Voronoi diagram

In mathematics, a Voronoi diagram, named after Georgy Voronoi, also called a Voronoi tessellation, a Voronoi decomposition, or a Dirichlet tessellation (after Lejeune Dirichlet), is a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space, e.g., by a discrete set of points.

In the simplest case, we are given a set of points S in the plane, which are the Voronoi sites. Each site s has a Voronoi cell V(s) consisting of all points closer to s than to any other site. The segments of the Voronoi diagram are all the points in the plane that are equidistant to two sites. The Voronoi nodes are the points equidistant to three (or more) sites.

Phase correlation

In image processing, phase correlation is a fast frequency-domain approach to estimate the relative translative movement between two images.

Given two input images and :

Recommendation system

Recommender systems form a specific type of information filtering (IF) technique that attempts to present information items (movies, music, books, news, images, web pages, etc.) that are likely of interest to the user. Typically, a recommender system compares the user's profile to some reference characteristics, and seeks to predict the 'rating' that a user would give to an item they had not yet considered. These characteristics may be from the information item (the content-based approach) or the user's social environment (the collaborative filtering approach).

When building the user's profile a distinction is made between explicit and implicit forms of data collection.

Eeny,meeny,miny, moe

Bloom Filters: Designing a Spellchecker « I POWER INFINITY

Bloom filters are highly space/time efficient probabilistic data structures that are used to solve the membership problem of a set, that is, given an element, it is used to find out whether the particular element belongs to the set or not. False positives can occur in the results (though we can really minimize its probability) but false negatives are not allowed.

Ever wondered how the browser/text editor spell checkers work? They tend to take some bare minimum space and are very time efficient. You guessed it right : Bloom Filters is the key! I have designed a Spellchecker in C language using bloom filters and would like to explain how it works, thereby explaining bloom filters in general.

Now, the data structure of the spell checker is basically a m-bit array. Moreover we have k hash f ...

Job-shop problem

The job-shop problem (JSP) is a problem in discrete or combinatorial optimization, and is a generalization of the famous travelling salesman problem. It is a prominent illustration of a class of problems in computational complexity theory which are hard to solve.

Let and be two finite sets. On account of the industrial origins of the problem, the M_i are called machines and the J_j are called jobs.

K-means algorithm

The k-means algorithm is an algorithm to cluster n objects based on attributes into k partitions, k < n. It is similar to the expectation-maximization algorithm for mixtures of Gaussians in that they both attempt to find the centers of natural clusters in the data. It assumes that the object attributes form a vector space. The objective it tries to achieve is to minimize total intra-cluster variance, or, the squared error function

where there are k clusters S_i, i = 1, 2, ..., k, and µ_i is the centroid or mean point of all the points x_j ∈ S_i.

The k-means clustering was invented in 1956.^[1] The most common form of the algorithm uses an iterative refinement heuristic known as Lloyd's algorithm.^[2] Lloyd's algorithm starts by partitioning the input points into k initial sets, either at random or using some heuristic data. It then calculates the mean point, or centroid, of each set. It constructs a new partition by associating each point with the closest centroid. Then the centroids are recalculated for the new clusters, and algorithm repeated by alternate application of these two steps until convergence, which is obtained when the points no longer switch clusters (or alternatively centroids are no longer changed).

Sorting algorithm#List of sorting algorithms

A* search algorithm

In computer science, A* (pronounced "A star") is a best-first, graph search algorithm that finds the least-cost path from a given initial node to one goal node (out of one or more possible goals).

It uses a distance-plus-cost heuristic function (usually denoted f(x)) to determine the order in which the search visits nodes in the tree. The distance-plus-cost heuristic is a sum of two functions: the path-cost function (usually denoted g(x), which may or may not be a heuristic) and an admissible "heuristic estimate" of the distance to the goal (usually denoted h(x)). The path-cost function g(x) is the cost from the starting node to the current node.

Since the h(x) part of the f(x) function must be an admissible heuristic, it must not overestimate the distance to the goal. Thus for an application like routing, h(x) might represent the straight-line distance to the goal, since that is physically the smallest possible distance between any two points (or nodes for that matter).