Linear Algebra and Artificial Intelligence
“Mathematics is the language with which God has written the universe” – Galileo Galilei
Linear Algebra plays a dominant role in the enhancement of technology and Mathematics is fundamental to understanding Artificial Intelligence. To quote Skyler Speakman, “Linear Algebra is the mathematics of the 21st century”.
Artificial Intelligence is an enhanced model of human intelligence mimicking human behaviour and beyond. As Alan Turing’s study points out, it is an imitation game posing a question on whether machines can really think.
Linear Algebra is the foundation of machine learning. An image is processed by the machine in the form of pixels and the use of matrices allow any function to be performed on the image. With the help of vectors and matrices, linear algebra allows mathematical operations to be performed. Data scientists can abstract data and models with the concepts of scalars, vectors, tensors, matrices, sets and sequences, topology, game theory, graph theory, functions, linear transformations, eigenvalues and eigenvectors.
Linear Algebra’s role in making the computer think and learn
1. Vectorization – Vectors are an ordered array of numbers. They are used to deal with inequalities and systems of equations for notational conveniences. They help AI solve problems related to regression, clustering, speech recognition, and machine translation.
2. Dimensionality Reduction – Transformation of data from a high dimensional space to a low dimensional space or simply put, reducing the number of input variables in a dataset to reduce the challenges in the predictive modelling task.
3. Computer Vision – Images are stored as a matrix and read in pixels. Each pixel has values that range from 0 to 255.
The logic that is applied to create an AI:
The pre-set equations and rules that make Artificial Intelligence work is the essence of the logic behind its working. Here machine’s competency is built to mimic human behaviour. Artificial intelligence uses the following three factors to derive logical conclusions.
1. Historical data from archived sources are used to construct logical rules that fit a certain scenario.
2. Fresh data is added to reiterate and support the logic
3. Further human interaction is utilized when conclusions are unclear
Logic here translates to “Boolean” values of true and false based on if… then statements. The whole crux of machine learning is that once human intervention allows to correct a decision, the machine will auto correct itself and learn, adopt and improve its ability to automate. Re-engineering human traits and characteristics into a machine to make them work with lesser or no human interference is what a successful AI system can boast of. The below-mentioned sub domain of AI will give a wider understanding into its functioning.
1. Machine Learning
2. Deep Learning
3. Neural Networks
4. Natural Language Processing
5. Computer Vision
6. Cognitive computing
Mathematics can help enhance analytical thinking which is the vital factor in Artificial Intelligence. Unlike the misconception that Artificial Intelligence is magic, math is the force that drives that magic.
“The difference between a great [data scientist] and a good one is like the difference between lightning and a lightning bug.” – Thomas C. Redman
Authors: Benila Jacob, Mark John