Digital Elevation Modeling with Heuristic Regression Techniques

Abstract

In this study, elevation values of the Mert River Basin of Samsun were estimated by M5 model tree (M5-tree) and Multivariate Adaptive Regression Splines (MARS) using base map which contains horizontal and vertical location informations. Results were compared with univariate and multivariate linear regression methods (MLR). In the study, three different input scenarios were tried as: (i) elevation forecast with X coordinate information, (ii) elevation forecast with Y coordinate information, (iii) elevation forecast with X and Y coordinate information. Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and coefficient of determination (R2) were utilized as comparison criteria. According to modeling results: (1) M5-tree regression method provided the best results, (2) MARS method was more suitable than the univariate and multivariate linear regression methods, (3) Single variable linear regression method provided the worst estimate, (4) M5-tree regression method can be successfully used in elevation modeling.

Keywords

• Digital Elevation Models
• M5-tree
• MARS
• Samsun.

Sezgisel Regresyon Teknikleri ile Sayısal Yükseklik Modellenmesi

Abstract

Bu çalışmada, Samsun Mert Irmağı Havzası’nda, hâlihazır haritalardan temin edilmiş yatay ve düşey koordinat bilgilerinin yer aldığı noktalardan yükseklik değerleri, M5 model ağacı (M5-tree) ve çok değişkenli uyarlamalı regresyon eğrileri (MARS) sezgisel regresyon yöntemleri kullanılarak tahmin edilmeye çalışılmıştır. Sonuçlar Tek ve Çok Değişkenli Regresyon (TDR-ÇDR) yöntemiyle karşılaştırılmıştır. Çalışmada 3 farklı giriş senaryosu incelenmiştir. Bunlar: X yönündeki koordinat bilgisiyle yükseklik tahmini (i); Y yönündeki koordinat bilgisiyle yükseklik tahmini (ii); X ve Y koordinat bilgisiyle yükseklik tahmini şeklindedir (iii). Karşılaştırma kriterleri olarak determinasyon katsayısı (R2), Ortalama Mutlak Hata (OMH) ve Karekök Ortalama Karesel Hata (KOKH) kullanılmıştır. Modelleme sonuçları incelendiğinde; (1) M5-tree regresyon yönteminin en iyi sonucu verdiği, (2) MARS yöntemi ÇDR ve TDR yöntemlerine göre daha iyi olduğu, (3) En kötü sonuç TDR yöntemi kullanılarak yapılan doğrusal regresyon modellemesinde tespit edilmiştir. (4) Özellikle, M5-tree sezgisel regresyon yönteminin yükseklik modellemesinde oldukça başarılı bir metot olduğu sonucuna ulaşılmıştır.

Keywords

• Sayısal Yükseklik Modeli
• M5-tree
• MARS
• Samsun.

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