{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T04:54:18Z","timestamp":1780376058792,"version":"3.54.1"},"reference-count":60,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,10]],"date-time":"2018-04-10T00:00:00Z","timestamp":1523318400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The recognition of spatial patterns within agricultural fields, presenting similar yield potential areas, stable through time, is very important for optimizing agricultural practices. This study proposes the evaluation of different clustering methodologies applied to multispectral satellite time series for retrieving temporally stable (constant) patterns in agricultural fields, related to within-field yield spatial distribution. The ability of different clustering procedures for the recognition and mapping of constant patterns in fields of cereal crops was assessed. Crop vigor patterns, considered to be related to soils characteristics, and possibly indicative of yield potential, were derived by applying the different clustering algorithms to time series of Landsat images acquired on 94 agricultural fields near Rome (Italy). Two different approaches were applied and validated using Landsat 7 and 8 archived imagery. The first approach automatically extracts and calculates for each field of interest (FOI) the Normalized Difference Vegetation Index (NDVI), then exploits the standard K-means clustering algorithm to derive constant patterns at the field level. The second approach applies novel clustering procedures directly to spectral reflectance time series, in particular: (1) standard K-means; (2) functional K-means; (3) multivariate functional principal components clustering analysis; (4) hierarchical clustering. The different approaches were validated through cluster accuracy estimates on a reference set of FOIs for which yield maps were available for some years. Results show that multivariate functional principal components clustering, with an a priori determination of the optimal number of classes for each FOI, provides a better accuracy than those of standard clustering algorithms. The proposed novel functional clustering methodologies are effective and efficient for constant pattern retrieval and can be used for a sustainable management of agricultural fields, depending on farming systems and environmental conditions in different regions.<\/jats:p>","DOI":"10.3390\/rs10040585","type":"journal-article","created":{"date-parts":[[2018,4,10]],"date-time":"2018-04-10T13:06:08Z","timestamp":1523365568000},"page":"585","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["A Comparison between Standard and Functional Clustering Methodologies: Application to Agricultural Fields for Yield Pattern Assessment"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8311-8615","authenticated-orcid":false,"given":"Simone","family":"Pascucci","sequence":"first","affiliation":[{"name":"Institute of Methodologies for Environmental Analysis, National Research Council of Italy, C.da Santa Loja, Tito Scalo, 85050 Potenza, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4570-1690","authenticated-orcid":false,"given":"Maria","family":"Carfora","sequence":"additional","affiliation":[{"name":"Istituto per le Applicazioni del Calcolo \u201cM. Picone\u201d, National Research Council of Italy, 80100 Naples, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Angelo","family":"Palombo","sequence":"additional","affiliation":[{"name":"Institute of Methodologies for Environmental Analysis, National Research Council of Italy, C.da Santa Loja, Tito Scalo, 85050 Potenza, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0587-8926","authenticated-orcid":false,"given":"Stefano","family":"Pignatti","sequence":"additional","affiliation":[{"name":"Institute of Methodologies for Environmental Analysis, National Research Council of Italy, C.da Santa Loja, Tito Scalo, 85050 Potenza, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3091-7680","authenticated-orcid":false,"given":"Raffaele","family":"Casa","sequence":"additional","affiliation":[{"name":"Department of Agriculture Forestry and Nature (DAFNE), University of Tuscia, 01100 Viterbo, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5473-1050","authenticated-orcid":false,"given":"Monica","family":"Pepe","sequence":"additional","affiliation":[{"name":"Institute for Electromagnetic Sensing of the Environment, National Research Council of Italy, 20133 Milano, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabio","family":"Castaldi","sequence":"additional","affiliation":[{"name":"Georges Lema\u00eetre Centre for Earth and Climate, Earth and Life Institute, Universite Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.compag.2015.01.012","article-title":"Multitemporal soil pattern analysis with multispectral remote sensing data at the field-scale","volume":"113","author":"Blasch","year":"2015","journal-title":"Comput. Electron. Agric."