from pPolis2024-05-27 pPolis2024-10-21 2024-10-21 :
[f"{x * 100:.1f}%" for x in pca.explained_variance_ratio_]
:
['29.1%', '18.8%', '7.5%', '5.1%', '3.2%', '3.0%', '2.4%', '2.1%', '2.0%', '1.7%', '1.6%', '1.5%', '1.3%', '1.3%', '1.2%', '1.2%', '1.0%', '1.0%', '1.0%', '0.9%', '0.9%', '0.8%', '0.8%', '0.8%', '0.8%', '0.8%', '0.7%', '0.7%', '0.7%', '0.6%', '0.6%', '0.6%', '0.6%', '0.6%', '0.5%', '0.5%', '0.5%', '0.4%', '0.4%', '0.4%', '0.4%', '0.0%']
len = 42
pca.n_features_in_ 592
pca.n_samples_ 42
Huh.
- I thought you were being PCA after the transposition, but that’s what I thought.
-
- No transposition: Calculates the covariance between questions and shows how much each question contributes to the new basis (principal components). This is useful for exploring the relationship between questions. - When transposing: Calculates the covariance between respondents and shows how much each respondent contributes to the principal components. This is useful for clustering respondents and finding patterns.
- You want to cluster respondents, so that’s correct.
P=592 (people) Q=42 (questions)
embedding.shape # (592, 2)
In order to consider how the answer to a given question i would contribute to the X-axis after a PCA using covariance among respondents by transposition, we first need to see how that question i affects the principal components of the respondents as a whole.
py
# Obtain PCA components
matrix_centered = matrix - matrix.mean(axis=0) # Mean centered
# pca.fit(matrix_centered.T) # Perform PCA based on respondents
# 1st principal component (X-axis)
pc1 = pca.components_[0] # 1st principal component vector (weights per respondent)
for col in matrix.columns:
question_vector = matrix_centered[col]
# contributions[col] = np.dot(question_vector, pc1)
c = np.dot(question_vector, pc1)
print(f"{col}: {c:.2f}: {readable.get(col, col)}")
Data is ready.
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