of finding a low distortion non-contracting embedding of M into line and tree metrics. • Our first result is that the problem of embedding M into the line, parameterized by the distortion d, is fixed parameter tractable (FPT). We describe an algorithm that on input (G, d) either constructs an embedding of M

We present several computationally efficient algorithms, and complexity results on low distortion mappings between metric spaces. An embedding between two metric spaces is a mapping between the two metric spcaes and the distortion of the embedding is the factor by which the distances change. We

We study the problem of minimum-distortion embedding of ultrametrics into the plane and higher dimensional spaces. Ultrametrics are a natural class of metrics that frequently occur in applications involving hierarchical clustering. Low-distortion embeddings of ultrametrics into the plane help

factorized model, and also improves over a full model trained on pre-selected features using the same memory requirements. We further adapt LORETA to learn positive semi-definite low-rank matrices, providing an online algorithm for low-rank metric learning. LORETA also shows consistent improvement over

ABSTRACT We study the problem of minimum-distortion embedding of ultra-metrics into the plane and higher dimensional spaces. Ultrametrics are a natural class of metrics that frequently occur in applicationsinvolving hierarchical clustering. Low-distortion embeddings of ultrametrics into the plane

Recently, we described a fast self-organizing algorithm for embedding a set of objects into a low-dimensional Euclidean space in a way that preserves the intrinsic dimensionality and metric structure of the data [Proc. Natl. Acad. Sci. U.S.A. 99 (2002) 15869–15872]. The method, called stochastic

. The basic algorithms underlying an automatic hardware synthesis environment using fully formal graphical requirements specifications as source language are outlined. The source language is real-time symbolic timing diagrams [3], which are a metric-time temporal logic such that hard real

and associated parameters, careful optimization, and low-power design techniques. In order to validate our claim we present proof of concept implementations of two different algorithms—Rabin’s Scheme and NtruEncrypt—and analyze their architecture and performance according to various established metrics like

Abstract- Many applications in computer graphics require complex, highly detailed models. However the level of detail may vary considerably for a given scenario. To control processing time at a low-end terminal, where presentation with high solution is not supported at all, it is often desirable

-trary shape in metric and vector spaces. Moreover, with a time complexity ranging from O(n log n) to O(n2) these al-gorithms are scalable to large data sets in a database system. In this paper, we propose CUDA-DClust, a massively par-allel algorithm for density-based clustering for the use of a Graphics