This program trains a fully connected feed-forward neural network to estimate if line-of-sight exists (binary, 0 or 1) for equally spaced points along a 2-dimensional terrain. The inputs to the model are the elevations of equally spaced points along the line-of-sight vector. The outputs are binary predictions of if line-of-sight exists between the observer and each point along the ground (the number nodes in the input and output layer are the same).
The data for this project was generated from 3D Elevation (3DEP) on the U.S. Geological Survey's (USGS) National Geospatial Program. It used 1/3 arc-second DEM data from three different regions of the United States: coastal, mountains, and plains. The data set consisted of random samples 2D slices of terrain 1,000 meters long and the associated line-of-sight calculations for each point relative to the observer. The data was sampled from three different regions:
- Coastal areas: 1,048,576 samples of terrain
- Mountainous areas: 2,000,000 samples of terrain
- Plains areas: 2,000,000 samples of terrain
The program used a fully-connected feed-forward neural network consisting of three hidden layers. The input layer and output layer have as many nodes as the length of the terrain vector that was being predicted and used an exponential linear activation function (elu). The first hidden layer used 250 hidden nodes with a leaky rectified linear activation function (LRelu). The second hidden layer also had 250 hidden nodes with a rectified linear (Relu) activation function. The third hidden layer had 500 nodes also with a Relu activation function. Each hidden layer was followed by a dropout layer with a 20% probability in order to increase its generalizability. Finally, the output layer used a sigmoid activation function. During the training process, the scaler used to normalize the data and the best neural network for each terrain set and prediction length are stored to the models folder.
The program calculates the accuracy of the trained model on predicting line-of-sight for distances from 100 meters to 1,000 meters. The model was trained with the training data (80% of the full dataset), a validation set (10% of the full dataset) was used for early stopping during training, and the models accuracy tested with a test set (10% of the full dataset withheld from all training). Early stopping occurred when the model observed an increase in the binary cross entropy loss function for the validation set with 10 epochs patience. The results show the intuitive results that the accuracy for predicting line-of-sight was greatest for plains-type of terrain and smallest for mountain-type terrain. Additionally, the accuracy generally decreased for predictions of longer sets (more distant) terrain.
The line-of-sight results are a binary label, 1 = the observer can see the distant point or 0 = the observer cannot see the distant point. The distribution of the 0 and 1 labels was not even in across the datasets. The imbalance can effect the accuracy metric so another way to observe the ability of the model to differentiate between the two cases is with the Receiver Operating Characteristic (ROC) curve. This is a plot of the false positive rate vs. true positive rate of the model. The Area Under the ROC Curve (AUC) is a metric that describes the ability of the model to differentiate between the two classes. The AUC for the three terrain types is shown in the figure below. Most AUC values were over 0.8 except for distances of 100 meters. At 100 meters, there was a strong imbalance between the classes because most points were visible.
The program loops through the three train sets and tests ten different distance measures from 0-100 meter out to 0-1000 meters in 100 meter increments. As a result, it takes about 10 hours to run on a standard home computer. The simulation is setup, run, and controlled from the FFNN_LOS_Increasing_Distance.py file. The simulation parameters are set in lines 40-57. The size of the training set is controlled by "training_size" and "validation_size." The "validation_size" is the percentage of the data left over after the training set is removed that should be allocated to the validation set. The maximum allowed epochs during the training of any dataset is controlled by the "epoch" variable. Note that the training may end before this epoch due to early stopping. The number of hidden nodes in each hidden layer (1-3) is controlled with "HL1," "HL2," and "HL3." The dropout at percentage (percent of each connections randomly removed from training at each epoch) is controlled with "dropout" and the slop of the negative portion of the leaky Relu is set with the "alpha1" variable. Finally, the learning rate of the adam optimizer is set with the "learning_rate" variable.
This simulation was built with the help of the following people:
- Jim Jablonski
- John Grant
This simulation was built using the following python libraries and versions:
- Python v3.7.6
- numpy v1.18.1
- matplotlib v3.1.3
- tensorflow v1.15.0
- keras v2.2.4
- scikit-learn v0.22.1
- pickpleshare v0.7.5
- h5py v2.10.0
- graphviz v2.38
- pydot v1.4.1