Can you learn Machine Learning without Linear Algebra ?
Machine learning is a field that has emerged out of numerous innovations in computational sciences, spanning centuries.
The answer to NO
Linear Algebra is a branch of mathematics that is widely used throughout science and engineering. Good understanding of linear algebra is essential for understanding and working with many ML algorithms, especially deep learning algorithms.
Scalars, Vectors, Tensors: Finding the modulus (size), the angle between vectors (dot or inner product) and projections of one vector onto another and to examine how the entries describing a vector will depend on what vectors we use to define the axes
Matrices: Matrices can transform a description of a vector from one basis (set of axes) to another. For example, figuring out how to apply a reflection to an image and manipulate images.
Length squared sampling in matrices, Singular value decomposition, Low-rank approximation are few techniques which are widely used in the data processing.
For example, the singular value decomposition finds the best-fitting k-dimensional subspace for k= 1,2,3,…, for the set of N data points. Here, “best” means minimising the sum of the squares of the perpendicular distances of the points to the subspace, or equivalently, maximising the sum of squares of the lengths of the projections of the points onto this subspace.
SVD is traditionally used in the principal component analysis (PCA), which in turn is popularly used for feature extraction and for knowing how significant the relationship among the features or properties is to an outcome.
The word ‘mathematics’ brings in a ton of concepts — and this might scare away the beginners. However, if one manages to look closely, then much of the maths used in basic ML is usually covered in high school.
The whole point here is to find the distance between points, the shorter path between points and for this, one needs linear algebra
The last century has seen tremendous innovation in the field of mathematics. New theories have been postulated and traditional theorems have been made robust by persistent mathematicians. And we are still reaping the benefits of their exhaustive endeavors to build intelligent machines. The field of machine learning is built on some ingenious mathematical and logical hypotheses and tools.
There are other rudimentary topics, which can make the life of a typical machine learning engineer easy:
- Law of large numbers
- The geometry of high dimensions
- Random walks in Euclidean space
- Gradient Descent methods
- Graph partitioning
- Bayesian or belief networks
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