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摘要
Background: Distance functions are fundamental for evaluating the differences between gene expression profiles. Such a function would output a low value if the profiles are strongly correlated-either negatively or positively-and vice versa. One popular distance function is the absolute correlation distance, d(a) = 1 - vertical bar rho vertical bar, where rho is similarity measure, such as Pearson or Spearman correlation. However, the absolute correlation distance fails to fulfill the triangle inequality, which would have guaranteed better performance at vector quantization, allowed fast data localization, as well as accelerated data clustering. @@@ Results: In this work, we propose d(r) = root 1 - vertical bar rho vertical bar as an alternative. We prove that dr satisfies the triangle inequality when rho represents Pearson correlation, Spearman corre-lation, or Cosine similarity. We show dr to be better than ds = root 1 - rho(2), another variant of da that satisfies the triangle inequality, both analytically as well as experimentally. We empirically compared drwith da in gene clustering and sample clustering experiment by real-world biological data. The two distances performed similarly in both gene clus-tering and sample clustering in hierarchical clustering and PAM (partitioning around medoids) clustering. However, d(r) demonstrated more robust clustering. According to the bootstrap experiment, dr generated more robust sample pair partition more frequently (P-value < 0.05). The statistics on the time a class "dissolved" also support the advantage of d(r) in robustness. @@@ Conclusion: d(r) , as a variant of absolute correlation distance, satisfies the triangle inequality and is capable for more robust clustering.
