An Algorithmic and Computational Exposition of Parametric and Centroidal Learners in Python

• SheshuKumar Vangala

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This paper presents a didactic, implementation-focused exploration of two foundational learning paradigms within artificial intelligence. We first examine a parametric supervised learner, constructing a linear hypothesis through ordinary least squares estimation, and derive its closed-form solution manually from a defined training set. The second paradigm is a centroid-based unsupervised partitioning algorithm, implemented via Lloyd's iterative refinement to minimize intra-cluster variance. Both algorithms are realized from first principles in Python, utilizing NumPy for numerical computation and matplotlib for spatial and relational visualization. The exposition illustrates the direct translation of mathematical formulations into executable NumPy code for two foundational algorithms. Complete source code is provided for pedagogical reproducibility.

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