## Volume 14, Number 5

#### Quantifying the Theory Vs. Programming Disparity using Spectral Bipartivity Analysis

and Principal Component Analysis

### Authors

Natarajan Meghanathan, Jackson State University, USA

### Abstract

Some students in the Computer Science and related majors excel very well in programming-related assignments, but not equally well in the theoretical assignments (that are not programming-based) and vice-versa. We refer to this as the "Theory vs. Programming Disparity (TPD)". In this paper, we propose a spectral bipartivity analysis-based approach to quantify the TPD metric for any student in a course based on the percentage scores (considered as decimal values in the range of 0 to 1) of the student in the course assignments (that involves both theoretical and programming-based assignments). We also propose a principal component analysis (PCA)-based approach to quantify the TPD metric for the entire class based on the percentage scores (in a scale of 0 to 100) of the students in the theoretical and programming assignments. The spectral analysis approach partitions the set of theoretical and programming assignments to two disjoint sets whose constituents are closer to each other within each set and relatively more different from each across the two sets. The TPD metric for a student is computed on the basis of the Euclidean distance between the tuples representing the actual numbers of theoretical and programming assignments vis-a-vis the number of theoretical and programming assignments in each of the two disjoint sets. The PCA-based analysis identifies the dominating principal components within the sets of theoretical and programming assignments and computes the TPD metric for the entire class as a weighted average of the correlation coefficients between the dominating principal components representing these two sets.

### Keywords

Spectral Analysis, Principal Component Analysis, Correlation Coefficient, Theory vs. Programming Disparity, Eigenvector, Bipartivity.