Minimal distance index — A new clustering performance metrics

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We define a new index for measuring clustering performance called the Minimal Distance Index. The index is based on representing clusters by characteristic objects containing the majority of cluster points. It performs well for both spherical and ellipsoidal clusters. This method can recognize all acceptable partitions with well-separated clusters. Among such partitions, our minimal distance index may identify the most appropriate one. The proposed index is compared with other most frequently used indexes in numerous examples with spherical and ellipsoidal clusters. It turned out that our proposed minimal distance index always recognizes the most appropriate partition, whereas the same cannot be said for other indexes found in the literature.Furthermore, among all acceptable partitions, the one with the largest number of clusters, not necessarily the most appropriate ones, has a special significance in image analysis. Namely, following Mahalanobis image segmentation, our index recognizes partitions that might not be the most appropriate ones but are the ones using colors that significantly differ from each other. The minimal distance index recognizes partitions with dominant colors, thus making it possible to select specific details in the image. We apply this approach to some real-world applications such as the plant rows detection problem, painting analysis, and iris detection. This may also be useful for medical image analysis.