What Matrix Factorization Meaning, Applications & Example
Technique for decomposing matrices used in recommender systems.
What is Matrix Factorization?
Matrix Factorization is a technique used to decompose a matrix into two or more smaller matrices. In machine learning, it is commonly used for recommendation systems to extract latent features from a user-item interaction matrix, helping to predict missing values.
Types of Matrix Factorization
- Singular Value Decomposition (SVD): Decomposes a matrix into three matrices: U (user features), Σ (singular values), and V (item features).
- Non-negative Matrix Factorization (NMF): Factorizes a matrix into two non-negative matrices, often used in text mining and recommender systems.
- Alternating Least Squares (ALS): Used in collaborative filtering, especially for large-scale recommendation systems.
Applications of Matrix Factorization
- Recommendation Systems: Used to predict user preferences for products or movies by uncovering hidden features.
- Image Compression: Reduces the dimensionality of images while preserving key features.
- Collaborative Filtering: Predicts missing ratings or preferences based on similar users or items.
Example of Matrix Factorization
from sklearn.decomposition import NMF
import numpy as np
# Sample user-item interaction matrix
matrix = np.array([[5, 0, 3], [4, 0, 0], [1, 0, 2]])
# Apply NMF
model = NMF(n_components=2)
W = model.fit_transform(matrix) # User feature matrix
H = model.components_ # Item feature matrix
# Reconstruct the original matrix
reconstructed_matrix = np.dot(W, H)
print(reconstructed_matrix)