ANN in High Dimensions
نویسنده
چکیده
1.1 Hypercube and Hamming distance Definition 1.1 The set of points Hd = {0, 1} is the d-dimensional hypercube. A point p = (p1, . . . , pd) ∈ Hd can be interpreted, naturally, as a binary string p1p2 . . . pd. The Hamming distance dH(p, q) between p, q ∈ Hd, is the number of coordinates where p and q disagree. It is easy to verify that the Hamming distance comply with the triangle inequality, and is as such a metric. As we saw in previous lectures, all we need to solve (1 + ε)-ANN, is it is enough to efficiently solve the approximate near neighbor problem. Namely, given a set P of n points in Hd, and radius r > 0 and parameter ε > 0, we want to decide for a query point q whether dH(q, P ) ≤ r or dH(q, P ) ≥ (1 + ε)r. Definition 1.2 For a set P of points, a data-structure NNbr≈(P, r, (1+ε)r) solves the approximate near neighbor problem, if given a query point q, the data-structure works as follows. • If d(q, P ) ≤ r then NNbr≈ outputs a point p ∈ P such that d(p, q) ≤ (1 + ε)r. • If d(q, P ) ≥ (1 + ε)r, in this case NNbr≈ outputs that “d(q, P ) ≥ r”. • If r ≤ d(q, P ) ≤ (1 + ε)r, either of the above answers is acceptable. Given such a data-structure NNbr≈(P, r, (1 + ε)r), one can construct a data-structure that answers ANN using O(log(n/ε)) queries.
منابع مشابه
Pedotransfer functions for estimating soil moisture content using fractal parameters in Ardabil province
Extended abstract 1- Introduction Soil moisture curve is an important characteristic of soil and its measurement is necessary for determining soil available water content for plant, evapotranspiration and irrigation planning. Direct measurements of soil moisture coefficients are time-consuming and costly. But it is possible to estimate these characteristics from readily available soil propert...
متن کاملEvaluation of the Noise Injection in High Dimensions
2 ANN Classifiers The noise injection into the training samples has been shown to lead to improvement of the generalization ability of artificial neural network(ANN) classifiers. In this paper, we investigate the positive effect of the noise injection on the generalization ability of ANN classifiers in high dimensions. We further show that the noise injection technique is very useful in situati...
متن کاملApplication of Artificial Neural Networks (ANN) and Image Processing for Prediction of the Geometrical Properties of Roasted Pistachio Nuts and Kernels
Roasting is the most common way for pistachio nuts processing, and the purpose of that was to increase the products total acceptability. Purpose of this study was to investigate the effect of temperature (90, 120 and 150°C), time (20, 35 and 50 min), and roasting air velocity (0.5, 1.5 and 2.5 m/s) on geometrical attributes of pistachio nuts and kernels including principle dimensions, shape fac...
متن کاملEntrepreneurship policy and innovative indicators of industrial companies: Evaluation by MCDM and ANN Methods
The present paper presented a methodology for prioritizing the innovative and entrepreneurial indicators using Multi Criteria Decision Making (MCDM) and Artificial Neural Networks (ANNs), taking into account three individual, organizational and cultural dimensions simultaneously in decision making procedure. This methodology has two main advantages: first, the speed of operation in the accounti...
متن کاملPrediction of scour dimension in the Plunge Pools below Outlet Bucket with Artificial intelligence method
Accurate prediction of sediment scour hole dimensions downstream of hydraulic structures, e.g. the outlet bucket, is a complex and not straight forward engineering problem encountered worldwide. Because of the complexities of the study, its comprehensive, simultaneous including water flow, sediment and applying all of the effective variables involved in scouring it is not easy possible. Dimens...
متن کامل