影像分類分析廣泛應用於許多科學領域，例如計算機視覺、異常檢測、生物學、醫學等。基於最小化 Kullback-Leibler (KL) 散度估計的最大概似估計方法在影像分類中很流行。然而，眾所周知，最大概似估計值對模型假設很敏感。如果存在數據異常值或模型錯誤設定，則可能導致有偏差的估計和不穩定的推論。其中一種補救措施是利用穩健的散度。在本篇論文中，我們引入了更一般化的 KL 散度，稱為 γ-散度。它提供了一種穩健的方法來排除異常值和模型錯誤指定的問題。我們提出了一個基於局部最小化 γ-散度的半參數分群結構，進一步考慮了影像的旋轉和平移性質。我們將所提出的方法命名為 γ-最大化期望值演算法。γ-最大化期望值演算法可以改進參數的估計。模擬研究結果顯示，與現今流行的方法相比，本篇所提出的方法表現良好。;Image clustering analysis is widely used in many scientific fields such as computer vision, anomaly detection, biology, medicine, etc. Maximum-likelihood based methods, which arise from the minimum Kullback-Leibler (KL) divergence estimation, are popular in image clustering. However, MLE is known to be sensitive to model assumptions. It can lead to biased estimation and unstable inference if there exist data outliers or model misspecification. A remedy is to introduce a robust divergence. In this thesis, a generalization of KL divergence, namely γ-divergence, is brought in. It provides a robust method to defend outliers and model misspecification. We propose a semi-parametric framework for clustering based on local minimization of γ-divergence, further considering rotation and translation of images. We name the proposed method the γ-Expectation–Maximization (γ-EM) algorithm. The γ-EM leads to improved parameter estimation. Numerical studies have demonstrated that the proposed method performs reasonably well in comparison with some popular methods.
