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DSC4812 FORECASTING: Exercise 2.10
# Load necessary libraries
library(nnet) # For neural network
library(NeuralNetTools) # For network visualization
library(caret) # For data partitioning and performance metrics
# Prepare the dataset
seeds_data <- read.table(header = FALSE, text = "
15.26 14.84 0.871 5.763 3.312 2.221 5.22 1
14.88 14.57 0.8811 5.554 3.333 1.018 4.956 1
14.29 14.09 0.905 5.291 3.337 2.699 4.825 1
13.84 13.94 0.8955 5.324 3.379 2.259 4.805 1
16.14 14.99 0.9034 5.658 3.562 1.355 5.175 1
14.38 14.21 0.8951 5.386 3.312 2.462 4.956 1
14.69 14.49 0.8799 5.563 3.259 3.586 5.219 1
14.11 14.1 0.8911 5.42 3.302 2.7 5 1
16.63 15.46 0.8747 6.053 3.465 2.04 5.877 1
16.44 15.25 0.888 5.884 3.505 1.969 5.533 1
15.26 14.85 0.8696 5.714 3.242 4.543 5.314 1
14.03 14.16 0.8796 5.438 3.201 1.717 5.001 1
13.89 14.02 0.888 5.439 3.199 3.986 4.738 1
13.78 14.06 0.8759 5.479 3.156 3.136 4.872 1
13.74 14.05 0.8744 5.482 3.114 2.932 4.825 1
14.59 14.28 0.8993 5.351 3.333 4.185 4.781 1
13.99 13.83 0.9183 5.119 3.383 5.234 4.781 1
15.69 14.75 0.9058 5.527 3.514 1.599 5.046 1
14.7 14.21 0.9153 5.205 3.466 1.767 4.649 1
12.72 13.57 0.8686 5.226 3.049 4.102 4.914 1
14.16 14.4 0.8584 5.658 3.129 3.072 5.176 1
14.11 14.26 0.8722 5.52 3.168 2.688 5.219 1
15.88 14.9 0.8988 5.618 3.507 0.7651 5.091 1
12.08 13.23 0.8664 5.099 2.936 1.415 4.961 1
15.01 14.76 0.8657 5.789 3.245 1.791 5.001 1
16.19 15.16 0.8849 5.833 3.421 0.903 5.307 1
13.02 13.76 0.8641 5.395 3.026 3.373 4.825 1
12.74 13.67 0.8564 5.395 2.956 2.504 4.869 1
14.11 14.18 0.882 5.541 3.221 2.754 5.038 1
13.45 14.02 0.8604 5.516 3.065 3.531 5.097 1
13.16 13.82 0.8662 5.454 2.975 0.8551 5.056 1
15.49 14.94 0.8724 5.757 3.371 3.412 5.228 1
14.09 14.41 0.8529 5.717 3.186 3.92 5.299 1
13.94 14.17 0.8728 5.585 3.15 2.124 5.012 1
15.05 14.68 0.8779 5.712 3.328 2.129 5.36 1
16.12 15 0.9 5.709 3.485 2.27 5.443 1
16.2 15.27 0.8734 5.826 3.464 2.823 5.527 1
17.08 15.38 0.9079 5.832 3.683 2.956 5.484 1
14.8 14.52 0.8823 5.656 3.288 3.112 5.309 1
14.28 14.17 0.8944 5.397 3.298 6.685 5.001 1
13.54 13.85 0.8871 5.348 3.156 2.587 5.178 1
13.5 13.85 0.8852 5.351 3.158 2.249 5.176 1
13.16 13.55 0.9009 5.138 3.201 2.461 4.783 1
15.5 14.86 0.882 5.877 3.396 4.711 5.528 1
15.11 14.54 0.8986 5.579 3.462 3.128 5.18 1
13.8 14.04 0.8794 5.376 3.155 1.56 4.961 1
15.36 14.76 0.8861 5.701 3.393 1.367 5.132 1
14.99 14.56 0.8883 5.57 3.377 2.958 5.175 1
14.79 14.52 0.8819 5.545 3.291 2.704 5.111 1
14.86 14.67 0.8676 5.678 3.258 2.129 5.351 1
14.43 14.4 0.8751 5.585 3.272 3.975 5.144 1
15.78 14.91 0.8923 5.674 3.434 5.593 5.136 1
14.49 14.61 0.8538 5.715 3.113 4.116 5.396 1
14.33 14.28 0.8831 5.504 3.199 3.328 5.224 1
14.52 14.6 0.8557 5.741 3.113 1.481 5.487 1
15.03 14.77 0.8658 5.702 3.212 1.933 5.439 1
14.46 14.35 0.8818 5.388 3.377 2.802 5.044 1
14.92 14.43 0.9006 5.384 3.412 1.142 5.088 1
15.38 14.77 0.8857 5.662 3.419 1.999 5.222 1
12.11 13.47 0.8392 5.159 3.032 1.502 4.519 1
11.42 12.86 0.8683 5.008 2.85 2.7 4.607 1
11.23 12.63 0.884 4.902 2.879 2.269 4.703 1
12.36 13.19 0.8923 5.076 3.042 3.22 4.605 1
13.22 13.84 0.868 5.395 3.07 4.157 5.088 1
12.78 13.57 0.8716 5.262 3.026 1.176 4.782 1
12.88 13.5 0.8879 5.139 3.119 2.352 4.607 1
14.34 14.37 0.8726 5.63 3.19 1.313 5.15 1
14.01 14.29 0.8625 5.609 3.158 2.217 5.132 1
14.37 14.39 0.8726 5.569 3.153 1.464 5.3 1
12.73 13.75 0.8458 5.412 2.882 3.533 5.067 1
17.63 15.98 0.8673 6.191 3.561 4.076 6.06 2
16.84 15.67 0.8623 5.998 3.484 4.675 5.877 2
17.26 15.73 0.8763 5.978 3.594 4.539 5.791 2
19.11 16.26 0.9081 6.154 3.93 2.936 6.079 2
16.82 15.51 0.8786 6.017 3.486 4.004 5.841 2
16.77 15.62 0.8638 5.927 3.438 4.92 5.795 2
