Framework overview

With this library is possible to quickly implement different classifiers based on Reservoir Computing (the family of approaches popularized in machine learning by Echo State Networks) for classifying multivariate time series.

Several options are available to customize the RC classifier, by selecting different configurations for each module.

1. The reservoir module specifies the reservoir configuration (e.g., bidirectional, leaky neurons, circle topology);
2. The dimensionality reduction module (optionally) applies a dimensionality reduction on the produced sequence of the reservoir's states;
3. The representation module defines how to represent the input time series from the sequence of reservoir's states;
4. The readout module specifies the model to use to perform the final classification.

This library also implements the reservoir model space as representation for the time series: details of the methodology can be found in the original paper.

Quick execution

Run the script example.py to perform a quick execution of the RC classifier on a benchmark dataset for classification of multivariate time series. The code has been tested on Python 3.5.

Required libraries:

• Tensorflow (tested on version 1.8.0)
• sklearn (tested on version 0.19.1)
• scipy

Configure the RC-classifier

The main class RC_classifier contained in modules.py permits to specify, train and test an RC-classifier. The RC-classifier is configured by passing to the constructor of the class RC_classifier a set of parameters. To get an idea, you can check in example.py where the parameters are specified through a dictionary (config).

The available configuration parameters are listed in the following and, for the sake of clarity, are grouped according to which module of the architecture they refer to.

1. Reservoir parameters:

• n_drop - number of transient states to drop
• bidir - use a bidirectional reservoir (True or False)
• reservoir - precomputed reservoir (oject of class Reservoir in reservoir.py; if None, the following structural hyperparameters must be specified:
  • n_internal_units = number of processing units in the reservoir
  • spectral_radius = largest eigenvalue of the reservoir matrix of connection weights (to guarantee the Echo State Property, set spectral_radius <= leak <= 1)
  • leak = amount of leakage in the reservoir state update (optional, None or 1.0 --> no leakage)
  • circ = if True, generate a determinisitc reservoir with circle topology where each connection has the same weight
  • connectivity = percentage of nonzero connection weights (ignored if circ = True)
  • input_scaling = scaling of the input connection weights (note that weights are randomly drawn from {-1,1})
  • noise_level = deviation of the Gaussian noise injected in the state update

2. Dimensionality reduction parameters:

• dimred_method - procedure for reducing the number of features in the sequence of reservoir states; possible options are: None (no dimensionality reduction), 'pca' (standard PCA) or 'tenpca' (tensorial PCA for multivariate time series data)
• n_dim - number of resulting dimensions after the dimensionality reduction procedure

3. Representation parameters:

• mts_rep - type of multivariate time series representation. It can be 'last' (last state), 'mean' (mean of all states), 'output' (output model space), or 'reservoir' (reservoir model space)
• w_ridge_embedding - regularization parameter of the ridge regression in the output model space and reservoir model space representation; ignored if mts_rep is None

4. Readout parameters:

• readout_type - type of readout used for classification. It can be 'lin' (ridge regression), 'mlp' (multilayer perceptron) or 'svm'
• w_ridge - regularization parameter of the ridge regression readout (only when readout_type is 'lin')
• mlp_layout - list with the sizes of MLP layers, e.g. [20,20,10] defines a MLP with 3 layers of 20, 20 and 10 units respectively (only when readout_type is 'mlp')
• batch_size - size of the mini batches used during training (only when readout_type is 'mlp')
• num_epochs - number of iterations during the optimization (only when readout_type is 'mlp')
• p_drop - probability of dropping connections in dropout (only when readout_type is 'mlp')
• w_l2 = weight of the L2 regularization (only when readout_type is 'mlp')
• learning_rate = learning rate in the gradient descent optimization (only when readout_type is 'mlp')
• nonlinearity = type of activation function; it can be {'relu', 'tanh', 'sigmoid', 'lin', 'maxout', 'kaf'} (only when readout_type is 'mlp')
• svm_gamma = bandwith of the RBF kernel (only when readout_type is 'svm')
• svm_C = regularization for the SVM hyperplane (only when readout_type is 'svm')

Train and test the RC-classifier

The training and test function requires in input training and test data, which must be provided as multidimensional NumPy arrays of shape [N,T,V], with:

• N = number of samples
• T = number of time steps in each sample
• V = number of variables in each sample

Training and test labels (Y and Yte) must be provided in one-hot encoding format, i.e. a matrix [N,C], where C is the number of classes.

Training

RC_classifier.train

Inputs:

• X, Y: training data and respective labels

Outputs:

• tr_time: time (in seconds) used to train the classifier

Test

RC_classifier.test

Inputs:

• Xte, Yte: test data and respective labels

Outputs:

• accuracy, F1 score: metrics achieved on the test data

Example

A simple example of how to perform MTS classification based on this library can be found in this notebook, from Madalina Ciortan.

Time series datasets

A collection of univariate and multivariate time series dataset is available for download here. The dataset are provided both in MATLAB and Python (Numpy) format. Original raw data come from UCI, UEA, and UCR public repositories.

Citation

Please, cite the original paper if you are using this library in your reasearch

@article{bianchi2018reservoir,
    title={Reservoir computing approaches for representation and classification of multivariate time series},
    author={Bianchi, Filippo Maria and Scardapane, Simone and L{\o}kse, Sigurd and Jenssen, Robert},
    journal={arXiv preprint arXiv:1803.07870},
    year={2018}
}

License

The code is released under the MIT License. See the attached LICENSE file.