Deep Neural Network Classifier for Multi-dimensional Functional Data

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Functional data pre-processing

• Given functional data , first use basis functions to extract projection scores by integration.

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Model input and output

• Input: Projection scores .
• Output: Binary class label k={-1, 1}.

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Model selection

Neural network hyperparameters

• J: number of projection scores for network inputs
• L: number of layers
• p: neurons per layer (uniform for all layers)
• B: maximal norm of weights

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Other hyperparameters

• Loss function: hinge loss
• Dropout rate: data dependent
• Batch size: data dependent
• Epoch number: data dependent
• Activation function: ReLU
• Optimizer: Adam

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Function descriptions

One dimensional functional data

• "dnn_1d_par.R": hyperparameter selection with training data. More details can be found in comments
• "dnn_1d.R": functional deep neural netowrks. More details can be found in comments

Two dimensional functional data

• "dnn_2d_par.R": hyperparameter selection with training data. More details can be found in comments
• "dnn_2d.R": functional deep neural netowrks. More details can be found in comments

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Examples

• "example_1d.R": , , where , , . Under class k, generate independently ,
  where , , , .

• "example_2d.R": , , where , , , . Under class k, generate independently ,
  where , , , .