17.32 15.91 0.8599 6.064 3.403 3.824 5.922 2
20.71 17.23 0.8763 6.579 3.814 4.451 6.451 2
18.94 16.49 0.875 6.445 3.639 5.064 6.362 2
17.12 15.55 0.8892 5.85 3.566 2.858 5.746 2
16.53 15.34 0.8823 5.875 3.467 5.532 5.88 2
18.72 16.19 0.8977 6.006 3.857 5.324 5.879 2
20.2 16.89 0.8894 6.285 3.864 5.173 6.187 2
19.57 16.74 0.8779 6.384 3.772 1.472 6.273 2
19.51 16.71 0.878 6.366 3.801 2.962 6.185 2
18.27 16.09 0.887 6.173 3.651 2.443 6.197 2
18.88 16.26 0.8969 6.084 3.764 1.649 6.109 2
18.98 16.66 0.859 6.549 3.67 3.691 6.498 2
21.18 17.21 0.8989 6.573 4.033 5.78 6.231 2
20.88 17.05 0.9031 6.45 4.032 5.016 6.321 2
20.1 16.99 0.8746 6.581 3.785 1.955 6.449 2
18.76 16.2 0.8984 6.172 3.796 3.12 6.053 2
18.81 16.29 0.8906 6.272 3.693 3.237 6.053 2
18.59 16.05 0.9066 6.037 3.86 6.001 5.877 2
18.36 16.52 0.8452 6.666 3.485 4.933 6.448 2
16.87 15.65 0.8648 6.139 3.463 3.696 5.967 2
19.31 16.59 0.8815 6.341 3.81 3.477 6.238 2
18.98 16.57 0.8687 6.449 3.552 2.144 6.453 2
18.17 16.26 0.8637 6.271 3.512 2.853 6.273 2
18.72 16.34 0.881 6.219 3.684 2.188 6.097 2
16.41 15.25 0.8866 5.718 3.525 4.217 5.618 2
17.99 15.86 0.8992 5.89 3.694 2.068 5.837 2
19.46 16.5 0.8985 6.113 3.892 4.308 6.009 2
19.18 16.63 0.8717 6.369 3.681 3.357 6.229 2
18.95 16.42 0.8829 6.248 3.755 3.368 6.148 2
18.83 16.29 0.8917 6.037 3.786 2.553 5.879 2
18.85 16.17 0.9056 6.152 3.806 2.843 6.2 2
17.63 15.86 0.88 6.033 3.573 3.747 5.929 2
19.94 16.92 0.8752 6.675 3.763 3.252 6.55 2
18.55 16.22 0.8865 6.153 3.674 1.738 5.894 2
18.45 16.12 0.8921 6.107 3.769 2.235 5.794 2
19.38 16.72 0.8716 6.303 3.791 3.678 5.965 2
19.13 16.31 0.9035 6.183 3.902 2.109 5.924 2
19.14 16.61 0.8722 6.259 3.737 6.682 6.053 2
20.97 17.25 0.8859 6.563 3.991 4.677 6.316 2
19.06 16.45 0.8854 6.416 3.719 2.248 6.163 2
18.96 16.2 0.9077 6.051 3.897 4.334 5.75 2
19.15 16.45 0.889 6.245 3.815 3.084 6.185 2
18.89 16.23 0.9008 6.227 3.769 3.639 5.966 2
20.03 16.9 0.8811 6.493 3.857 3.063 6.32 2
20.24 16.91 0.8897 6.315 3.962 5.901 6.188 2
18.14 16.12 0.8772 6.059 3.563 3.619 6.011 2
16.17 15.38 0.8588 5.762 3.387 4.286 5.703 2
18.43 15.97 0.9077 5.98 3.771 2.984 5.905 2
15.99 14.89 0.9064 5.363 3.582 3.336 5.144 2
18.75 16.18 0.8999 6.111 3.869 4.188 5.992 2
18.65 16.41 0.8698 6.285 3.594 4.391 6.102 2
17.98 15.85 0.8993 5.979 3.687 2.257 5.919 2
20.16 17.03 0.8735 6.513 3.773 1.91 6.185 2
17.55 15.66 0.8991 5.791 3.69 5.366 5.661 2
18.3 15.89 0.9108 5.979 3.755 2.837 5.962 2
18.94 16.32 0.8942 6.144 3.825 2.908 5.949 2
15.38 14.9 0.8706 5.884 3.268 4.462 5.795 2
16.16 15.33 0.8644 5.845 3.395 4.266 5.795 2
15.56 14.89 0.8823 5.776 3.408 4.972 5.847 2
15.38 14.66 0.899 5.477 3.465 3.6 5.439 2
17.36 15.76 0.8785 6.145 3.574 3.526 5.971 2
15.57 15.15 0.8527 5.92 3.231 2.64 5.879 2
15.6 15.11 0.858 5.832 3.286 2.725 5.752 2
16.23 15.18 0.885 5.872 3.472 3.769 5.922 2
13.07 13.92 0.848 5.472 2.994 5.304 5.395 3
13.32 13.94 0.8613 5.541 3.073 7.035 5.44 3
13.34 13.95 0.862 5.389 3.074 5.995 5.307 3
12.22 13.32 0.8652 5.224 2.967 5.469 5.221 3
11.82 13.4 0.8274 5.314 2.777 4.471 5.178 3
11.21 13.13 0.8167 5.279 2.687 6.169 5.275 3
11.43 13.13 0.8335 5.176 2.719 2.221 5.132 3
12.49 13.46 0.8658 5.267 2.967 4.421 5.002 3
12.7 13.71 0.8491 5.386 2.911 3.26 5.316 3
10.79 12.93 0.8107 5.317 2.648 5.462 5.194 3
11.83 13.23 0.8496 5.263 2.84 5.195 5.307 3
12.01 13.52 0.8249 5.405 2.776 6.992 5.27 3
12.26 13.6 0.8333 5.408 2.833 4.756 5.36 3
11.18 13.04 0.8266 5.22 2.693 3.332 5.001 3
11.36 13.05 0.8382 5.175 2.755 4.048 5.263 3
11.19 13.05 0.8253 5.25 2.675 5.813 5.219 3
11.34 12.87 0.8596 5.053 2.849 3.347 5.003 3
12.13 13.73 0.8081 5.394 2.745 4.825 5.22 3
11.75 13.52 0.8082 5.444 2.678 4.378 5.31 3
11.49 13.22 0.8263 5.304 2.695 5.388 5.31 3
