PCA Psychophysical Analysis

The question

For my Computational Linear Algebra for Large Scale Problems course, I used PCA to reduce 93 mixed psychophysical variables to five components. I then clustered the reduced data with K-Means and went back to the original variables to see whether those groups told a coherent story or were just convenient geometry.

What showed up

• Cluster 1: taller and heavier on average (178.6 cm, 73.3 kg), with stronger sensation-seeking signals.
• Cluster 0: shorter and lighter on average (169.3 cm, 59.3 kg), with a different anxiety/conformity pattern.
• Cluster 2: 60.6% female, with several psychological variables separating it from the other groups.
• Cluster 3: the least tidy group, including a much wider spread in weight (σ = 16.8).

Methodology

• Data Preprocessing: Ordinal Encoding for categorical variables, StandardScaler for numerical normalization.
• PCA: Condensed 93 features into 5 principal components while retaining structural integrity.
• K-Means Clustering: Segmented the population into 4 psychophysical profiles based on the principal components.
• Statistical Profiling: Analyzed cluster centroids to interpret correlations between height/weight and behavioral factors (extraversion, anxiety).