01/09/2026
NeuralNET Parameters
Do you want to see more videos like this? Then subscribe and turn on notifications! Don't forget to subscribe to my YouTube channel and RuTube channel.
Youtube : https://youtu.be/cisH3V93cqk/
Rutube : https://rutube.ru/video/5621e0c39dfe4f30eb028685567f7a42/
Combining of a backpropagation neural network to simulate coordinate system transformation (translation, rotation, scaling, and Euler angles) as the conventional linear models (Helmert transformations) are not efficient in handling complex distortions. Divides data automatically into test and training sets, trains model with early stopping in target error, with parameter adjustment to optimize performance, and breaks linear constraints through machine learning (with a neural network with backpropagation fitting the relationship between coordinates of two sets with different coordinate systems, highlighting adaptation to nonlinear distortions).
Mathematical Models
Neural Network
Made up of input, hidden, and output layers. Uses sigmoid activation function to provide nonlinearity, with backpropagation of errors utilized to update weights and regularization used to prevent overfitting. Trains to convert input coordinates to output differences so that nonlinear, complex relations can be modeled.
Data Normalization
Input data is normalized before training to the range -1 to 1 for increased stability. Denormalization is done after prediction to produce original values.
Influence Matrix
Used to calculate the measure of influence of all points with the model and impact on model parameters.
Statistical Metrics
Measures of Central Tendency
Arithmetic Mean: Average value of error values.
Median: Middle value of an ordered data.
Mode: Most common value.
Geometric Mean: Average value considering multiplicative effects.
Measures of Variability
Range: Maximum - minimum value.
Interquartile Range (IQR): Interquartile range of middle 50% of data.
Standard Deviation: Average deviation from mean.
Variance: Square of the average deviation.
Coefficient of Variation (CV): Relative variability.
Semi-Interquartile Range (SIQR): Half of the interquartile range.
Relative Standard Deviation (RSD): Percentage variability.
Regression Metrics
Mean Squared Error (MSE): Average squared error.
Root Mean Squared Error (RMSE): Square root of MSE.
Mean Absolute Error (MAE): Average absolute error.
Mean Absolute Percentage Error (MAPE): Percentage error.
Symmetric Mean Absolute Percentage Error (sMAPE): Symmetric percentage error.
Coefficient of Determination (R²): Explained variance.
Adjusted Coefficient of Determination (Adjusted R²): R² adjusted for number of predictors.
Advanced Statistical Measures
Theil's U Statistic: Comparison of predictions to a naive model.
Nash-Sutcliffe Efficiency (NSE): Efficiency of the model.
Kling-Gupta Efficiency (KGE): Overall evaluation metric.
Root Mean Squared Logarithmic Error (RMSLE): Logarithmic error.
Skewness: Asymmetry measure of distribution.
Kurtosis: Shape measure of distribution.
Pearson Correlation: Linear correlation.
Spearman Correlation: Rank correlation.
Kendall Tau: Rank correlation with ties.
Mean Bias Error (MBE): Average bias.
Normalized Root Mean Squared Error (nRMSE): Normalized RMSE.
Normalized Mean Absolute Error (nMAE): Normalized MAE.
Variance Inflation Factor (VIF): Multicollinearity measure.
Durbin-Watson Statistic: Autocorrelation in residuals.
Quantile Errors: Errors at a specific percentile.
Geometric and Coordinate Metrics
Average 3D Distance: Average distance error in 3D space.
Maximum 3D Distance: Maximum distance error in 3D space.
Mean Squared Distance: Average of the squared distances.
Average Error Per Axis: Error per coordinate axis.
Maximum Error Per Axis: Maximum error per axis.
Standard Deviation of Errors Per Axis: Error range per axis.
Detection of Outliers
Number and values of outliers found using the interquartile range (IQR) for finding extreme values.
Adjustment Statistics
Total Sum of Squared Residuals (PVV): Total error.
Standard Error of Adjustment: Overall precision.
Standard Errors Per Axis: Precision per coordinate axis.
RuTube Channel : https://rutube.ru/channel/1400643/
Youtube Channel : https://www.youtube.com/channel/UCNnd6dzXmsw7MeC1QlP4C4A
LinkeDin : https://www.linkedin.com/in/sasalazic/
SrbsBuk : https://srbsbuk.com/members-2/donlaki/
Telegram : https://t.me/geoalatiplus
web pages: http://geoalatiplus.in.rs
#геодезия #геодезија
Do you want to see more videos like this? Then subscribe and turn o...
