Silhouettes: a graphical aid to the interpretation and validation of cluster analysis
Journal of Computational and Applied Mathematics
Algorithms for clustering data
Algorithms for clustering data
A Validity Measure for Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Elements of information theory
Elements of information theory
A comparative study of goodness-of-fit tests for multivariate normality
Journal of Multivariate Analysis
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
A new approach to the BHEP tests for multivariate normality
Journal of Multivariate Analysis
A new cluster validity index for the fuzzy c-mean
Pattern Recognition Letters
A comparison of cluster validity criteria for a mixture of normal distributed data
Pattern Recognition Letters
Unsupervised Learning of Finite Mixture Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Visual cluster validity for prototype generator clustering models
Pattern Recognition Letters
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Stability-based validation of clustering solutions
Neural Computation
A new test for multivariate normality
Journal of Multivariate Analysis
Edgeworth Approximation of Multivariate Differential Entropy
Neural Computation
An objective approach to cluster validation
Pattern Recognition Letters
On fuzzy cluster validity indices
Fuzzy Sets and Systems
Relational visual cluster validity (RVCV)
Pattern Recognition Letters
A Projection Pursuit Algorithm for Exploratory Data Analysis
IEEE Transactions on Computers
Cluster Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
NEC: a hierarchical agglomerative clustering based on fisher and negentropy information
WIRN'05 Proceedings of the 16th Italian conference on Neural Nets
Some new indexes of cluster validity
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Survey of clustering algorithms
IEEE Transactions on Neural Networks
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We introduce a new validity index for crisp clustering that is based on the average normality of the clusters. Unlike methods based on inter-cluster and intra-cluster distances, this index emphasizes the cluster shape by using a high order characterization of its probability distribution. The normality of a cluster is characterized by its negentropy, a standard measure of the distance to normality which evaluates the difference between the cluster's entropy and the entropy of a normal distribution with the same covariance matrix. The definition of the negentropy involves the distribution's differential entropy. However, we show that it is possible to avoid its explicit computation by considering only negentropy increments with respect to the initial data distribution, where all the points are assumed to belong to the same cluster. The resulting negentropy increment validity index only requires the computation of covariance matrices. We have applied the new index to an extensive set of artificial and real problems where it provides, in general, better results than other indices, both with respect to the prediction of the correct number of clusters and to the similarity among the real clusters and those inferred.