustering provides no information about class membership (the class distribution within each cluster equals the overall class distribution), $H(C|K) = H(C)$ and $h = 0$ . If there is only one class ( $H(C) = 0$ ), $h$ is defined as $1$ .
Knowl 2 — Definition of Clustering Completeness
definition
Let $N$ be the total number of data points, $C = \{c_1, \dots, c_n\}$ be the ground-truth classes, and $K = \{k_1, \dots, k_m\}$ be the hypothesized clusters. Let $A = (a_{ck})$ be the contingency table where $a_{ck}$ is the number of data points in class $c \in C$ assigned to cluster $k \in K$ .

A clustering satisfies completeness if all data points that are members of a given class are assigned to the same cluster. Completeness $c$ is symmetrical to homogeneity and is defined as:

$c = \begin{cases} 1 & \text{if } H(K, C) = 0 \\ 1 - \frac{H(K|C)}{H(K)} & \text{otherwise} \end{cases}$

where the conditional entropy of the cluster distribution given the class $H(K|C)$ is:

$H(K|C) = - \sum_{c=1}^{|C|} \sum_{k=1}^{|K|} \frac{a_{ck}}{N} \log \left( \frac{a_{ck}}{\sum_{k'=1}^{|K|} a_{ck'}} \right)$

and the cluster entropy $H(K)$ is:

$H(K) = - \sum_{k=1}^{|K|} \frac{\sum_{c=1}^{|C|} a_{ck}}{N} \log \left( \frac{\sum_{c=1}^{|C|} a_{ck}}{N} \right)$

When all data points of each class are grouped into a single cluster, $H(K|C) = 0$ and $c = 1$ . In the worst case where each class is distributed across all clusters proportionally to the cluster sizes, $H(K|C) = H(K)$ and $c = 0$ . In the degenerate case where all data points are assigned to a single cluster ( $H(K) = 0$ ), $c$ is defined as $1$ .
Knowl 3 — Definition and Parameterized Weighting of V-Measure
equation
Given a clustering solution with homogeneity $h \in [0, 1]$ and completeness $c \in [0, 1]$ , the V-measure $V_\beta$ is defined as the weighted harmonic mean of $h$ and $c$ :

$V_\beta = \frac{(1 + \beta) \cdot h \cdot c}{(\beta \cdot h) + c}$

where $\beta > 0$ is a weighting parameter:
- If $\beta > 1$ , completeness $c$ is weighted more strongly than homogeneity $h$ .
- If $\beta < 1$ , homogeneity $h$ is weighted more strongly than completeness $c$ .
- If $\beta = 1$ , $V_1 = \frac{2 \cdot h \cdot c}{h + c}$ , giving equal weight to both criteria.
V-measure is bounded in $[0, 1]$ , with $1.0$ indicating a perfect clustering. Its computation is independent of the dataset size $N$ ( $n$ -invariance), the number of classes $|C|$ , the number of clusters $|K|$ , and the clustering algorithm used, and it requires no mapping step between clusters and classes.
Knowl 4 — The Problem of Matching in Cluster-to-Class Evaluation Measures
theoretical result
External cluster evaluation measures that rely on a post-processing mapping from clusters to ground-truth classes (including clustering F-measure, Misclassification Index, $H$ , $L$ , and $D$ ) suffer from two fundamental failure modes termed the problem of matching:
1. Ignoring non-majority cluster elements: For a matched cluster-class pair $(k_j, c_i)$ , precision and recall depend solely on the majority class $c_i$ . The composition of the remaining data points within cluster $k_j$ is ignored. Consequently, two clusterings with identical majority counts but different amounts of class mixing outside the majority class receive identical F-measure scores.
2. Ignoring unmatched clusters: When the number of clusters exceeds the number of classes ( $|K| > |C|$ ), clusters that are not selected as the best match for any class are omitted from the evaluation. Erroneous mixing of classes in these unmapped clusters does not penalize the metric.
Information-theoretic measures such as V-measure avoid these failure modes by evaluating the entire contingency table over all data points without requiring cluster-to-class assignment.
Knowl 5 — Seven Desirable Formal Properties for Cluster Evaluation Measures
definition
Let $M$ be an external cluster evaluation similarity measure (inverted for distance measures), let $C$ be the target partition (classes) with size $|C|$ and $|C_{\text{noise}}|$ noise classes, and let $K$ be the hypothesized partition (clusters) with size $|K|$ and $|K_{\text{noise}}|$ noise clusters. Let $|K_u| = |K| - |K_{\text{noise}}|$ and $|C_u| = |C| - |C_{\text{noise}}|$ be the number of useful clusters and classes. Let $\epsilon = \epsilon_1 + \epsilon_2 + \epsilon_3$ be the error mass, where $\epsilon_1$ is error across non-matching useful pairs, $\epsilon_2$ is error within noise clusters, and $\epsilon_3$ is error within noise classes.

