Tuesday 23 December 2014

K-NEAREST NEIGHBORS ALGORITHM

k-Nearest Neighbors Algorithm
In pattern recognition, the k-Nearest Neighbors algorithm (or k-NN for short) is a non-parametric Machine Learning method used for classification and regression. In both cases, the input consists of the k closest training examples in the feature space. The output depends on whether k-NN is used for classification or regression:
·         In k-NN classification, the output is a class membership. An object is classified by a majority vote of its neighbors, with the object being assigned to the class most common among its k nearest neighbors (k is a positive integer, typically small). If k = 1, then the object is simply assigned to the class of that single nearest neighbor.
·         In k-NN regression, the output is the property value for the object. This value is the average of the values of its k nearest neighbors.

Given N training Vectors, the k-Nearest neighbor algorithm identifies the k nearest neighbors of new element ‘c’ regardless of labels.
When k=1, each training vector defines a region in space, defining a voronoi partition of the space.
Remarks:
1.    Choose an odd value of k for a 2 class problem.
2.    K must not be multiple of number of classes.
k-NN is a type of instance-based learning, or lazy learning, where the function is only approximated locally and all computation is deferred until classification. The k-NN algorithm is among the simplest of all machine learning algorithms.
Both for classification and regression, it can be useful to weight the contributions of the neighbors, so that the nearer neighbors contribute more to the average than the more distant ones. For example, a common weighting scheme consists in giving each neighbor a weight of 1/d, where d is the distance to the neighbor.
The neighbors are taken from a set of objects for which the class (for k-NN classification) or the object property value (for k-NN regression) is known. This can be thought of as the training set for the algorithm, though no explicit training step is required.
Disadvantage of k Nearest Neighbor Algorithm
1.    A shortcoming of the k-NN algorithm is that it is sensitive to the local structure of the data.
2.    The main drawback of k-NN is the complexity in searching the nearest neighbors for each sample.

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