본 논문에서는 부분최소제곱회귀에 벌점함수를 적용하여 의미있는 변수들을 선택하는 문제에 대한 해를 벌점화 행렬분해를 이용하여 구하는 문제를 고려하였다. 가상자료를 통하여 L1 벌점함수와 Fused Lasso 벌점함수의 특성들과 효율성 등을 비교하였다.
Partial least squares is used for modeling two data set using latent variables of them. Such a partial least squares can be extended to the regression problem. In case that the number of variable increases, the number of latent variable also increases and we may have a difficulty in interpreting. Therefore, we eliminate irrelevant variables using a penalty function and obtain a simpler model and have a advantage in interpreting it. Penalized matrix decomposition method could be used for partial least squares regression for variable selection with any convex penalty functions and it turns out to be efficient and effective. We compared and Fused Lasso penalty functions for partial least squares regression models with simulated data sets. Penalized matrix decomposition algorithm produced satisfactory results in selection relevant subset of predictor variables. However, we have some severe biases with large penalties and we need further algorithm like generalized cross-validation to keep estimated coefficients not far from true values.