Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2019/2020
Scuola Scuola di Ingegneria Civile, Ambientale e Territoriale
Insegnamento 053799 - GEOSPATIAL DATA ANALYSIS [I.C.]
Cfu 10.00 Tipo insegnamento Corso Integrato
Docenti: Titolare (Co-titolari) Venuti Giovanna, Mussio Luigi

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Obiettivi dell'insegnamento

The integrated course (Mod A + Mod B) deals with a variety of predicting techniques applied to geospatial data and available in a variety of software suites like those devoted to Earth Observation data analysis or Geographic Information System data manipulation and visualization tools.

In the first module the basics of probability, statistics and linear algebra are revised and different numerical aspects arising in the solution of prediction problems are discussed.

The polynomial exact and least square interpolation problem and the exact cubic spline interpolation one are treated in the laboratory sessions.

The second module deals with data gridding and classification techniques, interpolation with combination of known base functions (including the discrete fourier transform), and finally with the stochastic interpolation.

The goal of the whole course is to make students aware of the mathematical background needed to properly apply those techniques. They will be asked to implement the geospatial data manipulation tools under study and apply them to simulated and real data.

Risultati di apprendimento attesi

Dublin descriptors

Expected learning outcomes of the integrated course (Mod A) + (Mod B)

Knowledge and understanding

Students will learn the mathematical formulation and some of the numerical issues of proposed geospatial data manipulation tools.


Applying knowledge and understanding

Students will be able to implement the studied techniques at a prototypal level. A number of laboratory sessions will be devoted to this aim.


Making judgements

Student will be asked to apply the algorithms they have developed to simulated and real dataset and make experiments to evaluate the impact of the different choices in the data processing on the results.



Students will be asked to report about their laboratory activities by an oral presentation, showing the findings of their data analysis.

Lifelong learning skills

Students will understand what data modeling means and what are the approximations introduced in data manipulation.

Argomenti trattati

Lectures proposed  (Mod. A)

An introduction to stochastic modeling: from random variables and random vectors to random processes and fields.

Review of basics: Random variables and random vectors. Mean and covariance propagation laws. Sample variables. Estimators. Tests. Observation error modeling and error covariance propagation within the least squares interpolation problem. Geometric interpretation of the least squares solution and the orthogonalization of the normal matrix. Outlier detection. 

Practice and laboratory sessions proposed  (Mod. A)

Practice lessons with numerical examples will be given and exercises will be proposed to make students more familiar with the proposed techniques. Laboratory sessions will be devoted to the implementation of the following algorithm:

- Exact and least squares polynomial interpolation. Test on least squares nested models. Test on least squares parameters.


Lectures proposed  (Mod. B)

Data gridding: nearest neighbor, distance weighted interpolation. Commission and omission error in data interpolation and error evaluation with the leave one out technique.

Data classification: hierarchical and optimization techniques. Stochastic techniques. Clasification quality evaluation.

Discrete Fourier Transform.

The stochastic modeling of deterministic interpolation residuals. The concepts of stationary signals and homogeneous and isotropic random fields, empirical variogram and covariance function estimation and the linear prediction with kriging techniques.

Practice and laboratory sessions proposed  (Mod. B)

Practice lessons with numerical examples will be given and exercises will be proposed to make students more familiar with the proposed techniques. Laboratory sessions will be devoted to the implementation of the following algorithm:

- Hierarchical Classification: divisive and agglomerative clustering algorithm implementation.  Partitioning around medoids by minimization of a target function. Maximum likelihood classification.


- Stochastic prediction: empirical covariance/variogram function estimation and modeling. Simple kriging and collocation.


- Gram-Schmidt orthogonalization. Cholesky decompostition.

- Least squares interpolation with linear and cubic splines. Tichonov regularization.



Mathematics and probability theory.

Modalità di valutazione

A unique exam will be held for the whole course (Mod A + Mod B)


To assess students’ ‘knowledge and understanding’  written test sessions will be held.

To assess their ability to ‘apply the knowledge’, to ‘make judgements’ as well as to assess their ‘communication skills’ students are asked to do a final oral presentation, reporting on an experimental activity carried out on a real dataset by using the software developed during the laboratory sessions.

During the oral presentation questions will be asked to better evaluate student’s awareness of the course topics and on the their general understanding of the data modeling problem.


Risorsa bibliografica facoltativaAthanasios Papoulis, S. Unnikrishna Pillai, Probability, random variables and stochastic processes, Editore: McGraw-Hill
Risorsa bibliografica facoltativaHans Wackernagel, Multivariate Geostatistics. An Introduction with Applications, Editore: Springer
Risorsa bibliografica facoltativaLeonard Kaufman, Peter J. Rousseeuw, Finding Groups in Data: An Introduction to Cluster Analysis, Editore: Wiley

Software utilizzato
Nessun software richiesto

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Informatico
Laboratorio Sperimentale
Laboratorio Di Progetto
Totale 100:00 150:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese
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Area Servizi ICT