An external clustering evaluation measure should satisfy seven formal properties:
- P1 (Cluster addition up to class count): For $|K_u| < |C|$ and $\Delta |K_u| \le (|C| - |K_u|)$ , $\frac{\Delta M}{\Delta |K_u|} > 0$ .
- P2 (Cluster addition beyond class count): For $|K_u| \ge |C|$ , $\frac{\Delta M}{\Delta |K_u|} < 0$ .
- P3 (Sensitivity to noise clusters): $\frac{\Delta M}{\Delta |K_{\text{noise}}|} < 0$ whenever $\epsilon_2 > 0$ .
- P4 (Sensitivity to useful error mass): $\frac{\partial M}{\partial \epsilon_1} \le 0$ , with equality strictly when $|K_u| = 1$ .
- P5 (Sensitivity to noise cluster error mass): $\frac{\partial M}{\partial \epsilon_2} \le 0$ , with equality strictly when $|K_{\text{noise}}| = 0$ .
- P6 (Sensitivity to noise classes): $\frac{\Delta M}{\Delta |C_{\text{noise}}|} < 0$ whenever $\epsilon_3 > 0$ .
- P7 (Sensitivity to noise class error mass): $\frac{\partial M}{\partial \epsilon_3} \le 0$ , with equality strictly when $|C_{\text{noise}}| = 0$ .

Knowl 6 — Satisfaction Rates of Desirable Properties Across Clustering Evaluation Measures

data/table

Systematic variation of clustering generation parameters ( $|K_u| \in \{2, \dots, 11\}$ , $|K_{\text{noise}}| \in \{0, \dots, 6\}$ , $|C_{\text{noise}}| \in \{0, \dots, 6\}$ , $\epsilon_1 \in \{0, 0.033, 0.066, 0.1\}$ , $\epsilon_2 \in \{0, 0.066, 0.133, 0.2\}$ , $\epsilon_3 \in \{0, 0.066, 0.133, 0.2\}$ with $|C|=5$ fixed) yields the following satisfaction rates for properties P1--P7 across major evaluation measures:

Property	Rand	Mirkin	Fowlkes	$\Gamma$	Jaccard	F-measure	$Q_0$	VI	V-Measure
P1	0.18	0.22	1.00	1.00	1.00	1.00	1.00	1.00	1.00
P2	1.00	1.00	0.76	1.00	0.89	0.98	1.00	1.00	1.00
P3	0.00	0.00	0.30	0.19	0.21	0.00	1.00	1.00	1.00
P4	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
P5	0.50	0.57	1.00	1.00	1.00	1.00	1.00	1.00	1.00
P6	0.20	0.20	0.41	0.26	0.52	0.87	1.00	1.00	1.00
P7	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00

V-Measure, Variation of Information (VI), and Dom's $Q_0$ satisfy all seven properties under 100% of tested conditions. In contrast, pair-matching measures (Rand, Mirkin, Fowlkes-Mallows, $\Gamma$ , Jaccard) and clustering F-measure fail properties P3 and P6 (rates dropping to 0.00), demonstrating insensitivity to the addition of noise clusters and noise classes.

