Functional Data Analysis & Depth Measures for ECG signals

The electrocardiogram (ECG) is a time record of the electrical acrtvity of heart, recorded by means of a set of 12 sensors placed in standard positions on human body. Its relatively simple acquisition procedure, together with its ability to emphasize morphological changes in presence of cardiac pathologies, render ECGs a major instrument to help diagnosing and monitoring heart illnesses.

The procedure of assessing the health state of subjects by analysing their ECGs can be profitably addressed from a statistical standpoint. In particular, specific inferential tools can be devised to predict the condition of patients based on features of their ECGs.
According to this perspective, the present MOX research line is devoted to the statistical study of ECGs, and in particular to the development of both ad-hoc and general techniques able to discriminate between physiological and pathological subjects (who may be affected, for instance, by bundle branch blocks or atrial fibrillations).

Methodologies & Results

ECGs can be naturally modelled as functional data, i.e. observations of stochastic processes with values in suitable function spaces. Functional data analysis is a recent research field showing great potential and collecting wide interest in both applied and theoretical statistics communities.
The activity of the group is aimed at:

  • developing and using adequate reconstruction techniques to pre-process the functional observations, without altering the morphology of signals;
  • developing and using instruments, like uni- and multivariate functional depths and functional boxplots, for the exploration of such infinite-dimensional, multivariate data, to induce an ordering on data and to detect potential outlying signals;
  • applying suitable dimension reduction techniques, in order to restrain the high complexity of multivariate functional signals and, at the same time, to retain all the important information on data;
  • devising inferential procedures, such as generalised models and supervised/unsupervised classification schemes, in order to solve the prediction problem by using the functional signals;
  • developping robust inferential tools for detecting (multivariate) functional outliers


LOGO_Prometeo   2008 -today (Ongoing)
PROMETEO (PROgetto Milano Ecg Teletrasmessi ExtraOspedaliero)
Commissioned by 118 (National free toll number for emergencies) of Milan



  1. Martino, A., Ghiglietti, A., Ieva, F., Paganoni, A.M. (2019) A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data. Statistical Methods & Applications, 28(2): 301-322
  2. Tarabelloni, N., Schenone, E., Collin, A., Ieva, F., Paganoni, A.M., Gerbeau, J.F. (2018) Statistical Assessment and Calibration of Numerical ECG Models. JP Journal of Biostatistics, 15(2): 151 – 173 (July-Dec 2018)
  3. Ieva, F., Paganoni, A.M. (2017) A taxonomy of outlier detection methods for robust classification in multivariate functional data. Statistical Papers. doi: 10.1007/s00362-017-0953-1
  4. Ghiglietti, A., Paganoni, A.M. (2017). Exact tests for the means of Gaussian stochastic processes. Statistics & Probability Letters, 131, 102-107.
  5. Ghiglietti, A., Ieva, F., Paganoni, A.M. (2017). Statistical inference for stochastic processes: two sample hypothesis tests. Journal of Statistical Planning and Inference,  180: 49−68.
  6. Ieva, F., Paganoni, A.M. (2016, online first 2013). Risk Prediction for Myocardial Infarction via Generalized Functional Regression Models. Statistical Methods in Medical Research. 25 (4): 1648-1660
  7. Tarabelloni, N., Ieva, F., Paganoni, A.M. (2016) Covariance Based Unsupervised Classification in Functional Data Analysis. Journal of Machine Learning Research. 17 (143): 1−21.
  8. Ieva, F., Paganoni, A.M. (2015) Discussion of “multivariate functional outlier detection” by M. Hubert, P. Rousseeuw and P. Segaert. Statistical Methods and Applications, 24 (2): 217-221
  9. Tarabelloni, N., Ieva, F., Biasi, R. and Paganoni, A.M.  (2015). Use of Depth Measure for Multivariate Functional Data in Disease Prediction: An Application to Electrocardiograph Signals. The International Journal of Biostatistics, 11(2), pp. 189-201. doi: 10.1515/ijb-2014-0041
  10. Ieva, F., Paganoni, A.M., Pigoli, D., Vitelli, V. (2013). Multivariate functional clustering for the analysis of ECG curves morphology. Journal of the Royal Statistical Society – Series C, 62(3): 401-418
  11. Ieva, F., Paganoni, A.M.. (2013). Depth Measures for Multivariate Functional Data. Communication in Statistics – Theory and Methods, 42(7): 1265-1276.

R Packages

  • roahd – Robust Analysis of High-dimensional Data
  • gmfd – Inference and Clustering of Functional Data


  • Dr. Francesco Palma, MD Thesis in Mathematical Engineering (2017)
    A bootstrap based inferential framework for Bultivariate Functional Data: an application to ECG signals
  • Dr. Feredico Indino, MD Thesis in Mathematical Engineering (2015)
    Analisi statistica di dati ad alta dimensionalità: un’applicazione ai segnali elettrocardiografici.
  • Dr. Silvia Giussani,  MD Thesis in Mathematical Engineering (2014)
    Modelli statistici per la previsione del rischio cardiovascolare: analisi di segnali elettrocardiografici
  • Dr. Rachele Biasi, MD Thesis in Mathematical Engineering (2013)
    Uso delle misure di profondità per dati funzionali multivariati nella previsione di patologie: un’applicazione ai segnali elettrocardiografici
  • Dr. Nicholas Tarabelloni, MD Thesis in Mathematical Engineering (2013)
    Metodi Numerici e Statistici per la Simulazione e la Validazione di ECG
  • Dr. Francesca Ieva, PhD Thesis in Mathematical Models and Methods for Engineering (2012)
    Statistical Methods for Classification in Cardiovascular Healthcare
  • Dr. Giovanni Cassarini, MD Thesis in Mathematical Engineering (2012)
    Metodi Statistici per l’ottimizzazione dei tempi di Percorrenza delle Ambulanze nella provincia di Milano


