Clustering of discretely observed diffusion processes

In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time. The mesh of observations is not required to shrink to zero. As distance between two observed paths, the quadratic distance of the corresponding estimated Markov operators is considered. Analysis of both synthetic data and real financial data from NYSE/NASDAQ stocks, give evidence that this distance seems capable to catch differences in both the drift and diffusion coefficients contrary to other commonly used metrics

Parsimonious Time Series Clustering

We introduce a parsimonious model-based framework for clustering time course data. In these applications the computational burden becomes often an issue due to the number of available observations. The measured time series can also be very noisy and sparse and a suitable model describing them can be hard to define. We propose to model the observed measurements by using P-spline smoothers and to cluster the functional objects as summarized by the optimal spline coefficients. In principle, this idea can be adopted within all the most common clustering frameworks. In this work we discuss applications based on a k-means algorithm. We evaluate the accuracy and the efficiency of our proposal by simulations and by dealing with drosophila melanogaster gene expression data

Machine Learning Methods for Monitoring of Quasi-Periodic Traffic in Massive IoT Networks

One of the central problems in massive Internet of Things (IoT) deployments is the monitoring of the status of a massive number of links. The problem is aggravated by the irregularity of the traffic transmitted over the link, as the traffic intermittency can be disguised as a link failure and vice versa. In this work we present a traffic model for IoT devices running quasi-periodic applications and we present both supervised and unsupervised machine learning methods for monitoring the network performance of IoT deployments with quasi-periodic reporting, such as smart-metering, environmental monitoring and agricultural monitoring. The unsupervised methods are based on the Lomb-Scargle periodogram, an approach developed by astronomers for estimating the spectral density of unevenly sampled time series