Knowl 7 — Comparative Analysis of V-Measure Against Variation of Information and Q0
theoretical result
Among the information-theoretic measures satisfying formal clustering criteria P1--P7, V-measure addresses specific structural limitations in Variation of Information ( $VI$ ) and Dom's $Q_0$ :
- Variation of Information ( $VI(C, K) = H(C|K) + H(K|C)$ ): $VI$ is unbounded above by any fixed constant across datasets; its upper bound depends on the maximum number of clusters $k^* \le n$ . Normalizing $VI$ by $\log n$ violates $n$ -invariance, whereas normalizing by $\frac{1}{2}\log k^*$ prevents comparison across studies using different $k^*$ . Furthermore, $VI$ combines conditional entropies additively without separating or weighting homogeneity versus completeness.
- Dom's $Q_0$ and $Q_2$ : $Q_0 = H(C|K) + \frac{1}{n}\sum_{k=1}^{|K|} \log \binom{h(k) + |C| - 1}{|C| - 1}$ incorporates a Minimum Description Length (MDL) model cost to penalize cluster count. This coding cost strictly penalizes higher $k$ , conflating model size with completeness and causing $Q_2$ to decrease rapidly even when additional clusters increase homogeneity without degrading completeness.
- V-Measure Advantages: Homogeneity $h$ and completeness $c$ are individually normalized to $[0, 1]$ , strictly $n$ -invariant and $k^*$ -invariant, and combined via a harmonic mean that permits explicit relative weighting ( $\beta$ ).
Knowl 8 — Document Clustering Evaluation on TDT-4 Corpus
empirical result
In a document clustering task on 1,884 news articles from the TDT-4 corpus spanning 12 ground-truth topics (represented by 484-dimensional tf-idf term vectors and clustered with k-means across cluster counts $k \in [1, 1000]$ ):
- V-Measure and $Q_2$ : Both metrics peak at $k = 35$ clusters, yielding a maximum V-measure of approximately $0.51$ . As $k$ increases toward 1000, $Q_2$ drops sharply due to its MDL model-cost penalty, whereas V-measure exhibits a much more moderate descent because improved cluster homogeneity balances lower completeness.
- Variation of Information ( $VI$ ): $VI$ distance increases nearly monotonically as $k$ increases (from $\approx 3.3$ at $k=1$ to $>5.0$ at $k=1000$ ), showing that raw $VI$ cannot be used to select the optimal number of clusters across different values of $k$ .
Knowl 9 — Pitch Accent Clustering Evaluation on Boston Directions Corpus
empirical result
In a prosodic clustering task using 10 acoustic $F_0$ and intensity features extracted from accented words in the Boston Directions Corpus to recover 5 ToBI pitch accent categories ( $H^*$ , $L^*$ , $L+H^*$ , $L^*+H$ , $H+!H^*$ ) using k-means across $k \in [1, 1000]$ :
- Overall clustering scores are substantially lower (V-measure $< 0.22$ ) than those obtained on document clustering (V-measure $\approx 0.51$ ), reflecting the relative difficulty of acoustic pitch accent disambiguation compared to topic clustering.
- $Q_2$ peaks prematurely at $k = 10$ and steadily drops as $k$ increases due to MDL cluster penalties. In contrast, V-measure increases around $k = 30$ clusters (reaching $\approx 0.21$ ). At this point, additional clusters increase homogeneity ( $rac{H(C|K)}{H(C)}$ decreases) while completeness ( $rac{H(K|C)}{H(K)}$ ) remains stable, demonstrating V-measure's ability to reward genuine clustering improvements that MDL-based penalties penalize.

Coverage note — No substantial contributed material was omitted. The standard k-means clustering algorithm and tf-idf feature extraction were omitted as standalone knowls as they are standard existing background methods.

