Based on the Temperley–Lieb algebra we define a class of one-dimensional Hamiltonians with nearest and next-nearest neighbour interactions. Using the regular representation we give ground states of this model as words of the algebra. Two point correlation functions can be computed employing the Temperley–Lieb relations. Choosing a spin2 representation of the algebra we obtain a generalization o...

Nearest neighbor classification expects the class conditional probabilities to be locally constant, and suffers from bias in high dimensions We propose a locally adaptive form of nearest neighbor classification to try to finesse this curse of dimensionality. We use a local linear discriminant analysis to estimate an effective metric for computing neighborhoods. We determine the local decision b...

A k-nearest neighbor (kNN) query determines the k nearest points, using distance metrics, from a given location. An all k-nearest neighbor (AkNN) query constitutes a variation of a kNN query and retrieves the k nearest points for each point inside a database. Their main usage resonates in spatial databases and they consist the backbone of many location-based applications and not only. In this w...

An Intelligent RAM for Nearest Neighbor Database Searching Aaron Lipman and Woodward Yang Abstract The nearest neighbor algorithm is well suited to an IRAM implementation, given its high bandwidth requirement between memory and processing. We have designed and implemented the Smart Access Memory (SAM) chip to retrieve the k nearest neighbors to a query point in a database of example data vector...

Many spectral estimation methods for irregularly sampled data tend to be heavily biased at higher frequencies or fail to produce a spectrum that is positive for all frequencies. A time series spectral estimator is introduced that applies the principles of a new automatic equidistant missing data algorithm to unevenly spaced data. This time series estimator approximates the irregular data by a n...

in this paper, we ask “can proximity to towns reduces poverty in rural areas?” for this study we have mapped all the villages in orissa. the study is based on small area poverty estimation methodology as well as the secondary data covering 47,395 villages and 109 towns. our main findings are (i) there is a relationship between the distance to nearest town and rural poverty and (ii) poverty leve...

When a spatial point process is observed through a bounded window, edge eeects hamper the estimation of characteristics such as the empty space function F , the nearest neighbour distance distribution G, and the second order moment function K. Here we propose and study product-limit type estimators of F; G and K based on the analogy with censored survival data: the distance from a xed point to ...

Given a regular matrix pencil A + μE, we consider the problem of determining the nearest singular matrix pencil with respect to the Frobenius norm. We present new approaches based on the solution of matrix differential equations for determining the nearest singular pencil A+∆A+ μ(E +∆E), one approach for general singular pencils and another one such that A+∆A and E + ∆E have a common left/right...

Nonlinear dimensionality reduction methods often rely on the nearest-neighbors graph to extract low-dimensional embeddings that reliably capture the underlying structure of high-dimensional data. Research however has shown that computing nearest neighbors of a point from a highdimensional data set generally requires time proportional to the size of the data set itself, rendering the computation...