TY - JOUR
AU - GRZENDA, Wioletta
AU - GORKIEWICZ, Maciej
PY - 2012/06/13
Y2 - 2024/09/07
TI - Exploring the 3D Surfaces with Modified Method of Steepest Descent
JF - Applied Medical Informatics
JA - Appl Med Inform
VL - 30
IS - 2
SE - Articles
DO -
UR - https://ami.info.umfcluj.ro/index.php/AMI/article/view/366
SP - 1-6
AB - <p><em>Aim</em>: To prove expediency of the steepest descent method to divide a given cloud of (Y, X1, X2) points into the spatial clusters with purpose to estimate a simple regression model Y = f(Z|X1,X2) at each cluster. <em>Material and Method</em>: The exemplary data sets {Y, X1, X2} were drawn randomly from assumed 3D surface: Y = f(X1,X2), and then a random noise was added to variable Y. A polynomial model Y = f(X1,X2) and a set of models Y = f(Z|X1,X2) were estimated separately, both under Akaike information criterion (AIC), and then compared with respect to their determination coefficients R-square, and the residualsâ€™ distributions. <em>Results</em>: In the artificial data set studied, the both compared methods after several iterations can provide regression models of the quite similar quality. <em>Conclusions</em>: Because the proposed novel method seems to be more robust to outliers, and easier to graphical presentations and to intuitive understanding than the conventional way of building a regression model, the proposed novel method can be recommended to use by non-statisticians, especially in situation when, besides usual moderate noise, the sporadic but influential measurement errors can occur.</p>
ER -