References

1.Ulrike Baldewein, Katrin Erk, Sebastian Pado, and Detlef Prescher. 2004. Semantic role labelling with similarity-based generalization using EM-based clustering. In Proceedings of Senseval’04, Barcelona.
2.Paul Boersma. 2001. Praat, a system for doing phonetics by computer. Glot International, 5(9-10):341–345.
3.Douglass R. Cutting, Jan O. Pedersen, David Karger, and John W. Tukey. 1992. Scatter/gather: A cluster-based approach to browsing large document collections. In Proceedings of the Fifteenth Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 318–329.
4.I. S. Dhillon, S. Mallela, and D. S. Modha. 2003. Information-theoretic co-clustering. In Proceedings of The Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining(KDD-2003), pages 89–98.
5.Byron E. Dom. 2001. An information-theoretic external cluster-validity measure. Technical Report RJ10219, IBM, October.
6.E. B. Fowlkes and C. L. Mallows. 1983. A method for comparing two hierarchical clusterings. Journal of the American Statistical Association, 78:553–569.
7.Benjamin C. M. Fung, Ke Wang, and Martin Ester. 2003. Hierarchical document clustering using frequent itemsets. In Proc. of the SIAM International Conference on Data Mining.
8.Julia Hirschberg. 2002. The pragmatics of intonational meaning. In Proc. Speech Prosody, pages 65–68.
9.L. Hubert and P. Arabie. 1985. Comparing partitions. Journal of Classification, 2:193–218.
10.L. Hubert and J. Schultz. 1976. Quadratic assignment as a general data analysis strategy. British Journal of Mathematical and Statistical Psychology, 29:190–241.
11.Bjornar Larsen and Chinatsu Aone. 1999. Fast and effective text mining using linear-time document clustering. In KDD ’99: Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining, pages 16–22, New York, NY, USA. ACM Press.
12.Gina-Anne Levow. 2006. Unsupervised and semi-supervised learning of tone and pitch accent. In Proceedings of the main conference on Human Language Technology Conference of the North American Chapter of the Association of Computational Linguistics, pages 224–231, Morristown, NJ, USA. Association for Computational Linguistics.
13.J. McQueen. 1967. Some methods for classification and analysis of multivariate observations. In Proc. of the Fifty Berkeley Symposium on Mathematical Statistics and Probability, pages 281–297.
14.Marina Meila and David Heckerman. 2001. An experimental comparison of model-based clustering methods. Mach. Learn., 42(1/2):9–29.
15.Marina Meila. 2007. Comparing clusterings – an information based distance. Journal of Multivariate Analysis, 98:873–895.
16.G. W. Milligan, S. C. Soon, and L. M. Sokol. 1983. The effect of cluster size, dimensionality and the number of clustes on recovery of true cluster structure. IEEE Transactions on Pattern Analysis and Machine Intelligence, 5:40–47.
17.Boris G. Mirkin. 1996. Mathematical classification and clustering. Kluwer Academic Press.
18.Christine Nakatani, Julia Hirschberg, and Barbara Grosz. 1995. Discourse structure in spoken language: Studies on speech corpora. In Working Notes of AAAI-95 Spring Symposiom on Empirical Methods in Discourse Interpretation.
19.Michael P. Oakes. 1998. Statistics for Corpus Linguistics. Edinburgh University Press.
20.M. Porter. 1980. An algorithm for suffix stripping. Program, 14(3):130–137.
21.William M. Rand. 1971. Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336):846–850, Dec.
22.J. Rissanen. 1978. Modeling by shortest data description. Automatica, 14:465–471.
23.J. Rissanen. 1989. Stochastic complexity in statistical inquiry. World Scientific Series in Computer Science, 15.
24.Sa-Im Shin and Key-Sun Choi. 2004. Automatic word sense clustering using collocation for sense adaptation. In The Second Global Wordnet Conference.
25.K. Silverman, M. Beckman, J. Pitrelli, M. Ostendorf, C. Wightman, P. Price, J. Pierrehumbert, and J. Hirschberg. 1992. Tobi: A standard for labeling english prosody. In Proc. of the 1992 International Conference on Spoken Language Processing, volume 2, pages 12–16.
26.S. Strassel and M. Glenn. 2003. Creating the annotated tdt-4 y2003 evaluation corpus. http://www.nist.gov/speech/tests/tdt/tdt2003/papers/ldc.ppt.
27.Stijn van Dongen. 2000. Performance criteria for graph clustering and markov cluster experiments. Technical report, CWI (Centre for Mathematics and Computer Science), Amsterdam, The Netherlands, The Netherlands.
28.C. J. Van Rijsbergen. 1979. Information Retrieval, 2nd edition. Dept. of Computer Science, University of Glasgow.
29.Santosh Vempala and Grant Wang. 2005. The benefit of spectral projection for document clustering. In Workshop on Clustering High Dimensional Data and its Applications Held in conjunction with Fifth SIAM International Conference on Data Mining (SDM 2005).
30.D. L. Wallace. 1983. Comment. Journal of the American Statistical Association, 78:569–576.
31.Peter Willett. 1988. Recent trends in hierarchic document clustering: a critical review. Inf. Process. Manage., 24(5):577–597.
32.Oren Zamir and Oren Etzioni. 1998. Web document clustering: A feasibility demonstration. In Research and Development in Information Retrieval, pages 46–54.
33.Yujing Zeng, Jianshan Tang, Javier Garcia-Frias, and Guang R. Gao. 2002. An adaptive meta-clustering approach: Combining the information from different clustering results. csb, 00:276.
34.Ying Zhao and George Karypis. 2001. Criterion functions for ducument clustering: Experiments and analysis. Technical Report TR 01–40, Department of Computer Science, University of Minnesota.

