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Jensen-cumulative entropy based separation indices for classification

Author

Listed:
  • Kharazmi, Omid
  • Buono, Francesco
  • Balakrishnan, Narayanaswamy

Abstract

In the first part of this article, by considering two cumulative Jensen-type divergence measures, namely, the Jensen-cumulative residual entropy (Jensen-CRE) and Jensen-cumulative past entropy (Jensen-CPE), we establish new theoretical upper bounds for these measures. Using these, we define efficiency indices for classification and threshold-based image segmentation in terms of these measures, which are normalized to take values in the unit interval (0,1). These indices serve as effective quantities derived from cumulative entropy-based measures, and two illustrative examples are also provided to demonstrate their practical applicability. In the second part of this article, we follow some real applications associated with the proposed measures. We present an application of the Jensen-CRE measure in the context of image quality assessment. Gaussian noise is added to the original image based on a specified signal-to-noise ratio to simulate different noise levels. We then apply the proposed relative efficiency separation index, based on the Jensen-CPE measure, within the framework of a new algorithm for image segmentation. The performance of the proposed method is then compared with well-known techniques such as Otsu’s thresholding and K-means clustering. The effectiveness and accuracy of the proposed method are quantitatively assessed using several evaluation metrics, including accuracy, recall, precision, specificity, F1-score, Dice coefficient, Jaccard index, and adjusted rand index, on three representative images selected from the Berkeley image segmentation database. The results in these cases demonstrate the effectiveness of the proposed Jensen-CRE measure for image quality assessment under Gaussian noise analysis, as well as its excellent performance in threshold-based image segmentation.

Suggested Citation

  • Kharazmi, Omid & Buono, Francesco & Balakrishnan, Narayanaswamy, 2025. "Jensen-cumulative entropy based separation indices for classification," Chaos, Solitons & Fractals, Elsevier, vol. 200(P3).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p3:s0960077925010422
    DOI: 10.1016/j.chaos.2025.117029
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    References listed on IDEAS

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    1. Park, Sangun & Rao, Murali & Shin, Dong Wan, 2012. "On cumulative residual Kullback–Leibler information," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2025-2032.
    2. Jorge Navarro & Francesco Buono & Jorge M. Arevalillo, 2023. "A New Separation Index and Classification Techniques Based on Shannon Entropy," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-24, December.
    3. Sangun Park & Hadi Alizadeh Noughabi & Ilmun Kim, 2018. "General cumulative Kullback–Leibler information," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(7), pages 1551-1560, April.
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