Tensor Decomposition
Tensor decomposition is a mathematical technique for breaking down multi-dimensional arrays (tensors) into simpler, interpretable components, analogous to matrix factorization but for higher-order data. It is widely used in machine learning, signal processing, and data analysis to reduce dimensionality, extract latent features, and uncover patterns in complex datasets. Common methods include CP decomposition, Tucker decomposition, and tensor singular value decomposition (t-SVD).
Developers should learn tensor decomposition when working with high-dimensional data, such as in computer vision (e.g., video analysis), natural language processing (e.g., word embeddings), or recommendation systems, to handle sparsity and improve computational efficiency. It is essential for tasks like data compression, anomaly detection, and multi-way data analysis, where traditional matrix methods fall short due to the tensor's multi-linear structure.