Citation

MLA

Rosenberg, A., and J. Hirschberg. “V-Measure: A Conditional Entropy-Based External Cluster Evaluation Measure”. Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning (EMNLP-CoNLL), 2007, pp. 410–20, https://aclanthology.org/D07-1043/.

APA

Rosenberg, A., & Hirschberg, J. (2007). V-Measure: A Conditional Entropy-Based External Cluster Evaluation Measure. Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning (EMNLP-CoNLL), 410–420. https://aclanthology.org/D07-1043/

Chicago

Rosenberg, A., and J. Hirschberg. 2007. “V-Measure: A Conditional Entropy-Based External Cluster Evaluation Measure”. Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning (EMNLP-CoNLL), 410–20. https://aclanthology.org/D07-1043/.

Harvard

Rosenberg, A. and Hirschberg, J. (2007) “V-Measure: A Conditional Entropy-Based External Cluster Evaluation Measure”, Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning (EMNLP-CoNLL). Association for Computational Linguistics, pp. 410–420. Available at: https://aclanthology.org/D07-1043/.

Vancouver

1. Rosenberg A, Hirschberg J (2007) V-Measure: A Conditional Entropy-Based External Cluster Evaluation Measure. In: Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning (EMNLP-CoNLL). Association for Computational Linguistics, pp 410–420

BibTeX

@inproceedings{rosenberg-hirschberg-2007-v,
    title = "{V}-Measure: A Conditional Entropy-Based External Cluster Evaluation Measure",
    author = "Rosenberg, Andrew  and
      Hirschberg, Julia",
    editor = "Eisner, Jason",
    booktitle = "Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning ({EMNLP}-{C}o{NLL})",
    month = jun,
    year = "2007",
    address = "Prague, Czech Republic",
    publisher = "Association for Computational Linguistics",
    url = "https://aclanthology.org/D07-1043/",
    pages = "410--420"
}

Metadata:ACL Anthology

Access the Paper

This paper is available from its original source. Click below to access the PDF.

Open PDF

License: https://creativecommons.org/licenses/by-nc-sa/4.0/

V-Measure: A Conditional Entropy-Based External Cluster Evaluation Measure

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — Definition of Clustering Homogeneity

Knowl 2 — Definition of Clustering Completeness

Knowl 3 — Definition and Parameterized Weighting of V-Measure

Knowl 4 — The Problem of Matching in Cluster-to-Class Evaluation Measures

Knowl 5 — Seven Desirable Formal Properties for Cluster Evaluation Measures

Knowl 6 — Satisfaction Rates of Desirable Properties Across Clustering Evaluation Measures

Knowl 7 — Comparative Analysis of V-Measure Against Variation of Information and Q0

Knowl 8 — Document Clustering Evaluation on TDT-4 Corpus

Knowl 9 — Pitch Accent Clustering Evaluation on Boston Directions Corpus

References

Citation

BibTeX

Access the Paper