  • ERCIM 2018, Pisa (IT), December 14-16, 2018
    Talk (invited): On Robust Nonparametric techniques for dealing with the Analysis of High Dimensional Data
  • ERCIM 2017, London (UK), December 15-18, 2017
    Talk (invited): A Bootstrap approach to the Inference on Dependence in Multivariate Functional Setting
  • Invited talk @ Department o Mathematics, University of Genova (IT), October 2017
    Title: “Nonparametric Inference for vital signs”
  • CLADAG 2017, Milan (IT), September 13-15, 2017
    Talk: A generalized Mahalanobis distance for the classification of functional data
  • ERCIM 2016, Sevilla (ES), December 9-11, 2016
    Talk (invited): Analyzing Dependence for Multivariate Functional Data
  • ERCIM 2016, Sevilla (ES), December 9-11, 2016
    Talk (invited): Inference on the means of functional data based on a Generalized Mahalanobis distance.
  • SIMAI 2016, Milano (I), September 13-16, 2016.
    Talk: Statistical Calibration of Numerical Models: Application to ECG Models
  • SIAM UQ 2016, Lausanne (CH), April 4-8, 2016
    Talk: Statistical Assessment and Calibration of  ECG Models
  • ERCIM 2015, London (UK), December 12-14, 2015
    Talk (invited): Robust Outlier Detection Methods for Functional Data
  • ISCB 2015, Utrecht (NL), August 23-27, 2015
    Talk: Robust classification of multivariate functional data
  • CLADAG 2015 – 10th Meeting of the Classification and Data Analysis Group, Santa Margherita di Pula (Italy), October 8-10, 2015.
    Talk: Robustified Classification of Multivariate Functional Data.
  • CLADAG 2015 – 10th Meeting of the Classification and Data Analysis Group, Santa Margherita di Pula (Italy), October 8-10, 2015.
    Talk: A generalized distance for inference on functional data.
  • ISNPS 2015 “Biosciences, Medicine and Novel NonParametric Methods”, Graz (AU), July 12-15, 2015
    Talk (invited): On the use of depth measures for Multivariate Functional Data
  • EMS 2015 – European Meeting of Statistics 2015, Amsterdam, July 06-10, 2015
    Talk: Robustification and Outlier Detection methods in Multivariate Functional Data
  • ISCB 2014 – 35th  conference of the International Society of Clinical Biostatistics, Vienna (Austria). August, 24-24, 2014
    Talk: Unsupervised classification of functional data based on covariance structures
  • ICB 2014 – 27th International Biometric Conference, Fizenze (Italy), July, 6-11, 2014
    Talk: Generalized regression models with functional covariates for disease prediction: an application to electrocardiographic signals
  • IWFOS 2014 – 3rd International Workshop on Functional and Operatorial Statistics, Stresa (Italy). June, 19-21, 2014
    Poster: Multivariate functional depth measures with variance-covariance driven weights
  • SIS 2014 Cagliari (Italy). June, 11-14, 2014
    Talk: Depth measures for multivariate functional data with data-driven weights
  • ERCIM 2013, London (UK), December 14-16, 2013
    Talk (invited): Supervised Learning from Multivariate Functional Data
  • 7th IMA Conference on Quantitative Modelling in the Management of Health and Social Care, Woburn House Conference Centre, 20 Tavistock Square, London (UK), March, 25-27, 2013
    Talk: Risk Prediction for Acute Myocardial Infarction via Generalized Functional Regression Models
  • Cladag 2012 Capri (Italy). September, 4-6, 2012
    Talk: Mixed effect models for provider profiling in cardiovascular healthcare context
  • ISCB 2012 – 33rd Annual Conference of the International Society for Clinical Biostatistics, Bergen (Norway). August, 19-23, 2012
    Poster: Mixed effect models for provider profiling in cardiovascular healthcare context
  • ISBA 2012 Kyoto (Japan). June, 25-29, 2012
    Poster: Semiparametric Bayesian modelling for hospital profiling and classification of patients with observed high survival probability
  • SIS 2012 Rome (Italy). June, 20-22, 2012
    Talk: Depth measures for the study of real and simulated ECG signals
  • CLADAG 2011 – 8th Scientific Meeting on CLAssification and Data Analysis Group of the Italian Statistical Society. University of Pavia, Pavia (Italy). September 7-9, 2011
    Talk (invited): Multivariate functional clustering for the analysis of ECG curves morphology.
  • 17EYSM – 17th European Young Statistician Meeting. Lisboa (Portugal). September 5-9, 2011
    Talk: Outlier detection for training sets in an unsupervised functional classification framework: an application to ECG signals
  • ERCIM’10 – 3rd International Conference on Computing and Statistics. Senate House, University of London, London (UK). Dec 9-12, 2010
    Poster: Statistics on ECGs: wavelet smoothing, registration and classification