12.54 13.67 0.8425 5.451 2.879 3.082 5.491 3
12.02 13.33 0.8503 5.35 2.81 4.271 5.308 3
12.05 13.41 0.8416 5.267 2.847 4.988 5.046 3
12.55 13.57 0.8558 5.333 2.968 4.419 5.176 3
11.14 12.79 0.8558 5.011 2.794 6.388 5.049 3
12.1 13.15 0.8793 5.105 2.941 2.201 5.056 3
12.44 13.59 0.8462 5.319 2.897 4.924 5.27 3
12.15 13.45 0.8443 5.417 2.837 3.638 5.338 3
11.35 13.12 0.8291 5.176 2.668 4.337 5.132 3
11.24 13 0.8359 5.09 2.715 3.521 5.088 3
11.02 13 0.8189 5.325 2.701 6.735 5.163 3
11.55 13.1 0.8455 5.167 2.845 6.715 4.956 3
11.27 12.97 0.8419 5.088 2.763 4.309 5 3
11.4 13.08 0.8375 5.136 2.763 5.588 5.089 3
10.83 12.96 0.8099 5.278 2.641 5.182 5.185 3
10.8 12.57 0.859 4.981 2.821 4.773 5.063 3
11.26 13.01 0.8355 5.186 2.71 5.335 5.092 3
10.74 12.73 0.8329 5.145 2.642 4.702 4.963 3
11.48 13.05 0.8473 5.18 2.758 5.876 5.002 3
12.21 13.47 0.8453 5.357 2.893 1.661 5.178 3
11.41 12.95 0.856 5.09 2.775 4.957 4.825 3
12.46 13.41 0.8706 5.236 3.017 4.987 5.147 3
12.19 13.36 0.8579 5.24 2.909 4.857 5.158 3
11.65 13.07 0.8575 5.108 2.85 5.209 5.135 3
12.89 13.77 0.8541 5.495 3.026 6.185 5.316 3
11.56 13.31 0.8198 5.363 2.683 4.062 5.182 3
11.81 13.45 0.8198 5.413 2.716 4.898 5.352 3
10.91 12.8 0.8372 5.088 2.675 4.179 4.956 3
11.23 12.82 0.8594 5.089 2.821 7.524 4.957 3
10.59 12.41 0.8648 4.899 2.787 4.975 4.794 3
10.93 12.8 0.839 5.046 2.717 5.398 5.045 3
11.27 12.86 0.8563 5.091 2.804 3.985 5.001 3
11.87 13.02 0.8795 5.132 2.953 3.597 5.132 3
10.82 12.83 0.8256 5.18 2.63 4.853 5.089 3
12.11 13.27 0.8639 5.236 2.975 4.132 5.012 3
12.8 13.47 0.886 5.16 3.126 4.873 4.914 3
12.79 13.53 0.8786 5.224 3.054 5.483 4.958 3
13.37 13.78 0.8849 5.32 3.128 4.67 5.091 3
12.62 13.67 0.8481 5.41 2.911 3.306 5.231 3
12.76 13.38 0.8964 5.073 3.155 2.828 4.83 3
12.38 13.44 0.8609 5.219 2.989 5.472 5.045 3
12.67 13.32 0.8977 4.984 3.135 2.3 4.745 3
11.18 12.72 0.868 5.009 2.81 4.051 4.828 3
12.7 13.41 0.8874 5.183 3.091 8.456 5 3
12.37 13.47 0.8567 5.204 2.96 3.919 5.001 3
12.19 13.2 0.8783 5.137 2.981 3.631 4.87 3
11.23 12.88 0.8511 5.14 2.795 4.325 5.003 3
13.2 13.66 0.8883 5.236 3.232 8.315 5.056 3
11.84 13.21 0.8521 5.175 2.836 3.598 5.044 3
12.3 13.34 0.8684 5.243 2.974 5.637 5.063 3
")
# Define column names
colnames(seeds_data) <- c('Area', 'Perimeter', 'Compactness', 'Kernel_Length',
'Kernel_Width', 'Asymmetry_Coeff', 'Kernel_Groove_Length', 'Class')
# Prepare the dataset (assuming seeds_data is already loaded and preprocessed as per previous steps)
seeds_data$Class <- as.factor(seeds_data$Class)
# Split the data into training and testing sets
set.seed(123)
trainIndex <- createDataPartition(seeds_data$Class, p = 0.7, list = FALSE)
trainData <- seeds_data[trainIndex, ]
testData <- seeds_data[-trainIndex, ]
# Scale features
trainX <- scale(trainData[, -8])
trainY <- class.ind(trainData$Class) # Convert classes to binary indicator variables
testX <- scale(testData[, -8], center = attr(trainX, "scaled:center"), scale = attr(trainX, "scaled:scale"))
# Train the neural network (as previously done)
nn_model <- nnet(trainX, trainY, size = 5, maxit = 1000, linout = FALSE, decay = 5e-4, trace = TRUE)
# Plot the network
plotnet(nn_model)
# Predict on the training and test sets
train_pred <- predict(nn_model, trainX, type = "class")
test_pred <- predict(nn_model, testX, type = "class")
# Convert predictions back to factor for confusion matrix
train_pred_factor <- as.factor(max.col(train_pred))
test_pred_factor <- as.factor(max.col(test_pred))
# Calculate Mean Squared Error for both training and test sets
train_mse <- mean((train_pred - trainY)^2)
test_mse <- mean((test_pred - class.ind(testData$Class))^2)
# Print MSEs
cat("Training MSE:", train_mse, "\n")
cat("Test MSE:", test_mse, "\n")
