Low Dimensional Euclidean Volume Preserving Embeddings
نویسنده
چکیده
Let P be an n-point subset of Euclidean space and d ≥ 3 be an integer. In this paper we study the following question: What is the smallest (normalized) relative change of the volume of subsets of P when it is projected into Rd . We prove that there exists a linear mapping f : P 7→ Rd that relatively preserves the volume of all subsets of size up to ⌊d/2⌋ within at most a factor of O (n2/d √ logn log logn).
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عنوان ژورنال:
- CoRR
دوره abs/1003.0511 شماره
صفحات -
تاریخ انتشار 2010