Learning Vector Quantization

Learning Vector quantization (LVQ) 1 attempts to construct a highly sparse model of the data by representing data classes by prototypes. Prototypes are vectors in the data spaced which are placed such that they achieve a good nearest-neighbor classification accuracy. More formally, for a dataset \{(x_1, y_1), ..., (x_m, y_m)\} LVQ attempts to place K prototypes w_1, ..., w_K with labels c_1, ..., c_K in the data space, such that as many data points as possible are correctly classified by assigning the label of the closest prototype. The number of prototypes K is a hyper-parameter to be specified by the user. Per default, we use 1 prototype per class.

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Dimensionality Reducation

The relevances learned by a GrlvqModel,:class:GmlvqModel,:class:LgmlvqModel,:class:MrslvqModel and LmrslvqModel can be applied for dimensionality reduction by projecting the data on the eigenvectors of the relevance matrix which correspond to the largest eigenvalues.

References:

1

“Learning Vector Quantization” Kohonen, Teuvo - Self-Organizing Maps, pp. 175-189, 1995.