Final answer:
PCA reduces dimensions by finding uncorrelated variables that capture the most data variance, without considering the response variable, which can affect interpretability. LASSO selects variables and shrinks some coefficients to zero, considering the response variable, thus often providing a more interpretable model.
Step-by-step explanation:
To compare PCA (Principal Component Analysis) and LASSO (Least Absolute Shrinkage and Selection Operator) in terms of how they perform dimension reduction and their interpretability, we must first understand what each technique does.
PCA is a technique that reduces the dimensionality of the data by finding the principal components that capture the most variance in the data. This is done by orthogonal transformation of the original variables into a new set of uncorrelated variables, which are the principal components. PCA does not consider the response variable when it performs dimension reduction. Interpretability can sometimes be challenging with PCA because the principal components are linear combinations of the original variables.
LASSO is a regression analysis method that performs both variable selection and regularization to enhance the prediction accuracy and interpretability of the statistical model it produces. LASSO does this by imposing a penalty on the absolute size of the regression coefficients. In terms of dimension reduction, LASSO shrinks some coefficients to zero, effectively removing those variables from the model. The variables with non-zero coefficients are selected by the LASSO algorithm, which makes LASSO models generally more interpretable than PCA because the remaining variables have a direct relationship with the response variable.
Thus, the key difference in dimension reduction is that PCA is unsupervised and does not consider the response variable, while LASSO is supervised and does consider the response. Regarding interpretability, LASSO tends to provide a more interpretable model, as it yields a subset of predictors that directly influence the response.