Anchored Hyperplane Location Problems

Maxmin location of an anchored ray in 3-space and related problems

Extending Anchored Learning to Machine Translation Evaluation

We compare two methods, Anchored Learning, and a simple new method (Hyperplane Distance), for finding Hard To Learn examples in Machine Learning tasks that use SVMs. These Hard To Learn examples can be corpus errors, or examples which are difficult to predict with the given set of features. The Anchored Learning method is extended to deal with various kernels and SV regression. A number of expe...

Median and center hyperplanes in Minkowski spaces--a unified approach

In this paper we will extend two known location problems from Euclidean n-space to all n-dimensional normed spaces, n¿ 2. Let X be a "nite set of weighted points whose a2ne hull is n-dimensional. Our "rst objective is to "nd a hyperplane minimizing (among all hyperplanes) the sum of weighted distances with respect to X. Such a hyperplane is called a median hyperplane with respect to X, and we w...

Data Envelopment Analysis, Genetic Algorithm, Hyperplane, Efficient Unit

Data Envelopment Analysis (DEA) is actually to obtain the efficiency using inputs and outputs, which can determine efficient and inefficient units with the help of performance calculations such that the efficiency for efficient DMUs is one and less than one for inefficient DMUs [1]. In some cases, the ranking of the decision-making units are not important for decision-makers, and they are only ...

A Nearly Quadratic Bound for the Decision Tree Complexity of k-SUM

We show that the k-SUM problem can be solved by a linear decision tree of depth O(n2 log2 n), improving the recent bound O(n3 log3 n) of Cardinal et al. [7]. Our bound depends linearly on k, and allows us to conclude that the number of linear queries required to decide the n-dimensional Knapsack or SubsetSum problems is only O(n3 logn), improving the currently best known bounds by a factor of n...