Fast Matrix Factorization with Non-Uniform Weights on Missing Data
This work addresses an incremental improvement in matrix factorization for recommendation systems by enhancing efficiency and performance in handling missing data.
The paper tackles the problem of matrix factorization for high-dimensional sparse data by proposing a fast learning method that applies non-uniform weights to missing entries, improving modeling fidelity without sacrificing efficiency. Experiments on recommendation benchmarks show the method's correctness, efficiency, and effectiveness, with time complexity scaling with observed entries rather than matrix size.
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an imbalanced learning problem, since the scale of missing entries is usually much larger than that of observed entries, but they cannot be ignored due to the valuable negative signal. For efficiency concern, existing work typically applies a uniform weight on missing entries to allow a fast learning algorithm. However, this simplification will decrease modeling fidelity, resulting in suboptimal performance for downstream applications. In this work, we weight the missing data non-uniformly, and more generically, we allow any weighting strategy on the missing data. To address the efficiency challenge, we propose a fast learning method, for which the time complexity is determined by the number of observed entries in the data matrix, rather than the matrix size. The key idea is two-fold: 1) we apply truncated SVD on the weight matrix to get a more compact representation of the weights, and 2) we learn MF parameters with element-wise alternating least squares (eALS) and memorize the key intermediate variables to avoid repeating computations that are unnecessary. We conduct extensive experiments on two recommendation benchmarks, demonstrating the correctness, efficiency, and effectiveness of our fast eALS method.