Reti neurali e monitoraggio ambientale

1. Reti neurali e monitoraggio ambientale Michele ScardiDipartimento di Biologia, Università di Roma ‘Tor Vergata’ Email: mscardi@mclink.it URL: http://www.mare-net.com/mscardi LE ACQUE SUPERFICIALI E I SEDIMENTI Istituto Superiore di Sanità, 15/11/2002

2. SECTION 1 INTRODUCING ARTIFICIAL NEURAL NETWORKS (ANNs)

3. “...a neural network is a system composed of many simple processing elements operating in parallel whose function is determined by network structure, connection strengths, and the processing performed at computing elements or nodes.” (DARPA Neural Network Study, 1988, AFCEA International Press, p. 60)

4. A SAMPLE APPLICATION:ANN MODELLING IN ESTUARY MANAGEMENT

5. skip A PHYTOPLANKTON PRIMARY PRODUCTION MODEL FOR CHESAPEAKE BAY Michele Scardi1 & Lawrence W. Harding, Jr.2 1. Dept. of Biology, Univ. of Roma “Tor Vergata”, Roma, Italy 2. Horn Point Lab., University of Maryland, USA

6. True color SeaWiFS image:New York-Chesapeake Bay(NASA-GSFC) • Predictive variables • latitude • longitude • depth • water temperature • salinity • log chlorophyll • log chlorophyll (Zp) • I0 (PAR) • k • Zp Phytoplankton primary production in Chesapeake Bay NN structure: 12 - 5 - 1 Output variable: primary production (mg C m-2 day-1)

7. training and validation sets (1982-96) testing set (1997)

8. Test data set: 1999-2000 CBPM-2(2001) CBPM-NN(1998) R2=0.430 CBPM-2/NN(2002) R2=0.604 6 predictive variables 12 predictive variables R2=0.431

9. August October June December February, April

10. Temp=8°C Temp=24°C

12. Sensitivity analysis

13. skip HOW DO ANNs WORK?JUST A LITTLE BIT OF THEORY…

14. Una rete neurale di tipoerrorback-propagation(EBP)a tre strati, con architettura 5-7-1

15. L’algoritmo EBP L’algoritmo EBP (Rumelhart et al., 1986) è di gran lunga il più diffuso fra gli algoritmi di training per le reti neuronali e può essere schematizzato come segue: • tutti i pesi sinaptici vengono quindi modificati in funzione dello scarto rilevato tra outputs e valori noti (error-backpropagation) • le connesioni sinaptiche sono inizializzate in maniera casuale • l’output della rete è confrontatocon i valorinoti del set di validazione • un training pattern è immesso nella rete neuronale se < E0 allora stop • se le condizioni di convergenzasono raggiunte, si termina il training, altrimenti si torna al punto 2

16. PP = f (I0, Zp, CHL) generalization overfitting

17. TO AVOID OVERFITTING: • early stopping • jittering (noise added to input patterns) • weight decay • training patterns in random order • etc.

18. MOREOVER, FOR GOOD GENERALIZATION: • inputs must contain enough information pertaining to targets • the relationship to be modeled must be “smooth” (i.e. small change in input --> small change in output) • the training set must be a sufficiently large and representative subset of the “real thing”

19. Ordinamento e classificazione: Self-Organizing Maps (SOMs) o Mappe di Kohonen

20. Campioni Oi O1 O2 O3 Op sp1 sp2 . . . Specie . . . spn O O O O O O O O O Vettori di riferimento (unità virtuali) O O O O . . . . . . . . . . . . . . . • Inizializzazione • Addestramento delle unità virtuali (iterativo) - scelta casuale di un’osservazione - identificazione della “best matching unit” (BMU) - addestramento della BMU e delle unità adiacenti • Proiezione delle osservazioni sulla mappa

21. Oj On O1 Al termine della proceduradi addestramento…

22. Oj Oj O1 O1 On On ... ... ... UVS ... ... ... UVk ... ... UV1 UV2 • Visualizzazione delle osservazioni • Visualizzazione delle Unità Virtuali

23. Ogni specie ha una diversa distribuzione… Specie 1 Specie 2 Specie i

24. Un’applicazione delleSelf-Organizing Maps (SOMs) Dati estratti da: Marina Cobolli, Marco Lucarelli e Valerio Sbordoni (1996).Le farfalle diurne delle piccole isole circumsarde.Biogeographia, 18: 569-582