# Check if error has improved by comparing with previous models' errors# Load necessary library
library(nnet) # For neural network training
# Assuming you have the seeds_data as in the previous example
# Preprocess the data if necessary (converting factors, scaling, etc.)
# Prepare the dataset
seeds_data <- read.table(header = FALSE, text = "
15.26 14.84 0.871 5.763 3.312 2.221 5.22 1
14.88 14.57 0.8811 5.554 3.333 1.018 4.956 1
14.29 14.09 0.905 5.291 3.337 2.699 4.825 1
13.84 13.94 0.8955 5.324 3.379 2.259 4.805 1
16.14 14.99 0.9034 5.658 3.562 1.355 5.175 1
14.38 14.21 0.8951 5.386 3.312 2.462 4.956 1
14.69 14.49 0.8799 5.563 3.259 3.586 5.219 1
14.11 14.1 0.8911 5.42 3.302 2.7 5 1
16.63 15.46 0.8747 6.053 3.465 2.04 5.877 1
16.44 15.25 0.888 5.884 3.505 1.969 5.533 1
15.26 14.85 0.8696 5.714 3.242 4.543 5.314 1
14.03 14.16 0.8796 5.438 3.201 1.717 5.001 1
13.89 14.02 0.888 5.439 3.199 3.986 4.738 1
13.78 14.06 0.8759 5.479 3.156 3.136 4.872 1
13.74 14.05 0.8744 5.482 3.114 2.932 4.825 1
14.59 14.28 0.8993 5.351 3.333 4.185 4.781 1
13.99 13.83 0.9183 5.119 3.383 5.234 4.781 1
15.69 14.75 0.9058 5.527 3.514 1.599 5.046 1
14.7 14.21 0.9153 5.205 3.466 1.767 4.649 1
12.72 13.57 0.8686 5.226 3.049 4.102 4.914 1
14.16 14.4 0.8584 5.658 3.129 3.072 5.176 1
14.11 14.26 0.8722 5.52 3.168 2.688 5.219 1
15.88 14.9 0.8988 5.618 3.507 0.7651 5.091 1
12.08 13.23 0.8664 5.099 2.936 1.415 4.961 1
15.01 14.76 0.8657 5.789 3.245 1.791 5.001 1
16.19 15.16 0.8849 5.833 3.421 0.903 5.307 1
13.02 13.76 0.8641 5.395 3.026 3.373 4.825 1
12.74 13.67 0.8564 5.395 2.956 2.504 4.869 1
14.11 14.18 0.882 5.541 3.221 2.754 5.038 1
13.45 14.02 0.8604 5.516 3.065 3.531 5.097 1
13.16 13.82 0.8662 5.454 2.975 0.8551 5.056 1
15.49 14.94 0.8724 5.757 3.371 3.412 5.228 1
14.09 14.41 0.8529 5.717 3.186 3.92 5.299 1
13.94 14.17 0.8728 5.585 3.15 2.124 5.012 1
15.05 14.68 0.8779 5.712 3.328 2.129 5.36 1
16.12 15 0.9 5.709 3.485 2.27 5.443 1
16.2 15.27 0.8734 5.826 3.464 2.823 5.527 1
17.08 15.38 0.9079 5.832 3.683 2.956 5.484 1
14.8 14.52 0.8823 5.656 3.288 3.112 5.309 1
14.28 14.17 0.8944 5.397 3.298 6.685 5.001 1
13.54 13.85 0.8871 5.348 3.156 2.587 5.178 1
13.5 13.85 0.8852 5.351 3.158 2.249 5.176 1
13.16 13.55 0.9009 5.138 3.201 2.461 4.783 1
15.5 14.86 0.882 5.877 3.396 4.711 5.528 1
15.11 14.54 0.8986 5.579 3.462 3.128 5.18 1
13.8 14.04 0.8794 5.376 3.155 1.56 4.961 1
15.36 14.76 0.8861 5.701 3.393 1.367 5.132 1
14.99 14.56 0.8883 5.57 3.377 2.958 5.175 1
14.79 14.52 0.8819 5.545 3.291 2.704 5.111 1
14.86 14.67 0.8676 5.678 3.258 2.129 5.351 1
14.43 14.4 0.8751 5.585 3.272 3.975 5.144 1
15.78 14.91 0.8923 5.674 3.434 5.593 5.136 1
14.49 14.61 0.8538 5.715 3.113 4.116 5.396 1
14.33 14.28 0.8831 5.504 3.199 3.328 5.224 1
14.52 14.6 0.8557 5.741 3.113 1.481 5.487 1
15.03 14.77 0.8658 5.702 3.212 1.933 5.439 1
14.46 14.35 0.8818 5.388 3.377 2.802 5.044 1
14.92 14.43 0.9006 5.384 3.412 1.142 5.088 1
15.38 14.77 0.8857 5.662 3.419 1.999 5.222 1
12.11 13.47 0.8392 5.159 3.032 1.502 4.519 1
11.42 12.86 0.8683 5.008 2.85 2.7 4.607 1
11.23 12.63 0.884 4.902 2.879 2.269 4.703 1
12.36 13.19 0.8923 5.076 3.042 3.22 4.605 1
13.22 13.84 0.868 5.395 3.07 4.157 5.088 1
