Multiple Regression, Principal Components Regression and Partial Least Squares Regression

2020 ◽  
Author(s):  
Iva Hrelja ◽  
Ivana Šestak ◽  
Aleksandra Perčin ◽  
Paulo Pereira ◽  
Igor Bogunović

<p>Fire is an important element of the ecosystems, nevertheless, high severity fires can have negative impacts on the ecosystems as consequence of the high temperatures reaches. High temperatures normally have detrimental impacts on soil properties. The objective of this work was to determine the relationship of spectral reflectance and soil pH, electrical conductivity (EC), carbonates (CaCO<sub>3</sub>) and total carbon (TC) content after a medium to high severity wildfire occurred in Croatia using linear and nonlinear calibration models.</p><p>Soils were sampled 2 days after a medium to high severity wildfire in Zadar County, Croatia. A total of 120 soil samples (0-5 cm) were collected from three different treatments (n= 40 per treatment): control (C), mean severity (MS), high severity (HS). Soil pH, EC, CaCO<sub>3</sub> and TC content were determined using standard laboratory methods.  Soil spectral measurements were carried out using a portable spectroradiometer (20 per treatment, 60 in total). Linear statistical model - partial least squares regression (PLSR) and non-linear - artificial neural network (ANN) were generated to estimate changes in soil pH, EC, CaCO<sub>3</sub> and TC content based on the original spectral reflectance and its first derivative in form of principal components (PC). One-way ANOVA revealed pH values were significantly different in all three treatments. EC, CaCO<sub>3</sub> and TC were significantly higher in HS plots compared with the other treatments.</p><p>Different wildfire severity indicated very collinear soil spectral response, but with certain variations of reflectance intensity. Control samples showed a higher reflectance than MS and HS samples. This is attributed to the low pH and TC content. Low reflectance of MS and HS samples could be explained by their increased pH and TC values. Soil pH was the only parameter that showed a high R<sup>2</sup> and low root mean squared error (RMSE) after Savitzky Golay smoothing and the first derivation. In PLSR model, strong to very strong correlation and low RMSE were obtained. ANN model also showed a high R<sup>2</sup> and lower RMSE for all properties except pH. Both models showed satisfactory results for prediction of the studied soil properties. ANN model predicted EC, CaCO<sub>3</sub>, and TC better, while PLSR proved to be a better model for pH prediction.</p><p><strong>Key words:</strong> soil reflectance, fire severity, principal components, partial least squares regression, neural networks</p><p>Acknowledgements</p><p>This work was supported by Croatian Science Foundation through the project "Soil erosion and degradation in Croatia" (UIP-2017-05-7834) (SEDCRO).</p>


2017 ◽  
Vol 23 (2) ◽  
pp. 250-274 ◽  
Author(s):  
Sven-Amin Lembke ◽  
Kyra Parker ◽  
Eugene Narmour ◽  
Stephen McAdams

Achieving a blended timbre for particular combinations of instruments, pitches, and articulations is a common aim of orchestration. This involves a set of factors that this study jointly assesses by correlating the perceptual degree of blend with the underlying acoustical characteristics. Perceptual blend ratings from two experiments were considered, with the stimuli consisting of: 1) dyads of wind instruments at unison and minor-third intervals and at two pitch levels, and 2) triads of wind and string instruments, including bowed and plucked string excitation. The correlational analysis relied on partial least-squares regression, as this technique is not restricted by the number and collinearity of regressors. The regressors encompassed acoustical descriptors of timbre (spectral, temporal, and spectrotemporal), as well as acoustical descriptors accounting for pitch and articulation. From regressor loadings in principal-components space, the major regressors leading to substantial and orthogonal contributions were identified. The regression models explained around 90% of the variance in the datasets, which was achievable with less than a third of all regressors considered initially. Blend seemed to be influenced by differences across intervals, pitch, and articulation. Unison intervals yielded more blend than did non-unison intervals, and the presence of plucked strings resulted in clearly lower blend ratings than for sustained instrument combinations. Furthermore, prominent spectral features of instrument combinations influenced perceived blend.


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