Regularization Methods Including Tikhonov

Regularization methods refer to techniques that impose constraints on model weights during training to prevent overfitting. Common regularization approaches include Tikhonov, TSVD, TTLS, TGSVD, and CSVD. Tikhonov regularization is a widely used method that achieves regularization by adding a penalty term of the squared sum of weights to the objective function. In implementation, this typically involves adding a lambda parameter multiplied by the L2 norm of the weight vector to the loss function. TSVD (Truncated Singular Value Decomposition) is a regularization method based on singular value decomposition, which demonstrates excellent performance in linear regression problems. The algorithm works by truncating small singular values in the decomposition to reduce model complexity. TTLS (Total Least Squares) is a regularization approach based on the total least squares principle, which can obtain optimal solutions through iterative solving. This method is particularly useful when both input and output data contain noise. TGSVD (Truncated Generalized Singular Value Decomposition) is a regularization technique based on generalized singular value decomposition that has found extensive applications in multivariate statistical analysis and image processing. It handles generalized eigenvalue problems through dimension reduction. CSVD (Component-wise Singular Value Decomposition) is a regularization method based on truncated singular value decomposition that simultaneously achieves dimensionality reduction and regularization. This approach selectively retains the most significant components while discarding noisy or irrelevant dimensions. In summary, regularization methods represent highly valuable techniques that have gained widespread adoption in practical applications across various machine learning and statistical modeling domains.