12.78 13.57 0.8716 5.262 3.026 1.176 4.782 1
12.88 13.5 0.8879 5.139 3.119 2.352 4.607 1
14.34 14.37 0.8726 5.63 3.19 1.313 5.15 1
14.01 14.29 0.8625 5.609 3.158 2.217 5.132 1
14.37 14.39 0.8726 5.569 3.153 1.464 5.3 1
12.73 13.75 0.8458 5.412 2.882 3.533 5.067 1
17.63 15.98 0.8673 6.191 3.561 4.076 6.06 2
16.84 15.67 0.8623 5.998 3.484 4.675 5.877 2
17.26 15.73 0.8763 5.978 3.594 4.539 5.791 2
19.11 16.26 0.9081 6.154 3.93 2.936 6.079 2
16.82 15.51 0.8786 6.017 3.486 4.004 5.841 2
16.77 15.62 0.8638 5.927 3.438 4.92 5.795 2
17.32 15.91 0.8599 6.064 3.403 3.824 5.922 2
20.71 17.23 0.8763 6.579 3.814 4.451 6.451 2
18.94 16.49 0.875 6.445 3.639 5.064 6.362 2
17.12 15.55 0.8892 5.85 3.566 2.858 5.746 2
16.53 15.34 0.8823 5.875 3.467 5.532 5.88 2
18.72 16.19 0.8977 6.006 3.857 5.324 5.879 2
20.2 16.89 0.8894 6.285 3.864 5.173 6.187 2
19.57 16.74 0.8779 6.384 3.772 1.472 6.273 2
19.51 16.71 0.878 6.366 3.801 2.962 6.185 2
18.27 16.09 0.887 6.173 3.651 2.443 6.197 2
18.88 16.26 0.8969 6.084 3.764 1.649 6.109 2
18.98 16.66 0.859 6.549 3.67 3.691 6.498 2
21.18 17.21 0.8989 6.573 4.033 5.78 6.231 2
20.88 17.05 0.9031 6.45 4.032 5.016 6.321 2
20.1 16.99 0.8746 6.581 3.785 1.955 6.449 2
18.76 16.2 0.8984 6.172 3.796 3.12 6.053 2
18.81 16.29 0.8906 6.272 3.693 3.237 6.053 2
18.59 16.05 0.9066 6.037 3.86 6.001 5.877 2
18.36 16.52 0.8452 6.666 3.485 4.933 6.448 2
16.87 15.65 0.8648 6.139 3.463 3.696 5.967 2
19.31 16.59 0.8815 6.341 3.81 3.477 6.238 2
18.98 16.57 0.8687 6.449 3.552 2.144 6.453 2
18.17 16.26 0.8637 6.271 3.512 2.853 6.273 2
18.72 16.34 0.881 6.219 3.684 2.188 6.097 2
16.41 15.25 0.8866 5.718 3.525 4.217 5.618 2
17.99 15.86 0.8992 5.89 3.694 2.068 5.837 2
19.46 16.5 0.8985 6.113 3.892 4.308 6.009 2
19.18 16.63 0.8717 6.369 3.681 3.357 6.229 2
18.95 16.42 0.8829 6.248 3.755 3.368 6.148 2
18.83 16.29 0.8917 6.037 3.786 2.553 5.879 2
18.85 16.17 0.9056 6.152 3.806 2.843 6.2 2
17.63 15.86 0.88 6.033 3.573 3.747 5.929 2
19.94 16.92 0.8752 6.675 3.763 3.252 6.55 2
18.55 16.22 0.8865 6.153 3.674 1.738 5.894 2
18.45 16.12 0.8921 6.107 3.769 2.235 5.794 2
19.38 16.72 0.8716 6.303 3.791 3.678 5.965 2
19.13 16.31 0.9035 6.183 3.902 2.109 5.924 2
19.14 16.61 0.8722 6.259 3.737 6.682 6.053 2
20.97 17.25 0.8859 6.563 3.991 4.677 6.316 2
19.06 16.45 0.8854 6.416 3.719 2.248 6.163 2
18.96 16.2 0.9077 6.051 3.897 4.334 5.75 2
19.15 16.45 0.889 6.245 3.815 3.084 6.185 2
18.89 16.23 0.9008 6.227 3.769 3.639 5.966 2
20.03 16.9 0.8811 6.493 3.857 3.063 6.32 2
20.24 16.91 0.8897 6.315 3.962 5.901 6.188 2
18.14 16.12 0.8772 6.059 3.563 3.619 6.011 2
16.17 15.38 0.8588 5.762 3.387 4.286 5.703 2
18.43 15.97 0.9077 5.98 3.771 2.984 5.905 2
15.99 14.89 0.9064 5.363 3.582 3.336 5.144 2
18.75 16.18 0.8999 6.111 3.869 4.188 5.992 2
18.65 16.41 0.8698 6.285 3.594 4.391 6.102 2
17.98 15.85 0.8993 5.979 3.687 2.257 5.919 2
20.16 17.03 0.8735 6.513 3.773 1.91 6.185 2
17.55 15.66 0.8991 5.791 3.69 5.366 5.661 2
18.3 15.89 0.9108 5.979 3.755 2.837 5.962 2
18.94 16.32 0.8942 6.144 3.825 2.908 5.949 2
15.38 14.9 0.8706 5.884 3.268 4.462 5.795 2
16.16 15.33 0.8644 5.845 3.395 4.266 5.795 2
15.56 14.89 0.8823 5.776 3.408 4.972 5.847 2
