Oja's rule is an unsupervised learning algorithm used in the field of neural networks and machine learning, particularly in the context of learning vector representations. It is a type of Hebbian learning rule, which is based on the principle that neurons that fire together, wire together. Oja's rule is specifically designed to allow a neural network to learn the principal components of the input data, effectively performing a form of principal component analysis (PCA).
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For a linear output , the second term limits the growth produced by the Hebbian term. On the averaged dynamics with , . For , positive-eigenvalue equilibria have norm and align with eigenvectors of . If inputs are centered, is their covariance matrix.