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Neural Fisher Discriminant Analysis: Optimal Neural Network Embeddings in Polynomial Time

Burak Bartan · Mert Pilanci

Hall E #639

Keywords: [ MISC: Representation Learning ] [ DL: Theory ] [ DL: Algorithms ] [ OPT: Convex ]


Fisher's Linear Discriminant Analysis (FLDA) is a statistical analysis method that linearly embeds data points to a lower dimensional space to maximize a discrimination criterion such that the variance between classes is maximized while the variance within classes is minimized. We introduce a natural extension of FLDA that employs neural networks, called Neural Fisher Discriminant Analysis (NFDA). This method finds the optimal two-layer neural network that embeds data points to optimize the same discrimination criterion. We use tools from convex optimization to transform the optimal neural network embedding problem into a convex problem. The resulting problem is easy to interpret and solve to global optimality. We evaluate the method's performance on synthetic and real datasets.

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