Drawing Simple Geometrical Shapes on Python from scratch, have you tried it? Now in this series of tasks, I am going to tackle some of the interesting image processing concepts from scratch using Python and then will compare them with the popular OpenCV framework. Last time I did Convolution operations from Scratch and RGB to […]

# Mathematics

## Making Fractal Shapes with Python

Fractal shapes are the continuous and never ending patterns that can be seen in the nature. But its quite different than the classical geometry in the sense of construction. Fractal shapes can be seen in many things in our nature where the shapes are repeating in itself with the same representation one popular example is […]

## DBSCAN Clustering Algorithm

DBSCAN is an example of clustering algorithm. Clustering is the process of organizing a collection of concrete or abstract things into classes of related objects. A cluster is a group of data objects that are distinct from the objects in other clusters yet comparable to one another within the same cluster. There are various example […]

## Vector Space Model in NLP

Lets begin with fundamentals for vector space model. All NLP applications require a basic understanding of how word vectors are represented in natural language processing. Because the first step in creating any NLP model is to express the word as some kind of number or coding. For instance, a word can be represented as a […]

## Introduction to Probability for Data Science: Getting Started

Introduction Hello there welcome to the new blog series about Probability in the Data Science field. Here in this blog, we will start from basic concepts needed in using Probability in some datasets. This blog is going to be very short and basic yet informative. Probability is all about measurement of some event’s occurrence. We […]

## If x is a subset of Y then, is inverse of x also a subset of Y?

Let $ f : X \rightarrow Y $ be a function. If B is subset of y then its inverse image $ f^-B $ is the subset of x define by $ f^-B = {x : f(x) \in B} $ Now prove the following. $ i. B_1 \subset B_2 \Rightarrow f^-B_1 \subset f^- B_1 $ […]

## If x belongs to the domain then does f(x) belong to the range?

Let $ F : x \Rightarrow y $ be a function. Then prove that $i. A_1 \subset A_2 \Rightarrow F(A_1) \subset F(A_2)$ $ii. F(\cup_i A_i) = \cup_i F(A_i) $ $iii.F(\cap_i A_i) \subset \cap_i f(A_i)$ Solution $ Let \ f: x \rightarrow y $ be a function. i. $Let\ y \in f(A_1)$ $Then\ \exists x \in […]

## Is the empty set a subspace of every vector space? Justify

Question: a. Is the empty set a subspace of every vector space ? Justify and let s = ${(a, b, (a + b):a, b \in R)}$ . Is a subspace of $R^3$ under the usual operation. Question: b. Let I = (-a , a) a > 0 be an open interval in R let v […]

## Writing a Logistic Regression Class from Scratch

Logistic Regression Logistic Regression is not exactly a regression but it performs a classification. As the name suggests, it uses the logistic function. This notebook is inspired by the github repo of Tarry Singh and I have referenced most of the codes from that repo. Please leave a star on it. Artificial Intelligence Deep Learning […]

## Writing a Linear Regression Class from Scratch Using Python

Linear Regression Introduction Before there was any ML algorithms, there was a concept and that was regression. Linear Regression is considered as the process of finding the value or guessing a dependent variable using the number of independent variables. Take for a example:- predicting a price of house using variables like, size of house, age […]