We present several quantum algorithms for performing nearest-neighbor learning. At the core of our algorithms are fast and coherent quantum methods for computing distance metrics such as the inner product and Euclidean distance. We prove upper bounds on the number of queries to the input data required to compute these metrics. In the worst case, our quantum algorithms lead to polynomial reducti...

Finding the nearest neighbor among a large collection of high dimensional vectors can be a computationally demanding task. In this paper, we pursue fast vector matching by representing vectors in IRn with lower dimensional projections in IR, m ≤ n. The key to creating and using the representative vectors is a lower bound on the Euclidean distance between arbitrary vectors in IRn based on the su...

Edit distance is not the only approach how distance between two character sequences can be calculated. Strings can be also compared in somewhat subtler geometric ways. A procedure inspired by Random Indexing can attribute an D-dimensional geometric coordinate to any character N-gram present in the corpus and can subsequently represent the word as a sum of N-gram fragments which the string conta...

In this work, one and two-dimensional lattices are studied theoretically by a statistical mechanical approach. The nearest and next-nearest neighbor interactions are both taken into account, and the approximate thermodynamic properties of the lattices are calculated. The results of our calculations show that: (1) even though the next-nearest neighbor interaction may have an insignificant ef...

In this paper, we have evaluated some techniques for the time series classification problem. Many distance measures have been proposed as an alternative to the Euclidean Distance in the Nearest Neighbor Classifier. To verify the assumption that the combination of various similarity measures may produce a more accurate classifier, we have proposed an algorithm to combine several measures based o...

In this paper, we have evaluated some techniques for the time series classification problem. Many distance measures have been proposed as an alternative to the Euclidean Distance in the Nearest Neighbor Classifier. To verify the assumption that the combination of various similarity measures may produce a more accurate classifier, we have proposed an algorithm to combine several measures based o...

The nearest-neighbor method is perhaps the simplest of all algorithms for predicting the class of a test example. The training phase is trivial: simply store every training example, with its label. To make a prediction for a test example, first compute its distance to every training example. Then, keep the k closest training examples, where k ≥ 1 is a fixed integer. Look for the label that is m...

We consider the Approximate Nearest Line Search (NLS) problem. Given a set L of N lines in the high dimensional Euclidean space R, the goal is to build a data structure that, given a query point q ∈ R, reports a line ` ∈ L such that its distance to the query is within (1+ ) factor of the distance of the closest line to the query point q. The problem is a natural generalization of the well-studi...

We propose an approximation algorithm for efficient correlation search in time series data. In our method, we use Fourier transform and neural network to embed time series into a low-dimensional Euclidean space. The given space is learned such that time series correlation can be effectively approximated from Euclidean distance between corresponding embedded vectors. Therefore, search for correl...