کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
404662 | 677442 | 2008 | 10 صفحه PDF | دانلود رایگان |
We perform a deeper analysis of an axiomatic approach to the concept of intrinsic dimension of a dataset proposed by us in the IJCNN’07 paper. The main features of our approach are that a high intrinsic dimension of a dataset reflects the presence of the curse of dimensionality (in a certain mathematically precise sense), and that dimension of a discrete i.i.d. sample of a low-dimensional manifold is, with high probability, close to that of the manifold. At the same time, the intrinsic dimension of a sample is easily corrupted by moderate high-dimensional noise (of the same amplitude as the size of the manifold) and suffers from prohibitively high computational complexity (computing it is an NP-complete problem). We outline a possible way to overcome these difficulties.
Journal: Neural Networks - Volume 21, Issues 2–3, March–April 2008, Pages 204–213