CESN

A new neural network architecture for time series classification and regression.

CESN architecture

Here we present and describe in detail a new neural network architecture called CESN, Convolutional Echo State Network, which results from the combination of the Convolutional Neural Networks (CNNs) and the Echo State Networks (ESNs). CESN results to be appropriate for Time Series Classification (TSC) tasks and Time Series Regression (TSR) tasks, just changing the output activation function and the loss function of the model. CESN architecture in details is shown in the figure below

• Input layer: It brings the input data, that can be univariate or multivariate timeseries, into the next layer.
• Reservoir layer: This layer aims to project the input data into a high dimensional space, trough temporal and non-linear activation functions of each neuron into the reservoir. This dimensional augmentation allows visualizing more patterns than the data in the original dimension. Mathematically can be describe in the following way.
• Convolutional layer: Same as the CNNs this layer consists of a convolutional and a pooling phase in which the features of the reservoir state are extracted in the same way performed in image classification.
• Flattening layer: In this layer approaching data from the convolutional layer are flatted to be fed into the next layer. This means that data coming from the convolutional layer, which is a tensor with rank 3 are mapped into a 1-D array, a vector, in order to be feed into the fully connected layer.
• Fully Connected layer: This is just a simple deep forward neural network used for the classification of time series transformed by the previous layer into a specific feature.

CESN - Classification

Dataset

CESN can be used for time series classification tasks. Here we present some examples how to use it for the classification task. We consider three different dataset, typically used in this context:

• SisFall dataset - https://github.com/your_username/repo_name
• ECG200 - https://timeseriesclassification.com/description.php?Dataset=ECG200
• ECG5000 - https://timeseriesclassification.com/description.php?Dataset=ECG5000

Here you can find the ECG200 and ECG500 dataset, while the SisFall dataset is avalaible at the following link

https://github.com/Fall-Prevention-Team/sisfallData

CESN implementation Here, the implementation of the CESN is done in two different way:

1. In the first one we separate the convolutional part from the reservoir part. In particular, we developed a code just to implent the Reservoir State. After collecting all the data, for each time series, we pass the data to the convolutional layer which is implemented using the open source library Keras. You can collect all the internal state of the reservoir for each time series using the following function:

 esn_train = ESN(N_inputs=n_input,
            N_reservoir=n_reservoir,
            noise=0.01,
            spectral_radius = 0.94,
            random_state=40)

where

• N_inputs
• N_reservoir
• noise
• spectral_radius
• random_state

internal_states = esn_train.fit_internal_state(input_ESN)

where input_ESN is the single time series to be fed into the keras model.

The keras model

2. In the second implementation we created a customized layer directly from Keras. So we don't need to generate the internal state anymore. This is done directly in the Keras model. You just have to create a vector with all the time series to be fed into the Keras model.

CESN - Regression

Still in progress ...