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.rse.2009.08.017","article-title":"An automated approach for reconstructing recent forest disturbance history using dense landsat time series stacks","volume":"114","author":"Huang","year":"2010","journal-title":"Remote Sens. Environ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.rse.2009.08.014","article-title":"Detecting trend and seasonal changes in satellite image time series","volume":"114","author":"Verbesselt","year":"2010","journal-title":"Remote Sens. Environ."},{"key":"ref_4","unstructured":"(2017, August 05). FARMSTAR. Available online: http:\/\/www.farmstar-conseil.fr\/."},{"key":"ref_5","unstructured":"(2017, October 01). ERMES (an Earth obseRvation Model Based ricE Information Service). Available online: http:\/\/www.ermes-fp7space.eu\/en\/about-ermes\/."},{"key":"ref_6","first-page":"229","article-title":"Remote sensing of soil properties in precision agriculture: A review","volume":"5","author":"Ge","year":"2011","journal-title":"Front. Earth Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"11125","DOI":"10.3390\/rs70911125","article-title":"Organic matter modeling at the landscape scale based on multitemporal soil pattern analysis using RapidEye data","volume":"7","author":"Blasch","year":"2015","journal-title":"Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1016\/j.biosystemseng.2012.08.009","article-title":"Twenty five years of remote sensing in precision agriculture: Key advances and remaining knowledge gaps","volume":"114","author":"Mulla","year":"2013","journal-title":"Biosyst. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.envsoft.2013.10.021","article-title":"Image time series processing for agriculture monitoring","volume":"53","author":"Eerens","year":"2014","journal-title":"Environ. Model. Softw."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bell\u00f3n, B., B\u00e9gu\u00e9, A., Lo Seen, D., de Almeida, C.A., and Sim\u00f5es, M. (2017). A remote sensing approach for regional-scale mapping of agricultural land-use systems based on NDVI time series. Remote Sens., 9.","DOI":"10.3390\/rs9060600"},{"key":"ref_11","unstructured":"Baruth, B., Royer, A., Klisch, A., and Genovese, A. (2008). The Use of Remote Sensing within the MARS Crop Yield Monitoring System of the European Commission, ISPRS, Commission VIII."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1589","DOI":"10.3390\/rs2061589","article-title":"Monitoring global croplands with coarse resolution earth observations: The Global Agriculture Monitoring (GLAM) Project","volume":"2","author":"Justice","year":"2010","journal-title":"Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.eja.2007.10.001","article-title":"Analysis of spatial relationships between soil and crop variables in a durum wheat field using a multivariate geostatistical approach","volume":"28","author":"Casa","year":"2008","journal-title":"Eur. J. Agron."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Castrignan\u00f2, A., Buttafuoco, G., Quarto, R., Vitti, C., Langella, G., Terribile, F., and Venezia, A. (2017). A combined approach of sensor data fusion and multivariate geostatistics for delineation of homogeneous zones in an agricultural field. Sensors, 17.","DOI":"10.3390\/s17122794"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1111\/1467-9868.00293","article-title":"Estimating the number of clusters in a data set via the gap statistic","volume":"63","author":"Tibshirani","year":"2001","journal-title":"J. Roy. Statist. Soc. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0377-0427(87)90125-7","article-title":"Silhouettes: A graphical aid to the interpretation and validation of cluster analysis","volume":"20","author":"Rousseeuw","year":"1987","journal-title":"J. Comput. Appl. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.patcog.2012.07.021","article-title":"An extensive comparative study of cluster validity indexes","volume":"46","author":"Arbelaitz","year":"2013","journal-title":"Pattern Recognit."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1016\/S0167-8655(99)00069-0","article-title":"An empirical comparison of four initialization methods for the K-means algorithm","volume":"20","author":"Lozano","year":"1999","journal-title":"Pattern Recognit. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/j.jaridenv.2007.01.004","article-title":"Applying a field spectroscopy technique for assessing successional trends of biological soil crusts in a semi-arid environment","volume":"70","author":"Zaady","year":"2007","journal-title":"J. Arid Environ."},{"key":"ref_20","unstructured":"Jain, A.K., and Flynn, P.J. (1996). Image segmentation using clustering. Advances in Image Understanding, Wiley-IEEE Computer Society Press."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/j.patrec.2009.09.011","article-title":"Data clustering: 50 years beyond K-means","volume":"31","author":"Jain","year":"2010","journal-title":"Pattern Recognit. