Large null sets in metric spaces

Near Neighbor Search in Large Metric Spaces

Given user data, one often wants to nd approximate matches in a large database. A good example of such a task is nding images similar to a given image in a large collection of images. We focus on the important and technically di cult case where each data element is high dimensional, or more generally, is represented by a point in a large metric spaceand distance calculations are computationally...

Clustering Large Datasets in Arbitrary Metric Spaces

Clustering partitions a collection of objects into groups called clusters, such that similar objects fall into the same group. Similarity between objects is defined by a distance function satisfying the triangle inequality; this distance function along with the collection of objects describes a distance space. In a distance space, the only operation possible on data objects is the computation o...

Regularity Properties of Null-Additive Fuzzy Measure on Metric Spaces

We shall discuss further regularity properties of null-additive fuzzy measure on metric spaces following the previous results. Under the null-additivity condition, some properties of the inner/outer regularity and the regularity of fuzzy measure are shown. Also the strong regularity of fuzzy measure is discussed on complete separable metric spaces. As an application of strong regularity, we pre...

Further properties of null-additive fuzzy measure on metric spaces

We shall continue to discuss further properties of null-additive fuzzy measure on metric spaces following the previous results. Under the null-additivity condition, some properties of the inner/outer regularity and the regularity of fuzzy measure are shown. Also the strong regularity of fuzzy measure is discussed on complete separable metric spaces. As an application of strong regularity, we pr...

A Note on Naturally Ordered Sets in Semi-metric Spaces