Comparing partitions Export

@article{citeulike:1923137, abstract = {The problem of comparing two different partitions of a finite set of objects reappears continually in the clustering literature. We begin by reviewing a well-known measure of partition correspondence often attributed to Rand (1971), discuss the issue of correcting this index for chance, and note that a recent normalization strategy developed by Morey and Agresti (1984) and adopted by others (e.g., Miligan and Cooper 1985) is based on an incorrect assumption. Then, the general problem of comparing partitions is approached indirectly by assessing the congruence of two proximity matrices using a simple cross-product measure. They are generated from corresponding partitions using various scoring rules. Special cases derivable include traditionally familiar statistics and/or ones tailored to weight certain object pairs differentially. Finally, we propose a measure based on the comparison of object triples having the advantage of a probabilistic interpretation in addition to being corrected for chance (i.e., assuming a constant value under a reasonable null hypothesis) and bounded between ±1.}, author = {Hubert, Lawrence and Arabie, Phipps}, citeulike-article-id = {1923137}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/BF01908075}, citeulike-linkout-1 = {http://www.springerlink.com/content/x64124718341j1j0}, day = {1}, doi = {10.1007/BF01908075}, journal = {Journal of Classification}, keywords = {cluster, comparison, segmentation, validation}, month = {December}, number = {1}, pages = {193--218}, posted-at = {2008-12-05 01:01:17}, priority = {2}, title = {Comparing partitions}, url = {http://dx.doi.org/10.1007/BF01908075}, volume = {2}, year = {1985} }

TY - JOUR ID - citeulike:1923137 L3 - citeulike-article-id:1923137 N2 - The problem of comparing two different partitions of a finite set of objects reappears continually in the clustering literature. We begin by reviewing a well-known measure of partition correspondence often attributed to Rand (1971), discuss the issue of correcting this index for chance, and note that a recent normalization strategy developed by Morey and Agresti (1984) and adopted by others (e.g., Miligan and Cooper 1985) is based on an incorrect assumption. Then, the general problem of comparing partitions is approached indirectly by assessing the congruence of two proximity matrices using a simple cross-product measure. They are generated from corresponding partitions using various scoring rules. Special cases derivable include traditionally familiar statistics and/or ones tailored to weight certain object pairs differentially. Finally, we propose a measure based on the comparison of object triples having the advantage of a probabilistic interpretation in addition to being corrected for chance (i.e., assuming a constant value under a reasonable null hypothesis) and bounded between ±1. IS - 1 JF - Journal of Classification EP - 218 TI - Comparing partitions VL - 2 SP - 193 KW - cluster KW - comparison KW - segmentation KW - validation AU - Hubert, Lawrence AU - Arabie, Phipps PY - 1985/12/01/ UR - http://dx.doi.org/10.1007/BF01908075 ER -