This R Markdown script sets up a neural network using the `neuralnet` package to approximate the square root of the sum of two input values. The training data is randomly generated, with each input feature scaled from 0 to 100. The neural network configuration has one hidden layer with three nodes, and the trained model's structure is visualized at the end.

The R code implements an image classification pipeline that includes data loading, exploratory analysis, logistic regression, clustering, and neural network modeling. It begins by loading images from a directory, resizing them, and organizing the data into a structured format. The dataset is explored using summary statistics. A multinomial logistic regression model is fitted after applying PCA for dimensionality reduction. Clustering techniques, including hierarchical clustering and K-means, are used to assess data groupings. Finally, a neural network model is developed to predict classes based on varying hidden layer sizes, and accuracy metrics are computed to evaluate model performance.