Multidimensional Data Visualization by Gintautas Dzemyda Olga Kurasova & Julius Žilinskas

Author:Gintautas Dzemyda, Olga Kurasova & Julius Žilinskas
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

After training the network, the remaining 30 points (10 of each species) are presented to the trained network, and their two-dimensional projections are obtained at the output of the network. The visualization results are presented in Fig. 4.6: Setosa—dark blue, Versicolor—dark red, and Virginica—dark green. Here, we see that the points unseen by the network have found proper places.

4.1.3.2 Auto-Associative Neural Network

An auto-associative feed-forward neural network [4, 124] allows the dimensionality reduction by taking the output values of all d neurons in the hidden, so-called bottleneck layer, where d is chosen equal to the dimensionality of a low-dimensional space. The n-dimensional training data are presented to both input and output layers to obtain a reduced d-dimensional representation in the bottleneck layer. So, this network is trained in an unsupervised way.

The auto-associative feed-forward neural network is often called as an auto- encoder network [38, 92]. It is a nonlinear generalization of the principal component analysis that uses an adaptive, multilayer encoder network to transform the multidimensional data into the low-dimensional space and a similar decoder network to recover the data from the low-dimensionality. It is discovered in [92] that the nonlinear auto-encoders work considerably better as compared to the widely used methods such as the principal component analysis or locally linear embedding.

An auto-associative feed-forward neural network consists of two parts: The first part transforms the initial multidimensional data to a low-dimensional space (mapping layer).

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