LDA shares a covariance shape

Understand the idea

LDA fits different class means with a shared within-class covariance shape, producing linear decision boundaries. Start by reading those means and comparing a shrinkage choice on training folds. The midpoint score identity is an optional deeper investigation, introduced beside its own code.

Understand shared class geometry and linear boundaries.Scroll the diagram horizontally if needed.

What the syntax does

LinearDiscriminantAnalysis(solver='lsqr', shrinkage='auto'): Creates a linear discriminant analysis classifier.
shrinkage: None, "auto", 0.1
solver=svd is the sklearn default.
The authored lsqr path supports shrinkage: None uses the covariance estimate directly, auto estimates shrinkage, and a number from 0 to 1 sets its strength.
Use matching training folds to investigate choices.
model.means_: Reads the fitted class-by-feature mean matrix; label its axes with classes_ and feature names.

Supplied for this practice

These objects are prepared afresh before your editor runs.

X: Feature dataframe for the declared population, preserving row indices.
X = df[['x1', 'x2']]
y: Target series, aligned with X.
y = df.label
X_train / X_test / y_train / y_test: Training feature rows from the declared split. Final-test feature rows from the declared split. Training targets, aligned with X_train. Final-test targets, aligned with X_test.
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42, stratify=y)
model: Already fitted on X_train, y_train. Fitted estimator or pipeline for the requested model family. Fitted on X_train, y_train; reuse without refitting.

Outputs you create

answer: The requested result, with the values, labels and row order described by this task.

COV90_SHARED · first 8 rows
`x1`	`x2`	`label`
-0.743901	-0.783885	A
-2.12019	-0.179627	A
1.34074	1.03856	A
-0.952592	-0.268834	A
-0.558928	-0.411972	A
-2.15048	-0.372685	A
-1.6208	0.506436	A
-0.975229	-0.834521	A

Your task

Build answer as a table of fitted LDA means, with model.classes_ as rows and X_train column names as columns.

answer

Hints

Think: Class means need the same feature names and class order used by the fitted model.

Tools: means_, classes_ and a labelled dataframe.

Approach: Read the fitted means and attach class rows plus training-feature columns.

Explained solution

answer=pd.DataFrame(model.means_,index=model.classes_,columns=X_train.columns)

The table exposes each class centre while leaving the shared covariance assumption conceptually separate.