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.

Contents:

API

GLVQ

RSLVQ

Utils

Examples

Generalized Learning Vector Quantization

Generalized Relevance Learning Vector Quantization (GRLVQ)

Generalized Matrix Learning Vector Quantization (GMLVQ)

Localized Generalized Matrix Learning Vector Quantization (LGMLVQ)

Implementation Details

Robust Soft Learning Vector Quantization

Matrix Robust Soft Learning Vector Quantization (MRSLQV)

Local Matrix Robust Soft Learning Vector Quantization (LMRSLVQ)

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.