15.38 14.66 0.899 5.477 3.465 3.6 5.439 2
17.36 15.76 0.8785 6.145 3.574 3.526 5.971 2
15.57 15.15 0.8527 5.92 3.231 2.64 5.879 2
15.6 15.11 0.858 5.832 3.286 2.725 5.752 2
16.23 15.18 0.885 5.872 3.472 3.769 5.922 2
13.07 13.92 0.848 5.472 2.994 5.304 5.395 3
13.32 13.94 0.8613 5.541 3.073 7.035 5.44 3
13.34 13.95 0.862 5.389 3.074 5.995 5.307 3
12.22 13.32 0.8652 5.224 2.967 5.469 5.221 3
11.82 13.4 0.8274 5.314 2.777 4.471 5.178 3
11.21 13.13 0.8167 5.279 2.687 6.169 5.275 3
11.43 13.13 0.8335 5.176 2.719 2.221 5.132 3
12.49 13.46 0.8658 5.267 2.967 4.421 5.002 3
12.7 13.71 0.8491 5.386 2.911 3.26 5.316 3
10.79 12.93 0.8107 5.317 2.648 5.462 5.194 3
11.83 13.23 0.8496 5.263 2.84 5.195 5.307 3
12.01 13.52 0.8249 5.405 2.776 6.992 5.27 3
12.26 13.6 0.8333 5.408 2.833 4.756 5.36 3
11.18 13.04 0.8266 5.22 2.693 3.332 5.001 3
11.36 13.05 0.8382 5.175 2.755 4.048 5.263 3
11.19 13.05 0.8253 5.25 2.675 5.813 5.219 3
11.34 12.87 0.8596 5.053 2.849 3.347 5.003 3
12.13 13.73 0.8081 5.394 2.745 4.825 5.22 3
11.75 13.52 0.8082 5.444 2.678 4.378 5.31 3
11.49 13.22 0.8263 5.304 2.695 5.388 5.31 3
12.54 13.67 0.8425 5.451 2.879 3.082 5.491 3
12.02 13.33 0.8503 5.35 2.81 4.271 5.308 3
12.05 13.41 0.8416 5.267 2.847 4.988 5.046 3
12.55 13.57 0.8558 5.333 2.968 4.419 5.176 3
11.14 12.79 0.8558 5.011 2.794 6.388 5.049 3
12.1 13.15 0.8793 5.105 2.941 2.201 5.056 3
12.44 13.59 0.8462 5.319 2.897 4.924 5.27 3
12.15 13.45 0.8443 5.417 2.837 3.638 5.338 3
11.35 13.12 0.8291 5.176 2.668 4.337 5.132 3
11.24 13 0.8359 5.09 2.715 3.521 5.088 3
11.02 13 0.8189 5.325 2.701 6.735 5.163 3
11.55 13.1 0.8455 5.167 2.845 6.715 4.956 3
11.27 12.97 0.8419 5.088 2.763 4.309 5 3
11.4 13.08 0.8375 5.136 2.763 5.588 5.089 3
10.83 12.96 0.8099 5.278 2.641 5.182 5.185 3
10.8 12.57 0.859 4.981 2.821 4.773 5.063 3
11.26 13.01 0.8355 5.186 2.71 5.335 5.092 3
10.74 12.73 0.8329 5.145 2.642 4.702 4.963 3
11.48 13.05 0.8473 5.18 2.758 5.876 5.002 3
12.21 13.47 0.8453 5.357 2.893 1.661 5.178 3
11.41 12.95 0.856 5.09 2.775 4.957 4.825 3
12.46 13.41 0.8706 5.236 3.017 4.987 5.147 3
12.19 13.36 0.8579 5.24 2.909 4.857 5.158 3
11.65 13.07 0.8575 5.108 2.85 5.209 5.135 3
12.89 13.77 0.8541 5.495 3.026 6.185 5.316 3
11.56 13.31 0.8198 5.363 2.683 4.062 5.182 3
11.81 13.45 0.8198 5.413 2.716 4.898 5.352 3
10.91 12.8 0.8372 5.088 2.675 4.179 4.956 3
11.23 12.82 0.8594 5.089 2.821 7.524 4.957 3
10.59 12.41 0.8648 4.899 2.787 4.975 4.794 3
10.93 12.8 0.839 5.046 2.717 5.398 5.045 3
11.27 12.86 0.8563 5.091 2.804 3.985 5.001 3
11.87 13.02 0.8795 5.132 2.953 3.597 5.132 3
10.82 12.83 0.8256 5.18 2.63 4.853 5.089 3
12.11 13.27 0.8639 5.236 2.975 4.132 5.012 3
12.8 13.47 0.886 5.16 3.126 4.873 4.914 3
12.79 13.53 0.8786 5.224 3.054 5.483 4.958 3
13.37 13.78 0.8849 5.32 3.128 4.67 5.091 3
12.62 13.67 0.8481 5.41 2.911 3.306 5.231 3
12.76 13.38 0.8964 5.073 3.155 2.828 4.83 3
12.38 13.44 0.8609 5.219 2.989 5.472 5.045 3
12.67 13.32 0.8977 4.984 3.135 2.3 4.745 3
11.18 12.72 0.868 5.009 2.81 4.051 4.828 3
12.7 13.41 0.8874 5.183 3.091 8.456 5 3
12.37 13.47 0.8567 5.204 2.96 3.919 5.001 3
12.19 13.2 0.8783 5.137 2.981 3.631 4.87 3
11.23 12.88 0.8511 5.14 2.795 4.325 5.003 3