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/s10596-009-9136-z","article-title":"Weighted model-based clustering for remote sensing image analysis","volume":"14","author":"Richards","year":"2010","journal-title":"Comput. Geosci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Ma, A., Zhong, Y., and Zhang, L. (2016). Spectral-Spatial Clustering with a Local Weight Parameter Determination Method for Remote Sensing Imagery. Remote Sens., 8.","DOI":"10.3390\/rs8020124"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1007\/s11629-017-4357-4","article-title":"Watershed classification by remote sensing indexes: A fuzzy c-means clustering approach","volume":"14","author":"Choubin","year":"2017","journal-title":"J. Mt. Sci."},{"key":"ref_25","first-page":"849","article-title":"On spectral clustering: Analysis and an algorithm","volume":"Volume 14","author":"Dietterich","year":"2002","journal-title":"Advances in Neural Information Processing Systems"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s11222-007-9033-z","article-title":"A tutorial on spectral clustering","volume":"17","year":"2007","journal-title":"Stat. Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1492","DOI":"10.1126\/science.1242072","article-title":"Clustering by fast search and find of density peaks","volume":"344","author":"Rodriguez","year":"2014","journal-title":"Science"},{"key":"ref_28","first-page":"55","article-title":"Sparse manifold clustering and embedding","volume":"24","author":"Elhamifar","year":"2011","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_29","unstructured":"Murphy, J.M., and Maggioni, M. (arXiv, 2017). Nonlinear Unsupervised Clustering of Hyperspectral Images with Applications to Anomaly Detection and Active Learning, Computer Science\u2014Computer Vision and Pattern Recognition, arXiv."},{"key":"ref_30","unstructured":"Little, A., Maggioni, M., and Murphy, J.M. (arXiv, 2017). Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms, arXiv."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Little, A., and Byrd, A. (2015, January 9\u201311). A Multiscale Spectral Method for Learning Number of Clusters. Proceedings of the 2015 IEEE 14th International Conference on Machine Learning and Applications (ICMLA), Miami, FL, USA.","DOI":"10.1109\/ICMLA.2015.119"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Kok, J.N., Koronacki, J., Mantaras, R.L., Matwin, S., Mladeni\u010d, D., and Skowron, A. (2017). Spectral Clustering and Embedding with Hidden Markov Models. Machine Learning: ECML 2007. ECML 2007. Lecture Notes in Computer Science, Springer.","DOI":"10.1007\/978-3-540-74958-5"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s11634-013-0158-y","article-title":"Functional data clustering: A survey","volume":"8","author":"Jacques","year":"2014","journal-title":"Adv. Data Anal. Classif."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1111\/j.1467-9876.2012.01062.x","article-title":"Multivariate functional clustering for the morphological analysis of electrocardiograph curves","volume":"62","author":"Ieva","year":"2013","journal-title":"J. R. Stat. Soc. Ser. C"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1111\/j.1541-0420.2011.01714.x","article-title":"Multilevel Functional Clustering Analysis","volume":"68","author":"Serban","year":"2012","journal-title":"Biometrics"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1002\/env.2370","article-title":"Bivariate functional data clustering: Grouping streams based on a varying coefficient model of the stream water and air temperature relationship","volume":"27","author":"Li","year":"2015","journal-title":"Environmetrics"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/s10182-015-0253-9","article-title":"On the performance of two clustering methods for spatial functional data","volume":"99","author":"Romano","year":"2015","journal-title":"Adv. Stat. Anal."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.spasta.2017.01.006","article-title":"Spatial clustering of curves with an application of satellite data","volume":"20","author":"Gaetan","year":"2017","journal-title":"Spat. Stat."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1002\/env.2185","article-title":"Functional clustering of water quality data in Scotland","volume":"23","author":"Haggarty","year":"2012","journal-title":"Environmetrics"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.neucom.2014.09.048","article-title":"K-means algorithms for functional data","volume":"151","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2619","DOI":"10.1016\/j.csda.2011.03.011","article-title":"Principal components for multivariate functional data","volume":"55","author":"Berrendero","year":"2011","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1214\/08-AOAS206","article-title":"Multilevel functional principal component analysis","volume":"3","author":"Di","year":"2009","journal-title":"Ann. Appl. Stat."