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The standard algorithm for hierarchical agglomerative clustering (HAC) has a time complexity of <math>\mathcal{O}(n^3)</math> and requires <math>\mathcal{O}(n^2)</math> memory, which makes it too slow for even medium data sets. However, for some special cases, optimal efficient agglomerative methods (of complexity <math>\mathcal{O}(n^2)</math>) are known: SLINK<!--boldface per WP:R#PLA--> for single-linkage and CLINK for complete-linkage clustering. With a heap the runtime of the general case can be reduced to <math>\mathcal{O}(n^2 \log n)</math> at the cost of further increasing the memory requirements. In many cases, the memory overheads of this approach are too large to make it practically usable.

The standard algorithm for hierarchical agglomerative clustering (HAC) has a time complexity of <math>\mathcal{O}(n^3)</math> and requires <math>\mathcal{O}(n^2)</math> memory, which makes it too slow for even medium data sets. However, for some special cases, optimal efficient agglomerative methods (of complexity <math>\mathcal{O}(n^2)</math>) are known: SLINK<!--boldface per WP:R#PLA--> for single-linkage and CLINK for complete-linkage clustering. With a heap the runtime of the general case can be reduced to <math>\mathcal{O}(n^2 \log n)</math> at the cost of further increasing the memory requirements. In many cases, the memory overheads of this approach are too large to make it practically usable.

'''<font color="#ff8000"> 层次凝聚聚类Hierarchical agglomerative clustering</font>'''(HAC)的标准算法的时间复杂度为 < math > mathical { o }(n ^ 3) </math > ，并且需要 < math > mathcal { o }(n ^ 2) </math > 占用内存，这使得它对于中等数据集来说效率太低了。然而，对于某些特殊情况，已知的最佳有效凝聚方法(复杂度 < math > mathcal { o }(n ^ 2) </math >)是: 单连锁的 SLINK < ! ——粗体 wp: r # pla-- > 和完全连锁的 CLINK。对于数据群而言，一般情况下的运行时可以缩减为 < math > mathcal { o }(n ^ 2 log n) </math > ，代价是进一步增加内存需求。在许多情况下，这种方法的内存开销太大，并不实用。

'''<font color="#ff8000"> 层次凝聚聚类Hierarchical agglomerative clustering</font>'''(HAC)的标准算法的时间复杂度为 < math > mathical { o }(n ^ 3) </math > ，并且需要 < math > mathcal { o }(n ^ 2) </math > 占用内存，这使得它对于中等数据集来说效率太低了。然而，对于某些特殊情况，已知的最佳有效凝聚方法(复杂度 < math > mathcal { o }(n ^ 2) </math >)是: 单连锁的 SLINK < ! ——粗体 wp: r # pla-- > 和完全连锁的 CLINK。对于数据群而言，一般情况下的运行时可以缩减为 < math > mathcal { o }(n ^ 2 log n) </math > ，代价是进一步增加内存需求。在多数情况下，这种方法的内存开销太大，并不实用。