Neighbourhood Components Analysis
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High Quality Content by WIKIPEDIA articles! Neighbourhood components analysis is an unsupervised learning method for clustering multivariate data into distinct classes according to a given distance metric over the data. Functionally, it serves the same purposes as the k-Nearest Neighbour algorithm, and makes direct use of a related concept termed stochastic nearest neighbours. Neighbourhood components analysis aims at "learning" a distance metric by finding a linear transformation of input data such that the average LOO-classification performance is maximized in the transformed space. The key ...
High Quality Content by WIKIPEDIA articles! Neighbourhood components analysis is an unsupervised learning method for clustering multivariate data into distinct classes according to a given distance metric over the data. Functionally, it serves the same purposes as the k-Nearest Neighbour algorithm, and makes direct use of a related concept termed stochastic nearest neighbours. Neighbourhood components analysis aims at "learning" a distance metric by finding a linear transformation of input data such that the average LOO-classification performance is maximized in the transformed space. The key insight to the algorithm is that a matrix A corresponding to the transformation can be found by defining a differentiable objective function for A, followed by use of an iterative solver such as conjugate gradient descent. One of the benefits of this algorithm is that the number of classes k can be determined as a function of A, up to a scalar constant. This use of the algorithm therefore addresses the issue of model selection.
