We propose a transformation method to circumvent the problems with high dimensional data. For each object in the data, we create an itemset of the k-nearest neighbors of that object, not just for one of the dimensions, but for many views of the data. On the resulting collection of sets, we can mine frequent itemsets; that is, sets of points that are frequently seen together in some of the views...

Let Bn be an increasing sequence of regions in d-dimensional space with volume n and with union d. We prove a general central limit theorem for functionals of point sets, obtained either by restricting a homogeneous Poisson process to Bn, or by by taking n uniformly distributed points in Bn. The sets Bn could be all cubes but a more general class of regions Bn is considered. Using this general ...

We propose a new algorithm that simultaneously estimates the intrinsic dimension and intrinsic entropy of random data sets lying on smooth manifolds. The method is based on asymptotic properties of entropic graph constructions. In particular, we compute the Euclidean -nearest neighbors ( NN) graph over the sample points and use its overall total edge length to estimate intrinsic dimension and e...

SVI is a promising new scheme for indexing high-dimensional points and vectors for use in vector retrieval and for nding the k-nearest neighbours. SVI performs an approximate search; that is, it trades oo the completeness of the search for speed. The indexing scheme is built around a rule that was found by applying data mining techniques to sets of random vectors. This approach could well lead ...

A data structure is said to be succinct if it uses an amount of space that is close to the informationtheoretic lower bound, but still allows for efficient query processing. Quadtrees are among the most widely used data structures for answering queries on point sets in Euclidean space. In this paper we present a succinct quadtree structure. Our data structure can efficiently answer approximate ...

We present a method of surface reconstruction from high-density scatter points P = {p1, p2, ..., pN} without a normal vector in R3. This method first sets a uniform grid and deforms each cell of the grid by fitting the vertex of each cell to the nearest of the input points. It then constructs triangles according to the pattern of the vertices’s state in each cell. Our method can work fast with ...