Mathematics

Converting Color Images to Grayscale using numpy and some Mathematics

An extremely magnified image at the end is just blocks of colors called pixels, where each pixel is formed by the combination of Red, Blue and Green, our primary colors.¬†RGB color space or RGB color system, constructs all the colors from the combination of the¬†intensities of Red, Green and Blue colors. The red, green and …

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Mathematics of Principal component analysis

Principal component analysis is a method used to reduce the number of dimensions in a dataset without losing much information. It’s used in many fields such as face recognition and image compression, and is a common technique for finding patterns in data and also in the visualization of higher dimensional data. PCA is all about …

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Maths behind Polynomial regression

Polynomial regression is a process of finding a polynomial function that takes the form¬†f(¬†x¬†)¬†=¬†c0¬†+¬†c1¬†x¬†+¬†c2¬†x2¬†‚čĮ¬†cn¬†xn¬†where¬†n¬†is the degree of the polynomial and¬†c¬†is a set of coefficients. Through polynomial regression we try to find an nth degree polynomial function which is the closest approximation of our data points. Below is a sample random dataset which has been regressed …

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Math behind Linear Regression with Python code

Simple linear regression¬†is a statistical method you can use to study relationships between two continuous (quantitative) variables: independent variable (x) – also referred to as¬†predictor or explanatory variable dependant variable (y) – also referred to as¬†response or¬†outcome The goal of any regression model is to predict the value of y (dependant variable) based on the …

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Possibly the easiest explanation of differentiation and Integration in Calculus

I have read a lot of books on Calculus but “Calculus Made Easy” by Silvanus P. Thompson stands out as possibly the easiest book to read on this topic. It totally lives up to its name. The first chapter opens up with an impressive introduction on the difference between dx &¬†‚ąę.¬† d which merely means …

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