What are latent factors in matrix factorization?

What Are Latent Factors in Matrix Factorization? Latent factors in matrix factorization are hidden features derived from data to explain relationships between users and items in recommendation systems. For example, in a user-movie rating matrix, latent factors might represent abstract qualities like genre preference, movie pacing, or thematic depth. These factors are not explicitly labeled in the data but are inferred mathematically by decomposing the original matrix into two smaller matrices: one representing users and their affinity to latent factors, and the other representing items and their alignment with those same factors. The dot product of these matrices approximates the original data, enabling predictions (e.g., how a user might rate an unviewed movie).

How Are Latent Factors Determined? Matrix factorization algorithms, like Singular Value Decomposition (SVD) or Alternating Least Squares (ALS), learn latent factors by minimizing the error between predicted and observed values in the training data. For instance, if User A rates Movie X as 5/5, the model adjusts the latent factor vectors for both the user and movie until their product (plus biases) matches 5. Each factor is a numerical weight, and the model iteratively refines these weights using optimization techniques like gradient descent. The number of latent factors (e.g., 10, 50, 100) is a hyperparameter chosen by the developer. A higher number allows the model to capture finer details but risks overfitting, while fewer factors generalize better but may miss nuanced patterns.

Practical Considerations for Developers When implementing matrix factorization, developers must balance computational efficiency and model performance. For example, in a Python library like Surprise or TensorFlow, you might set n_factors=50 to define the latent space dimensionality. Regularization (e.g., L2 penalty) is often added to prevent overfitting by discouraging large weights in the factor matrices. Additionally, latent factors are not always interpretable—while one factor might loosely correlate with “action movies,” others may represent combinations of traits. Evaluating factors often involves testing prediction accuracy on held-out data rather than analyzing their meaning. Tools like matrix visualization or clustering can help developers inspect whether factors capture meaningful structure, but their primary role is to improve recommendation quality, not to provide human-readable explanations.