Bhattacharyya distance巴塔查亚距离
In statistics, machine learning, and data science, Bhattacharyya distance measures the similarity of two probability distributions. It is closely related to the Bhattacharyya coefficient, which measures the overlap between two statistical samples or populations.
Both measures are named after Anil Kumar Bhattacharya, a statistician who worked in the 1930s at the Indian Statistical Institute.
Bhattacharyya distance, a divergence measure, finds extensive applications in artificial intelligence.
This distance metric is pivotal in various AI domains, such as feature extraction and selection research, image processing, speaker recognition, and phone clustering.
Notably, researchers have even proposed a unique concept called “Bhattacharyya space,” which serves as a technique for texture segmentation. This innovative approach aids in identifying significant features, further enhancing the effectiveness of Bhattacharyya distance in AI applications.
Bhattacharyya and Mahalanobi’s Distance
The Mahalanobis distance used in Fisher’s Linear Discriminant Analysis is a particular case of the Bhattacharyya Distance.
The Bhattacharyya coefficient is an approximate measurement of the overlap between two statistical samples. The coefficient can determine the relative closeness of the two samples being considered. Calculating the Bhattacharyya coefficient involves a rudimentary integration of the overlap of the two samples.
Bhattacharyya Distance vs. Kullback-Leibler (KL) Divergence
The main difference between the two is that Bhattacharyya is a metric and KL is not, so you must consider what information you want to extract about your data points.
In the context of control theory and the study of the problem of signal selection, the Bhattacharyya distance is superior to the Kullback-Leibler distance.
在统计学、机器学习和数据科学中，巴塔查亚(Bhattacharyya)距离衡量两个概率分布的相似度。它与巴塔查亚系数密切相关，后者衡量两个统计样本或总体之间的重叠。
这两项指标均以20世纪30年代在印度统计研究所工作的统计学家阿尼尔·库马尔·巴塔查亚(Anil Kumar Bhattacharya)的名字命名。
巴塔查亚距离(Bhattacharyya distance)是一种散度度量，在人工智能中有着广泛的应用。
这种距离度量在各种人工智能领域都至关重要，例如特征提取和选择研究、图像处理、说话人识别和电话聚类。
值得注意的是，研究人员甚至提出了一个名为“巴塔查亚空间Bhattacharyya space”的独特概念，作为纹理分割技术。这种创新方法有助于识别重要特征，进一步增强巴塔查亚距离在人工智能应用中的有效性。
巴塔查亚和马哈拉诺比的距离
Fisher线性判别分析中使用的Mahalanobis距离是Bhattacharyya距离的特例。
巴塔查亚系数是两个统计样本之间重叠的近似测量。该系数可以确定所考虑的两个样本的相对接近程度。计算巴塔查亚系数涉及两个样本重叠的基本积分。
Bhattacharyya距离与Kullback-Leibler (KL)散度
两者之间的主要区别在于Bhattacharyya是一个指标，而KL不是，因此您必须考虑要提取有关数据点的哪些信息。
在控制理论和信号选择问题的研究中，Bhattacharyya距离优于Kullback-Leibler距离。
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信源：人工智能先锋通讯 |丹尼·布维尼克
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