Training Echo State Networks with Regularization through Dimensionality Reduction

In this paper we introduce a new framework to train an Echo State Network to predict real valued time-series. The method consists in projecting the output of the internal layer of the network on a space with lower dimensionality, before training the output layer to learn the target task. Notably, we enforce a regularization constraint that leads to better generalization capabilities. We evaluate the performances of our approach on several benchmark tests, using different techniques to train the readout of the network, achieving superior predictive performance when using the proposed framework. Finally, we provide an insight on the effectiveness of the implemented mechanics through a visualization of the trajectory in the phase space and relying on the methodologies of nonlinear time-series analysis. By applying our method on well known chaotic systems, we provide evidence that the lower dimensional embedding retains the dynamical properties of the underlying system better than the full-dimensional internal states of the network

Simplifying Clustering with Graph Neural Networks

The objective functions used in spectral clustering are generally composed of two terms: i) a term that minimizes the local quadratic variation of the cluster assignments on the graph and; ii) a term that balances the clustering partition and helps avoiding degenerate solutions. This paper shows that a graph neural network, equipped with suitable message passing layers, can generate good cluster assignments by optimizing only a balancing term. Results on attributed graph datasets show the effectiveness of the proposed approach in terms of clustering performance and computation time

Local Short Term Electricity Load Forecasting: Automatic Approaches

Short-Term Load Forecasting (STLF) is a fundamental component in the efficient management of power systems, which has been studied intensively over the past 50 years. The emerging development of smart grid technologies is posing new challenges as well as opportunities to STLF. Load data, collected at higher geographical granularity and frequency through thousands of smart meters, allows us to build a more accurate local load forecasting model, which is essential for local optimization of power load through demand side management. With this paper, we show how several existing approaches for STLF are not applicable on local load forecasting, either because of long training time, unstable optimization process, or sensitivity to hyper-parameters. Accordingly, we select five models suitable for local STFL, which can be trained on different time-series with limited intervention from the user. The experiment, which consists of 40 time-series collected at different locations and aggregation levels, revealed that yearly pattern and temperature information are only useful for high aggregation level STLF. On local STLF task, the modified version of double seasonal Holt-Winter proposed in this paper performs relatively well with only 3 months of training data, compared to more complex methods

Bidirectional deep-readout echo state networks

We propose a deep architecture for the classification of multivariate time series. By means of a recurrent and untrained reservoir we generate a vectorial representation that embeds temporal relationships in the data. To improve the memorization capability, we implement a bidirectional reservoir, whose last state captures also past dependencies in the input. We apply dimensionality reduction to the final reservoir states to obtain compressed fixed size representations of the time series. These are subsequently fed into a deep feedforward network trained to perform the final classification. We test our architecture on benchmark datasets and on a real-world use-case of blood samples classification. Results show that our method performs better than a standard echo state network and, at the same time, achieves results comparable to a fully-trained recurrent network, but with a faster training

Critical bursts in filtration

Particle detachment bursts during the flow of suspensions through porous media are a phenomenon that can severely affect the efficiency of deep bed filters. Despite the relevance in several industrial fields, little is known about the statistical properties and the temporal organization of these events. We present experiments of suspensions of deionized water carrying quartz particles pushed with a peristaltic pump through a filter of glass beads measuring simultaneously pressure drop, flux and suspension solid fraction. We find that the burst size distribution scales consistently with a power-law, suggesting that we are in the presence of a novel experimental realization of a self-organized critical system. Temporal correlations are present in the time series, alike in other phenomena as earthquakes or neuronal activity bursts, and also an analog to Omori's law can be shown. The understanding of bursts statistics could provide novel insights in different fields, e.g. in filter and petroleum industries.Comment: 7 pages, 9 figure

Time Series Cluster Kernel for Learning Similarities between Multivariate Time Series with Missing Data

Similarity-based approaches represent a promising direction for time series analysis. However, many such methods rely on parameter tuning, and some have shortcomings if the time series are multivariate (MTS), due to dependencies between attributes, or the time series contain missing data. In this paper, we address these challenges within the powerful context of kernel methods by proposing the robust \emph{time series cluster kernel} (TCK). The approach taken leverages the missing data handling properties of Gaussian mixture models (GMM) augmented with informative prior distributions. An ensemble learning approach is exploited to ensure robustness to parameters by combining the clustering results of many GMM to form the final kernel. We evaluate the TCK on synthetic and real data and compare to other state-of-the-art techniques. The experimental results demonstrate that the TCK is robust to parameter choices, provides competitive results for MTS without missing data and outstanding results for missing data.Comment: 23 pages, 6 figure

Time series kernel similarities for predicting Paroxysmal Atrial Fibrillation from ECGs

We tackle the problem of classifying Electrocardiography (ECG) signals with the aim of predicting the onset of Paroxysmal Atrial Fibrillation (PAF). Atrial fibrillation is the most common type of arrhythmia, but in many cases PAF episodes are asymptomatic. Therefore, in order to help diagnosing PAF, it is important to design procedures for detecting and, more importantly, predicting PAF episodes. We propose a method for predicting PAF events whose first step consists of a feature extraction procedure that represents each ECG as a multi-variate time series. Successively, we design a classification framework based on kernel similarities for multi-variate time series, capable of handling missing data. We consider different approaches to perform classification in the original space of the multi-variate time series and in an embedding space, defined by the kernel similarity measure. We achieve a classification accuracy comparable with state of the art methods, with the additional advantage of detecting the PAF onset up to 15 minutes in advance