13.2 13.66 0.8883 5.236 3.232 8.315 5.056 3
11.84 13.21 0.8521 5.175 2.836 3.598 5.044 3
12.3 13.34 0.8684 5.243 2.974 5.637 5.063 3
")
# Define column names
colnames(seeds_data) <- c('Area', 'Perimeter', 'Compactness', 'Kernel_Length',
'Kernel_Width', 'Asymmetry_Coeff', 'Kernel_Groove_Length', 'Class')
# Convert Class to a factor and one-hot encode if necessary for the neural network
seeds_data$Class <- as.factor(seeds_data$Class)
# Split the data into training and testing sets (optional, usually for evaluation)
set.seed(123)
trainIndex <- createDataPartition(seeds_data$Class, p = 0.7, list = FALSE)
trainData <- seeds_data[trainIndex, ]
testData <- seeds_data[-trainIndex, ]
# Scale features (important for neural networks)
trainX <- scale(trainData[, -8])
trainY <- class.ind(trainData$Class) # Convert classes to indicator variables
testX <- scale(testData[, -8], center = attr(trainX, "scaled:center"), scale = attr(trainX, "scaled:scale"))
# Train the neural network without setting a strict max iteration limit
# Here we set maxit to a very high value; adjust size (number of hidden nodes) as needed
nn_model <- nnet(trainX, trainY, size = 5, maxit = 1e6, linout = FALSE, decay = 5e-4, trace = TRUE)
# Summary of the model
summary(nn_model)
# Load necessary libraries
if (!require(neuralnet)) { install.packages("neuralnet"); library(neuralnet) }
if (!require(caret)) { install.packages("caret"); library(caret) }
if (!require(dplyr)) { install.packages("dplyr"); library(dplyr) }
# Set up the data for reproducibility
set.seed(123)
# Define control for cross-validation using the caret package
train_control <- trainControl(method = "cv", number = 10)
# Prepare the training and test datasets (85% for training, 15% for testing)
sample_index <- createDataPartition(seeds_data$Class, p = 0.85, list = FALSE)
train_data <- seeds_data[sample_index, ]
test_data <- seeds_data[-sample_index, ]
# Ensure column names are consistent
colnames(train_data) <- c("V1", "V2", "V3", "V4", "V5", "V6", "V7", "Class")
colnames(test_data) <- c("V1", "V2", "V3", "V4", "V5", "V6", "V7", "Class")
# Define the neural network model formula
nn_formula <- as.formula("Class ~ V1 + V2 + V3 + V4 + V5 + V6 + V7")
# Train the neural network model with two hidden layers of 3 nodes each
nn_cv_model <- train(
nn_formula,
data = train_data,
method = "nnet",
trControl = train_control,
tuneGrid = expand.grid(size = c(3, 3), decay = 0.01),
MaxNWts = 1000,
maxit = 1000,
trace = FALSE,
linout = FALSE
)
# Make predictions on the test data
predicted_values <- predict(nn_cv_model, test_data)
# Calculate the mean performance (accuracy) of the model
accuracy <- mean(predicted_values == test_data$Class)
# Display the predicted vs actual values and the accuracy
comparison_df <- data.frame(
Actual = test_data$Class,
Predicted = predicted_values
)
print("Predicted vs Actual Outputs:")
print(comparison_df)
print(paste("Mean Performance (Accuracy):", accuracy))
# Discussion on performance
if (accuracy < 0.7) {
print("The network's performance is low. Consider experimenting with different architectures or hyperparameters.")
} else {
print("The network's performance is acceptable.")
