The difference between defining a step in pipline or as a step in param_grid, e.g. dimensionality reduction

Question

In this scikit-learn documentation:

https://scikit-learn.org/stable/auto_examples/compose/plot_compare_reduction.html#sphx-glr-auto-examples-compose-plot-compare-reduction-py

I can not figure out the purpose of having dimensionality reduction in both the pipe and param_grid ; In other words what would happen if all the dimensionality reductions where defined in either pipe or param_grid ? Here is the code:

pipe = Pipeline(  
    [
        # the reduce_dim stage is populated by the param_grid
        ("reduce_dim", "passthrough"),
        ("classify", LinearSVC(dual=False, max_iter=10000)),
    ]
)  

N_FEATURES_OPTIONS = [2, 4, 8]
C_OPTIONS = [1, 10, 100, 1000]
param_grid = [
    {
        "reduce_dim": [PCA(iterated_power=7), NMF()],
        "reduce_dim__n_components": N_FEATURES_OPTIONS,
        "classify__C": C_OPTIONS,
    },
    {
        "reduce_dim": [SelectKBest(chi2)],
        "reduce_dim__k": N_FEATURES_OPTIONS,
        "classify__C": C_OPTIONS,
    },
]
reducer_labels = ["PCA", "NMF", "KBest(chi2)"]

grid = GridSearchCV(pipe, n_jobs=1, param_grid=param_grid)
X, y = load_digits(return_X_y=True)
grid.fit(X, y)  

Answer 1

It needs to be in the param_grid because you want to try different options.

And it also needs to be in the pipeline otherwise the option that you try at a given point in time won't be used at all.