Features Of Space Expansion

1333 Words Apr 9th, 2016 6 Pages
Feature Space Expansion

Firstly the feature space would be increased in dimension, by the addition of new features. Due to the analysis done on feature production, it was noted that by generalising feature production and consumption (in the neural network), a lot of time could be saved in the long run. This meant when the feature space was to be expanded, it would be important to create the feature production in a scalable manner.

Neural Network Expansion

Secondly, the neural network would be extended from a simple input-output neural network to one with a variable number of inputs, layers, and hidden neurons. The addition of more layers would allow more complex planes to partition the feature space - as sometimes simple planes cannot adequately classify data. For example, consider the classification of a data-set similar to the output of a XOR gate.
Consider four input data-points of (0, 0), (0, 1), (1, 0), and (1, 1), with respective outputs 0,1,1,0, where 1 represents positive classification, and 0 represents negative classification. This provides an example of a classification which has very high error when classified without a hidden layer. This is because a linear combination of the input coefficients can only define a partition which is a straight line.
Any linear partition of these inputs can at most correctly classify three of four data-points. This is because the data-points are linearly inseparable. However, with a more complex neural network, such as one
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