Nonextensive Pythagoras' Theorem

@misc{citeulike:1669193, abstract = {ullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And hence, this property is referred to as Pythagoras' theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches of statistical estimation theory like information geometry. Equvalent of Pythagoras' theorem in the generalized nonextensive formalism is established in (Dukkipati at el., Physica A, 361 (2006) 124-138). In this paper we give a detailed account of it.}, author = {Dukkipati, Ambedkar }, citeulike-article-id = {1669193}, eprint = {cs/0611030}, keywords = {pythagoras}, month = {Sep}, posted-at = {2007-09-18 14:22:05}, priority = {2}, title = {Nonextensive Pythagoras' Theorem}, url = {http://arxiv.org/abs/cs/0611030}, year = {2007} }

TY - ELEC ID - citeulike:1669193 L3 - citeulike-article-id:1669193 TI - Nonextensive Pythagoras' Theorem N2 - ullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And hence, this property is referred to as Pythagoras' theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches of statistical estimation theory like information geometry. Equvalent of Pythagoras' theorem in the generalized nonextensive formalism is established in (Dukkipati at el., Physica A, 361 (2006) 124-138). In this paper we give a detailed account of it. KW - pythagoras AU - Dukkipati, Ambedkar PY - 2007/Sep/12/ UR - http://arxiv.org/abs/cs/0611030 ER -