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Nguyen, C., Starek, M.J., Tissot, P., and Gibeaut, J. (2018). Unsupervised Clustering Method for Complexity Reduction of Terrestrial Lidar Data in Marshes. Remote Sens., 10.","DOI":"10.3390\/rs10010133"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Tu, W., Hu, Z., Li, L., Cao, J., Jiang, J., Li, Q., and Li, Q. (2018). Portraying Urban Functional Zones by Coupling Remote Sensing Imagery and Human Sensing Data. Remote Sens., 10.","DOI":"10.3390\/rs10010141"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/s11004-007-9129-1","article-title":"Kriging and semivariogram deconvolution in the presence of irregular geographical units","volume":"40","author":"Goovaerts","year":"2008","journal-title":"Math. Geosci."},{"key":"ref_46","unstructured":"FAO-ISRIC-ISSS (1998). World Reference Base for Soil Resources, Food and Agriculture Organization. World Soil Resources Report 84."},{"key":"ref_47","unstructured":"(2016, October 10). ENVI\/IDL Scientific Programming Language. Available online: http:\/\/www.envi geospatial.com\/ProductsandSolutions\/GeospatialProducts\/IDL.aspx."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1117\/12.410341","article-title":"Status of Atmospheric Correction Using a MODTRAN4-based Algorithm","volume":"Volume 4049","author":"Matthew","year":"2000","journal-title":"SPIE Proceedings, Algorithms for Multispectral, Hyperspectral, and Ultraspectral Imagery VI"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Yengoh, G.T., Dent, D., Olsson, L., Tengberg, A.E., and Tucker, C.J. (2016). Use of the Normalized Difference Vegetation Index (NDVI) to Assess Land Degradation at Multiple Scales, Springer International Publishing.","DOI":"10.1007\/978-3-319-24112-8"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Reichenau, T.G., Korres, W., Montzka, C., Fiener, P., Wilken, F., Stadler, A., Waldhoff, G., and Schneider, K. (2016). Spatial Heterogeneity of Leaf Area Index (LAI) and Its Temporal Course on Arable Land: Combining Field Measurements, Remote Sensing and Simulation in a Comprehensive Data Analysis Approach (CDAA). PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0158451"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.rse.2011.10.030","article-title":"Continuous monitoring of forest disturbance using all available Landsat imagery","volume":"122","author":"Zhu","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.ins.2015.06.039","article-title":"Recovering the number of clusters in data sets with noise features using feature rescaling factors","volume":"324","author":"Hennig","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_53","unstructured":"(2017, October 10). R. Package Fda. Available online: https:\/\/cran.r-project.org\/web\/packages\/fda\/fda.pdf."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2438","DOI":"10.1080\/01431161.2015.1041174","article-title":"Influence of acquisition time and resolution on wheat yield estimation at the field scale from canopy biophysical variables retrieved from SPOT satellite data","volume":"36","author":"Castaldi","year":"2015","journal-title":"Int. J. Remote Sens."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1038\/nmeth.3583","article-title":"Comparing the performance of biomedical clustering methods","volume":"12","author":"Wiwie","year":"2015","journal-title":"Nat. Methods"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s11119-016-9462-9","article-title":"Geostatistical modelling of within-field soil and yield variability for management zones delineation: A case study in a durum wheat field","volume":"18","author":"Buttafuoco","year":"2017","journal-title":"Precis. Agric."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Buttafuoco, G., Castrignan\u00f2, A., Cucci, G., Rinaldi, M., and Ruggieri, S. (2015). An approach to delineate management zones in a durum wheat field: Validation using remote sensing and yield mapping. Precision Agriculture \u201915, Wageningen Academic Publishers.","DOI":"10.3920\/978-90-8686-814-8_29"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/s11119-014-9347-8","article-title":"An approach for assessing the effects of site-specific fertilization on crop growth and yield of durum wheat in organic agriculture","volume":"15","author":"Diacono","year":"2014","journal-title":"Precis. Agric."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Casa, R., Castaldi, F., Pascucci, S., Basso, B., and Pignatti, S. (2013). Geophysical and hyperspectral data fusion techniques for in-field estimation of soil properties. Vadose Zone J., 12.","DOI":"10.2136\/vzj2012.0201"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.rse.2016.03.025","article-title":"Evaluation of the potential of the current and forthcoming multispectral and hyperspectral imagers to estimate soil texture and organic carbon","volume":"179","author":"Castaldi","year":"2016","journal-title":"Remote Sens. Environ."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/4\/585\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:00:10Z","timestamp":1760194810000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/4\/585"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,10]]},"references-count":60,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["rs10040585"],"URL":"https:\/\/doi.org\/10.3390\/rs10040585","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,10]]}}}