PCA and N-Gram Language Model

This project contains two components implemented in Python:

1. A Principal Component Analysis (PCA) module for dimensionality reduction and image reconstruction.
2. A character-level N-gram language model supporting probability computation and text generation.

PCA Functions

• load_and_center_dataset(filename): Loads data and centers it by subtracting the mean.
• get_covariance(dataset): Computes the sample covariance matrix.
• get_eig(S, k): Returns the top k eigenvalues and eigenvectors.
• get_eig_prop(S, prop): Returns eigenvectors explaining more than a given variance proportion.
• project_and_reconstruct_image(image, U): Projects an image into PCA subspace and reconstructs it.
• display_image(...): Displays original and reconstructed images side by side.

N-Gram Language Model

• fit(text): Builds n-gram counts from training text.
• logprob(s): Computes log-probability of a string.
• prob(s): Computes string probability.
• next_char_distribution(context): Returns the next-character distribution.
• generate(num_chars, seed): Generates text from the model.

How to Use

Place your .npy dataset or text input in the project directory and call the appropriate functions.

File Structure

• pca_and_ngram.py — main implementation file
• test_ngram.py — small test/demo script for the n-gram model
• dataset.npy — sample data (optional)
• README.md

Requirements

Python 3
NumPy
SciPy
Matplotlib

Install them with:

pip install -r requirements.txt

Author

Macy Xiang
https://github.com/macyxiangA