A Note on Circular Decomposable Metrics

The Structure of Circular Decomposable Metrics

The Kalmanson Complex

Let X be a finite set of cardinality n. The Kalmanson complex Kn is the simplicial complex whose vertices are non-trivial X-splits, and whose facets are maximal circular split systems over X. In this paper we examine Kn from three perspectives. In addition to the T -theoretic description, we show that Kn has a geometric realization as the Kalmanson conditions on a finite metric. A third descrip...

Dimension Reduction in the l1 norm

The Johnson-Lindenstrauss Lemma shows that any set of n points in Euclidean space can be mapped linearly down to O((log n)/ǫ) dimensions such that all pairwise distances are distorted by at most 1 + ǫ. We study the following basic question: Does there exist an analogue of the JohnsonLindenstrauss Lemma for the l1 norm? Note that Johnson-Lindenstrauss Lemma gives a linear embedding which is inde...

Studies Into the Omission of Take-Down Tension System in Circular Kniting Machanes (TECHNICAL NOTE)

This paper reports on an attempt to modify a circular knitting machine such that it would operate without the need for a customary tension system where a kinitting machine can operate without an asymmetric take-down system preliminary results appear promising and warrant further development. 

Optimal Decision-Theoretic Classification Using Non-Decomposable Performance Metrics

We provide a general theoretical analysis of expected out-of-sample utility, also referred to as decisiontheoretic classification, for non-decomposable binary classification metrics such as F-measure and Jaccard coefficient. Our key result is that the expected out-of-sample utility for many performance metrics is provably optimized by a classifier which is equivalent to a signed thresholding of...