International Journal of Innovative Research in Computer and Communication Engineering
ISSN Approved Journal | Impact factor: 8.771 | ESTD: 2013 | Follows UGC CARE Journal Norms and Guidelines
| Monthly, Peer-Reviewed, Refereed, Scholarly, Multidisciplinary and Open Access Journal | High Impact Factor 8.771 (Calculated by Google Scholar and Semantic Scholar | AI-Powered Research Tool | Indexing in all Major Database & Metadata, Citation Generator | Digital Object Identifier (DOI) |
| TITLE | Why Linear Algebra Is Fundamental to Algorithmic Thinking: A Structured Analysis of Vectors, Transformations, Dimensionality, and Computational Representation |
|---|---|
| ABSTRACT | Linear algebra is often said to be the basis of machine learning, but without a clear link to the operations of the algorithms it's hard to grasp. This study explores the impact of vectors, distance measure, matrix decompositions, transformations, and dimensionality on the functioning of a working classification algorithm. The reason for choosing Fashion-MNIST is that every 28×28 grayscale image can be easily and naturally stored as a 784-dimensional vector, and each image has a meaningful class label. Instead of starting with a trained machine-learning model, the analysis started from the underlying binary data, validating and decoding the data, investigating vector geometry, building class centroids, nearest-centroid classification, principal component analysis (PCA) of the covariance matrix, testing low-dimensional representations, manipulating coordinate geometry, and testing the computational costs. The results reveal that the Euclidean classification of centroids is quite accurate, with a 67.68% accuracy on the results using no learned nonlinear features, and that 24 principal components preserve 67.30% of accuracy while discarding 96.94% of dimensions, and that a full orthogonal coordinate transformation achieves 100% accuracy on all 10,000 predictions, and that selectively reweighting one principal direction can change thousands of predictions. The results have shown that linear algebra enables algorithms to be computationally feasible but it also plays a key role in the very nature of the similarity or information that an algorithm considers, as well as the nature of what it considers to be a useful structure for computation. |
| AUTHOR | ATTHARV BHAGCHANDKA Student, Shri Ram School Moulsari, Gurgaon, India |
| VOLUME | 188 |
| DOI | DOI: 10.15680/IJIRCCE.2026.1409011 |
| pdf/11_Why Linear Algebra Is Fundamental to Algorithmic Thinking A Structured Analysis of Vectors, Transformations, Dimensionality, and Computational Representation.pdf | |
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| References |
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