}# Install the truncnorm package if it is not already installed
if (!requireNamespace("truncnorm", quietly = TRUE)) {
install.packages("truncnorm")
}
# Load the truncnorm package
library(truncnorm)
# Generate truncated normal distribution numbers
truncated_normal_numbers <- rtruncnorm(10000, a = -2, b = 2, mean = 0, sd = 1)
# Plot the histogram of the truncated normal distribution
hist(truncated_normal_numbers, main = "Histogram of Truncated Normal Distribution", xlab = "Value", ylab = "Frequency")# Load necessary libraries
library(nnet) # For neural network
library(NeuralNetTools) # For network visualization
library(caret) # For data partitioning and performance metrics
# Load the dataset (assuming seeds_data.csv is the dataset file)
seeds_data <- read.csv("seeds_data.csv")
# Prepare the dataset (assuming seeds_data is already loaded and preprocessed as per previous steps)
seeds_data$Class <- as.factor(seeds_data$Class)
# Split the data into training and testing sets
set.seed(123)
trainIndex <- createDataPartition(seeds_data$Class, p = 0.7, list = FALSE)
trainData <- seeds_data[trainIndex, ]
testData <- seeds_data[-trainIndex, ]
# Scale features
trainX <- scale(trainData[, -8])
trainY <- class.ind(trainData$Class) # Convert classes to binary indicator variables
testX <- scale(testData[, -8], center = attr(trainX, "scaled:center"), scale = attr(trainX, "scaled:scale"))
# Train the neural network (as previously done)
nn_model <- nnet(trainX, trainY, size = 5, maxit = 1000, linout = FALSE, decay = 5e-4, trace = TRUE)
# Plot the network
plotnet(nn_model)
# Predict on the training and test sets
train_pred <- predict(nn_model, trainX, type = "class")
test_pred <- predict(nn_model, testX, type = "class")
# Convert predictions back to factor for confusion matrix
train_pred_factor <- as.factor(max.col(train_pred))
test_pred_factor <- as.factor(max.col(test_pred))
# Calculate Mean Squared Error for both training and test sets
train_mse <- mean((train_pred - trainY)^2)
test_mse <- mean((test_pred - class.ind(testData$Class))^2)
# Print MSEs
cat("Training MSE:", train_mse, "\n")
cat("Test MSE:", test_mse, "\n")
# Check if error has improved by comparing with previous models' errors# Install NeuralNetTools if not already installed
if (!require("NeuralNetTools")) install.packages("NeuralNetTools")
library(NeuralNetTools)
# Install neuralnet if not already installed
if (!require("neuralnet")) install.packages("neuralnet")
library(neuralnet)
# Example of creating a neural network model
# Note: Replace this with your actual model creation code
# nn_model <- neuralnet(Class ~ Var1 + Var2 + Var3, data = trainData, hidden = c(5,3), linear.output = FALSE)
# For demonstration purposes, let's create a simple neural network model
# using the iris dataset
data(iris)
set.seed(123)
iris$setosa <- ifelse(iris$Species == "setosa", 1, 0)
iris$versicolor <- ifelse(iris$Species == "versicolor", 1, 0)
iris$virginica <- ifelse(iris$Species == "virginica", 1, 0)
trainData <- iris[, c("Sepal.Length", "Sepal.Width", "Petal.Length", "Petal.Width", "setosa", "versicolor", "virginica")]
nn_model <- neuralnet(setosa + versicolor + virginica ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width,
data = trainData, hidden = c(5, 3), linear.output = FALSE)
# Plot the neural network
plotnet(nn_model)
# Make predictions on the test data
testX <- trainData[, c("Sepal.Length", "Sepal.Width", "Petal.Length", "Petal.Width")]
predictions <- predict(nn_model, testX)
# Convert the predicted values back to the original class labels
pred_class <- apply(predictions, 1, which.max)
# Calculate the misclassification error
actual_class <- apply(trainData[, c("setosa", "versicolor", "virginica")], 1, which.max)
misclass_error <- mean(pred_class != actual_class)
# Print the error
cat("Misclassification Error:", misclass_error, "\n")
# Optionally: Print improvement message based on previous error rate
# If you have a previous error rate, compare and display improvement:
# previous_error <- 0.1 # Example previous error rate
# cat("Error improvement compared to previous model:", (previous_error - misclass_error), "\n")# Install and load necessary library
if (!requireNamespace("neuralnet", quietly = TRUE)) {
install.packages("neuralnet")
}
library(neuralnet)
# Load or create the 'scaled_seeds_data' dataset
# Assuming 'scaled_seeds_data' is a data frame that needs to be loaded or created
# For example, you might load it from a CSV file:
# scaled_seeds_data <- read.csv("path_to_your_scaled_seeds_data.csv")
# Assuming the neural network model 'nn' needs to be trained first
# Define the formula for the neural network
formula <- as.formula(paste("V8 + V9 + V10 ~", paste(names(scaled_seeds_data)[1:7], collapse = " + ")))
# Train the neural network
nn <- neuralnet(formula, data = scaled_seeds_data, hidden = c(5, 3), linear.output = FALSE)
# Predict the training data
predicted <- neuralnet::compute(nn, scaled_seeds_data[, 1:7])$net.result
predicted_class <- apply(predicted, 1, which.max)
# Confusion matrix
actual_class <- apply(scaled_seeds_data[, 8:10], 1, which.max)
table(actual_class, predicted_class)if (!requireNamespace("fitur", quietly = TRUE)) {
install.packages("fitur")
}
library(fitur)
rdunif(10, 1, 10)if (!requireNamespace("distr", quietly = TRUE)) {
install.packages("distr")
}
library(distr)
dis <- AbscontDistribution(d = function(x){exp(-(x^2)/8)/sqrt(8*pi)})
custom_continuous_numbers <- r(dis)(10)
LCG <- function(n, m, a, c, X0) {
X <- numeric(length=n)
Xn <- X0
for (i in 1:n) {
Xn <- (a * Xn + c) %% m
X[i] <- Xn
}
return(X)
}
# Test the function with parameters m = 8, a = 5, and c = 1
test_result <- LCG(10, 8, 5, 1, 0)
print(test_result)result <- LCG(10, 63, 17, 3, 0)
print(result)X <- LCG(1000, 137, 7, 21, 0)/137
plot(X[1:999], X[2:1000], asp=1)
m <- 1024
a <- 317
c <- 93
seed <- 0
X <- LCG(1000, m, a, c, seed)/m
plot(X[1:999], X[2:1000], asp=1)
m <- 2^32 - 1
a <- 1664525
c <- 1013904223
seed <- 0
X <- LCG(1000, m, a, c, seed)/m
plot(X[1:999], X[2:1000], asp=1)