Multilayer Perceptron

class dtaianomaly.anomaly_detection.MultilayerPerceptron(window_size: str | int, error_metric: Literal['mean-absolute-error', 'mean-squared-error'] = 'mean-absolute-error', forecast_length: int = 1, hidden_layers: list[int] = (64, 32), dropout_rate: float = 0.2, activation_function: Literal['linear', 'relu', 'sigmoid', 'tanh'] = 'relu', batch_normalization: bool = True, stride: int = 1, standard_scaling: bool = True, batch_size: int = 32, data_loader_kwargs: dict[str, any] = None, optimizer: Literal['adam', 'sgd'] | Callable[[any], Optimizer] = 'adam', learning_rate: float = 0.001, compile_model: bool = False, compile_mode: Literal['default', 'reduce-overhead', 'max-autotune', 'max-autotune-no-cudagraphs'] = 'default', n_epochs: int = 10, loss_function: Module = MSELoss(), device: str = 'cpu', seed: int = None)[source]

Use a multilayer perceptron to detect anomalies.

The multilayer perceptron is a fully connected neural network which will detect anomalies based on forecasting. Given a subsequence in the time series, the network will learn to forecast the future values. Because anomalies are unexpected events, they are difficult to forecast. Hence, by computing the difference between the forecasted value and the actually observed values, the neural network can detect anomalies.

The architecture of the multilayer perceptron consists of blocks, in which each block applies the following operations: fully-connected layer \(\rightarrow\) batch normalization \(\rightarrow\) activation function \(\rightarrow\) dropout layer. The first and final layers of the network has no batch normalization, the final layer of the network has no dropout.

Parameters:

window_size (int or str) – The window size to use for extracting sliding windows from the time series. This value will be passed to compute_window_size().
error_metric ({"mean-absolute-error", "mean-squared-error"}, default="mean-absolute-error") – The error measure between the reconstructed window and the original window.
hidden_layers (list of ints, default=[64, 32]) – The number of neurons in each hidden layer. If an empty list is given, then the input layer is directly connected to the output layer.
dropout_rate (float in interval [0, 1[, default=0.2) – The dropout rate for the dropout layers. If the dropout rate is 0, no dropout layers will be added to the auto encoder.
activation_function ({"linear", "relu", "sigmoid", "tanh"} default="relu") – The activation function to use at the end of each layer.
batch_normalization (bool = True,) – Whether to add batch normalization after each layer or not.
stride (int, default=1) – The stride, i.e., the step size for extracting sliding windows from the time series.
standard_scaling (bool, default=True) – Whether to standard scale each window independently, before feeding it to the network.
batch_size (int, default=32) – The size of the batches to feed to the network.
data_loader_kwargs (dictionary, default=None) – Additional kwargs to be passed to the data loader. For more information, see: https://docs.pytorch.org/docs/stable/data.html
optimizer ({"adam", "sgd"} or callable default="adam") – The optimizer to use for learning the weights. If “adam” is given, then the torch.optim.Adam optimizer will be used. If “sgd” is given, then the torch.optim.SGD optimizer will be used. Otherwise, a callable should be given, which takes as input the network parameters, and then creates an optimizer.
learning_rate (float, default=1e-3) – The learning rate to use for training the network. Has no effect if optimize is a callable.
compile_model (bool, default=False) – Whether the network architecture should be compiled or not before training the weights. For more information, see: https://docs.pytorch.org/docs/stable/generated/torch.compile.html
compile_mode ({"default", "reduce-overhead", "max-autotune", "max-autotune-no-cudagraphs"}, default="default") – Method to compile the architecture. For more information, see: https://docs.pytorch.org/docs/stable/generated/torch.compile.html
n_epochs (int, default=10) – The number of epochs for which the neural network should be trained.
loss_function (torch.nn.Module, default=torch.nn.MSELoss()) – The loss function to use for updating the weights.
device (str, default="cpu") – The device on which te neural network should be trained. For more information, see: https://docs.pytorch.org/docs/stable/tensor_attributes.html#torch-device
seed (int, default=None) – The seed used for training the model. This seed will update the torch and numpy seed at the beginning of the fit method.

window_size_

The effectively used window size for this anomaly detector.

Type:: int

optimizer_

The optimizer used for learning the weights of the network.

Type:: torch.optim.Optimizer

neural_network_

The PyTorch network architecture.

Type:: torch.nn.Module

Examples

>>> from dtaianomaly.anomaly_detection import MultilayerPerceptron
>>> from dtaianomaly.data import demonstration_time_series
>>> x, y = demonstration_time_series()
>>> mlp = MultilayerPerceptron(10, seed=0).fit(x)
>>> mlp.decision_function(x)
array([1.8944391 , 1.8944391 , 1.83804671, ..., 0.59621549, 0.54421651,
       0.05852008]...)