25. 55 specie 28 specie identificate in 30 isole

26. Specie Accordo PMA 0 0.000 0 okPBR 0 0.000 0 okPRA 1 0.947 1 okPDA 1 0.761 1 okCCR 1 0.939 1 okGCL 1 0.947 1 okLSI 0 0.000 0 okLCE 1 0.761 1 okCJA 0 0.178 0 okVAT 1 1.000 1 okVCA 1 0.939 1 okHNE 1 0.761 1 okHAR 1 0.939 1 okMJU 0 0.178 0 okPCE 1 0.939 1 okCCO 1 1.000 1 okPAE 0 0.186 0 okLTI 1 1.000 1 okLPH 1 1.000 1 okLBO 0 0.000 0 okLPI 0 0.000 0 okCAR 1 0.761 1 okLCO 0 0.053 0 okAAG 0 0.000 0 okACR 1 0.947 1 okPIC 1 0.939 1 okCAL 0 0.125 0 okGPU 1 0.761 1 ok UV TAV ASI SPI SER PAS MAD SPT PAL CAV ILT SAN SPA SOF CAP FIG LEB BAR CAM MLT MAL MOL LIN OGL Una SOM 8 x 5 basata sui dati di presenza/assenza delle farfalle diurne in un sottoinsieme delle piccole isole circumsarde LAV SMA LAP BUD RAZ SST TAV MOR

27. ASI SMA SPI LAV MAD LAP SER PAS SPT PAL CAV D D D ILT BUD SAN SOF D CAP RAZ FIG D D LEB BAR CAM MLT MAL SST MOL TAV LIN MOR OGL La matrice U consente di visualizzare le distanzefra gli elementi di una SOM. SPA SPA

28. 2 ASI SMA SPI LAV S S T MAD SER LAP 1 . 5 PAS R A Z B U D 1 SPT S P A PAL CAV M O L M O R S O F F I G 0 . 5 S A N T A V ILT BUD SAN SPA SOF C A P CAP RAZ FIG L I N 0 I L T S P I P A L L A P S M A L E B M L T L A V O G L LEB P A S B A R C A M - 0 . 5 BAR CAM M A D MLT M A L C A V S P T S E R - 1 A S I MAL SST MOL TAV LIN MOR OGL - 1 . 5 - 2 - 1 0 1 2 3 Self-Organizing Map vs. Analisi delle Coordinate Principali

29. Libythea celtis (Laicharting, 1782) Foto: www.leps.it

30. Gonepteryx cleopatra (L., 1767) Foto: www.leps.it

31. Colias crocea (Geoffroy, 1785) Foto: www.leps.it

32. Vanessa atalanta (L., 1758) Foto: www.leps.it

33. Numero di specie Superficie Superficie / perimetro Altitudine Distanza dalla Sardegna I descrittori ambientali possono essere rapresentati sulle SOMs.

34. Gonepteryx cleopatra Altitudine Foto: www.leps.it

35. SECTION 2 CONCEPTS IN ANN MODELLING: SOME PHYTOPLANTKON PRIMARY PRODUCTION CASE STUDIES

36. skip IMPROVING A GLOBAL MODEL OF PHYTOPLANKTON PRIMARY PRODUCTION Michele Scardi Dept. of Biology, Univ. of Roma “Tor Vergata”, Roma, Italy

37. Phytoplankton primary production sampling sites

38. A global model of phytoplankton primary production (Scardi, 2000) • Predictive variables: • surface biomass • surface irradiance • surface temperature • date* • longitude • latitude • * 2 variables, i.e. 7-7-1 NN

39. Water column depth as a co-predictor for primary production • Depth affects PP via: • water column dynamics • upwelling regions • coastal fronts • nutrient dynamics • freshwater run-off • etc.

41. Primary production predictors and co-predictors: • Phytoplankton surface biomass (as Chl concentration) • Surface irradiance • Surface temperature • Latitude • Longitude • Date • Average depth • St. dev. of depth • Day length 1.25° Lon x 0.75° Lat window

42. MSE=405117 MSE=330233 7-7-1 NN model(Scardi, 2000) 11-14-1 NN model(with bathymetricpredictive co-variables)

43. The largest improvementsin square error occurred within this range(2257 out of 2522 cases) The 7-7-1 NN model performed slightly better than the 11-14-1 NN model with co-predictors only when PP>5000 mg C m-2 day-1

44. 7-7-1 11-14-1 0% 25% 50% 75%

45. 7-7-1 NN model (Scardi, 2000) 11-14-1 NN model (with bathymetric predictive co-variables)

46. 11-14-1 NN model of phytoplankton primary production: a sensitivity analysis relative MSE

47. skip AN EMPIRICAL MODEL CONSTRAINED BYA BIOLOGICAL RULE Michele Scardi Dept. of Biology, Univ. of Roma “Tor Vergata”, Roma, Italy

48. Phytoplankton primary production sampling sites in WesternMediterranean Sea

49. surface chlorophyll depth-integrated primary production surface irradiance surface temperature A simple 3-4-1 neural network modelof phytoplankton primary production

50. BIOLOGICAL RULE There are no more than one relativemaximum and four relative minima in a PP=f(I0 ,B0) surface NN TRAINING RULE If more maxima and/or minima are found, then a penalty is added to the MSE during the NN training for each exceeding maximum or minimum.