Regression\classification

When linking explanatory and response variables, the outcome can be either classification or regression. In classification problems, the output would be a prediction/classification of discrete values. For instance, based on all input data, trees could be classified into healthy and diseased groups. On the other hand, regression algorithms are used to predict the continuous values, such as the amount of yield in an orchard. For both classification and regression several methods are available and for each method some statistical criteria assess the accuracy. However, linear regression, due to its simplicity and interpretability has gained a lot of attention and is implemented in numerous studies. Table 5 includes explanatory variable, response variable and modeling methods used in the selected papers that are focused on remote sensing application for nut crops discussed in previous sections. As it is shown in the table, more than 70 percent of the papers have used linear regression as a primary, or in some cases secondary, modeling method.

In general, analysis methods can be categorized into two general classes of linear and nonlinear algorithms. Among linear algorithms, simple (one input variable) and multiple (multiple input variables) linear regressions (MLR) are the most common methods utilized in numerous agricultural studies for predicting yield[1], LAI [2], stem water potential[3], nitrogen status[4], and many more. MLR has attracted lots of attention especially since it can be combined with the feature selection step to select the most contributing factors and the best model at the same time. Forward Selection, Backward Elimination, and Stepwise Selection are the highly reported methods that evaluate the model step by step based on their statistical significance and contribution to the response variable's variance (Regression Sum of Squares). For a limited number of input variables, linear regressions are very reliable, and the relationship between the input variables and the response can be easily interpreted. However, in some remote sensing studies, especially recent publications that include several sensors, many variables are extracted to predict a response factor and the increasing number of explanatory variables makes the MLR model selection process more challenging. Moreover, many agricultural processes are better represented by nonlinear models than linear models[5]. As a result, alternatives to linear approaches, such as computational methods, emerged regardless of their complexity and lack (or difficulty) of interpretability.

Table 6 - Analysis parameters of the selected papers

 Crop Explanatory variable (s) Response variable(s) Modeling method Other methods used Reference Alm. NDVI SWP Linear regression - [6] Alm. Temperature Stomatal conductance Linear regression - [7] Alm. Height, volume, bloom density Yield Tukey HSD test Linear regression [8] / [9] Pista. RGB image Tree heights T-test Linear regression [10] Alm. EBI1 Bloom coverage Linear regression SVM2 [11] Alm. Inter/intra-crown σT3 SWP Linear regression - [12] Alm. Tc – Ta4 / CWSI SWP Linear regression 2nd order polynomial regression [13] Pista. CWSI/DLSI5 SWP Non-Linear regression Linear regression [14] Alm. 46+ VIs Red leaf blotch (disease) Multivariate Analyses ANOVA, HSD Tukey, SVM, LDA6 [15] Alm. SIF7/ CWSI Stomatal conductance ANOVA Linear regression, Tukey HSD test [16] A/P NDVI/ CWSI SWP Non-Linear regression Linear regression [17] Alm. Tc – Ta /CWSI VPD8 Linear regression - [18] A/P Four water sensitive spectral indices9 CWC10 Continuous wavelet analysis Linear regression, Multiple linear regression [19] Alm. 15 input variables11 Yield Stochastic Gradient Boosting (ML12) [20] Alm. UAVSAR L-band Land Cover type Jeffries-Matusita distance Classification [21] A/W/P Spectral & Thermal bands LST13 ANOVA post-hoc Tukey's tests [22] Pista. METRIC14 ET Linear regression Stepwise linear regression [23] Alm. METRIC ET Linear regression - [24] Pista. DEM15, NDVI Tree Elevation Classification - [25]
 1- Enhanced Bloom Index 2- Support Vector Machine- Classification 3- The standard deviation of temperature  4- Differential between canopy and air temperature 5- Days Since Last Irrigation 6- Linear Discriminant Analysis 7- Solar-induced fluorescence 8- Vapor Pressure Deficit 9- The Water Index (WI), NDWI, The Normalized Difference Infrared Index (NDII) 10- Canopy Water Content 11- Historic yield, orchard age, temperature, NDVI, etc. 12- Machine Learning 13- land surface temperature 14- Mapping Evapotranspiration at high Resolution with Internalized Calibration (Inputs: NDVI, LST, Albedo, LAI) 15- Digital Elevation Mode

Computational intelligence (artificial intelligence) and expert systems, such as Artificial Neural Networks (ANN) or more advanced machine learning methods, which are considered a subdivision of nonlinear algorithms, have gained increasing attention due to several reasons: their ability to handle quantitative and qualitative data simultaneously, their capacity to weight variables based on their importance, their potential to manage both linear and nonlinear responses, and the growing computational power of new computers[26]. Since these methods use their internal transformations (through weights and activation functions), an optimal combination of the features (engineered features) will be formed inside the algorithms[27], making these techniques a powerful modeling tool in many fields. Methods such as ANN[28], Regression (decision) Trees (RT) [29], Partial Least Squares Regression (PLSR) [30], and Random Forest (RF)[31]  are widely utilized in agricultural fields. However, regardless of their outstanding success in different areas, artificial intelligence methods need a relatively large number of samples (labels) that dwarfs their advantage in most remote sensing applications. As a result, finding a technique that combines artificial intelligence with other statistical methods to preserve AI methods' advantages while minimizing their need for large amounts of samples is of broad and current interest.

As we discussed throughout this paper, due to the dynamic and complex nature of agricultural environments, numerous factors can affect the response variable to a certain extend. Moreover, remote sensing data might have different spectral, spatial, and temporal resolutions. An ambitious model should take all the determining factors into account, weight them based on their importance level, and use all available information so that the combination of inputs can represent a more accurate prediction. To reach such a model, a data fusion framework is needed to combine data from various layers of information to fill the knowledge gap.

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