Question: [25] The sum distance E4 = K(x|y) + K(y|x) is a metric by Theorem 8.3.6. Prove that its normalization defined by e4 = (K(x|y) +

[25] The sum distance E4 = K(x|y) + K(y|x) is a metric by Theorem 8.3.6.

Prove that its normalization defined by e4 = (K(x|y) +

K(y|x))/K(x, y) takes values in [0, 1] and is also a metric.

Source: [M. Li, J.H. Badger, X. Chen, S. Kwong, P. Kearney, and H.

Zhang, Bioinformatics 17:2(2001), 149–154].

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