In multivariate calibrations, locally weighted partial least squared regression (LWPLSR) is an efficient prediction method when heterogeneity of data generates nonlinear relations (curvatures and clustering) between the response and the explicative variables. This is frequent in agronomic data sets that gather materials of different natures or origins. LWPLSR is a particular case of weighted PLSR (WPLSR; ie, a statistical weight different from the standard 1/n is given to each of the n calibration observations for calculating the PLS scores/loadings and the predictions). In LWPLSR, the weights depend from the dissimilarity (which has to be defined and calculated) to the new observation to predict. This article compares two strategies of LWPLSR: (a) "LW": the usual strategy where, for each new observation to predict, a WPLSR is applied to the n calibration observations (ie, entire calibration set) vs (b) "KNN-LW": a number of k nearest neighbors to the observation to predict are preliminary selected in the training set and WPLSR is applied only to this selected KNN set. On three illustrating agronomic data sets (quantitative and discrimination predictions), both strategies overpassed the standard PLSR. LW and KNN-LW had close prediction performances, but KNN-LW was much faster in computation time. KNN-LW strategy is therefore recommended for large data sets. The article also presents a new algorithm for WPLSR, on the basis of the "improved kernel #1" algorithm, which is competitor and in general faster to the already published weighted PLS nonlinear iterative partial least squares (NIPALS). K E Y W O R D Sdiscrimination, locally weighted calibration, near-infrared spectroscopy, partial least squares, regression

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Recent literature reflects the substantial progress in combining spatial, temporal and spectral capacities for remote sensing applications. As a result, new issues are arising, such as the need for methodologies that can process simultaneously the different dimensions of satellite information. This paper presents PLS regression extended to three-way data in order to integrate multiwavelengths as variables measured at several dates (time-series) and locations with Sentinel-2 at a regional scale. Considering that the multi-collinearity problem is present in remote sensing time-series to estimate one response variable and that the dataset is multidimensional, a multiway partial least squares (N-PLS) regression approach may be relevant to relate image information to ground variables of interest. N-PLS is an extension of the ordinary PLS regression algorithm where the bilinear model of predictors is replaced by a multilinear model. This paper presents a case study within the context of agriculture, conducted on a time-series of Sentinel-2 images covering regional scale scenes of southern France impacted by the heat wave episode that occurred on 28 June 2019. The model has been developed based on available heat wave impact data for 107 vineyard blocks in the Languedoc-Roussillon region and multispectral time-series predictor data for the period May to August 2019. The results validated the effectiveness of the proposed N-PLS method in estimating yield loss from spectral and temporal attributes. The performance of the model was evaluated by the R2 obtained on the prediction set (0.661), and the root mean square of error (RMSE), which was 10.7%. Limitations of the approach when dealing with time-series of large-scale images which represent a source of challenges are discussed; however, the N–PLS regression seems to be a suitable choice for analysing complex multispectral imagery data with different spectral domains and with a clear temporal evolution, such as an extreme weather event.

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