In this article, a few applications of Fourier Series in solving differential equations will be described. All the problems are taken from the **edx Course: MITx - 18.03Fx: Differential Equations Fourier Series and Partial Differential Equations**. The article will be posted in two parts (two separate blongs)

First a basic introduction to the Fourier series will be given and then we shall see how to solve the following ODEs / PDEs using Fourier series:

- Find…

Added by Sandipan Dey on July 4, 2020 at 5:00pm — 1 Comment

In this article a few more popular image processing problems along with their solutions are going to be discussed. Python image processing libraries are going to be used to solve these problems.

As described here, here is the algorithm:

- The cumulative histogram is computed for each image dataset, see the figure below.
- For any…

Added by Sandipan Dey on August 16, 2018 at 1:30pm — No Comments

In this article a few more popular image processing problems along with their solutions are going to be discussed. Python image processing libraries are going to be used to solve these problems.

Also, the spread in the frequency domain inversely proportional to the spread in the spatial domain. Here is the proof:…

ContinueAdded by Sandipan Dey on August 16, 2018 at 1:00pm — No Comments

In this article a few popular image processing problems along with their solutions are going to be discussed. Python image processing libraries are going to be used to solve these problems.

- A
*gray-scale*image can be thought of a 2-D function*f(x,y)*of the pixel…

Added by Sandipan Dey on August 16, 2018 at 1:00pm — No Comments

This problem also appeared as an assignment problem in the coursera online course *Mathematics for Machine Learning: Multivariate Calculus. *The description of the problem is taken from the assignment itself.

In this assignment, we shall train a neural network to draw a curve. The curve takes *one input* variable, the…

Added by Sandipan Dey on May 31, 2018 at 10:00pm — No Comments

Although a support vector machine model (binary classifier) is more commonly built by solving a quadratic programming problem in the dual space, it can be built fast by solving the primal optimization problem also. In this article a *Support Vector Machine *implementation is going to be described by solving the *primal optimization…*

Added by Sandipan Dey on April 28, 2018 at 3:30pm — No Comments

In this article, couple of implementations of the support vector machine binary classifier with quadratic programming libraries (in R and python respectively) and application on a few datasets are going to be discussed.

The next figure describes the basics of Soft-Margin SVM (without kernels).

**SVM in a nutshell**

- Given a (training) dataset consisting of positive and negative class instances.
- Objective is to find…

Added by Sandipan Dey on April 23, 2018 at 9:30am — No Comments

In this article the multi-armed bandit framework problem and a few algorithms to solve the problem is going to be discussed. This problem appeared as a lab assignment in the edX course DAT257x: Reinforcement Learning Explained by Microsoft. The problem description is taken from the assignment itself.

Given a set of actions with some unknown reward distributions, …

ContinueAdded by Sandipan Dey on April 4, 2018 at 9:30am — No Comments

In this article, the problem of *learning word representations* with neural network from scratch is going to be described. This problem appeared as an assignment in the *Coursera course Neural Networks for Machine Learning*, taught by

In this article…

ContinueAdded by Sandipan Dey on March 18, 2018 at 12:00am — No Comments

In this article, ** object detection** using the very powerful

Added by Sandipan Dey on March 11, 2018 at 11:30pm — 3 Comments

In this article an implementation of the *Lucas-Kanade optical flow algorithm* is going to be described. This problem appeared as an assignment in a computer vision course from UCSD. The inputs will be sequences of images (subsequent frames from a video) and the algorithm will output an optical flow field (u, v) and trace the motion of the moving objects. The problem description is taken from the assignment itself.

Added by Sandipan Dey on February 28, 2018 at 11:30am — No Comments

In this article, an implementation of an efficient graph-based image segmentation technique will be described, this algorithm was proposed by Felzenszwalb et. al. from MIT. The slides on this paper can be found from Stanford Vision Lab.. The algorithm is closely related…

ContinueAdded by Sandipan Dey on February 28, 2018 at 11:30am — No Comments

This article is inspired by this SIGGRAPH paper by Levin et. al, for which they took this patent , the paper was referred to in the course CS1114 from Cornell. This method is also discussed in the coursera online image processing course by NorthWestern University. Some part of the problem description is taken from the paper itself. Also, one can refer to the implementation provided by the authors in matlab, the following …

ContinueAdded by Sandipan Dey on February 13, 2018 at 1:00pm — No Comments

In this article, *interactive image segmentation* with *graph-cut* is going to be discussed. and it will be used to segment the source object from the background in an image. This segmentation technique was proposed by Boycov and Jolli in this paper.

Let’s implement…

ContinueAdded by Sandipan Dey on February 13, 2018 at 10:30am — No Comments

The following problem appeared in an assignment in the Princeton course COS 126 . The problem description is taken from the course itself.

Write a program that plots a Sierpinski triangle, as illustrated below. Then develop a program that plots a recursive patterns of your own design.…

ContinueAdded by Sandipan Dey on January 24, 2018 at 10:00am — No Comments

In this article a few simple applications of Markov chain are going to be discussed as a solution to a few text processing problems. These problems appeared as assignments in a few courses, the descriptions are taken straightaway from the courses themselves.

Added by Sandipan Dey on January 16, 2018 at 8:30pm — No Comments

This problem appeared as an assignment in the online coursera course * Convolution Neural Networks* by

In this assignment, we shall:

- Implement the neural style transfer algorithm
- Generate novel artistic images using our algorithm

Most of the…

ContinueAdded by Sandipan Dey on January 2, 2018 at 1:00pm — 2 Comments

The following problems are taken from the projects / assignments in the edX course Python for Data Science and the coursera course Applied Machine Learning in Python (UMich).

● The IMDB Movie Dataset (MovieLens 20M) is used for the analysis.

● The dataset is downloaded from …

Added by Sandipan Dey on December 16, 2017 at 1:30pm — 5 Comments

he following problems are taken from a few assignments from the coursera courses * Introduction to Deep Learning (by Higher School of Economics) *and

Added by Sandipan Dey on November 25, 2017 at 2:00pm — 4 Comments

The following problems appeared as a programming assignment in the Computation Photography course (CS445) at UIUC. The description of the problem is taken from the assignment itself. In this assignment, a python implementation of the problems will be described instead of matlab, as expected in the course.

- The goal of this assignment is to implement the
for**image quilting algorithm**

texture synthesis and transfer,…

Added by Sandipan Dey on October 24, 2017 at 1:30pm — No Comments

- Fourier Series and Differential Equations with some applications in R (Part 1)
- Solving Some Image Processing Problems with Python libraries - Part 3
- Solving Some Image Processing Problems with Python libraries - Part 2
- Solving Some Image Processing Problems with Python libraries - Part 1
- Few Machine Learning Problems (with Python implementation)
- Implementing PEGASOS: Primal Estimated sub-GrAdient SOlver for SVM, Logistic Regression and Application in Sentiment Classification (in Python)
- Implementing a Soft-Margin Kernelized Support Vector Machine Binary Classifier with Quadratic Programming in R and Python

- SIR Epidemic model for influenza A (H1N1): Modeling the outbreak of the pandemic in Kolkata, West Bengal, India, 2010
- A Semi-Supervised Classification Algorithm using Markov Chain and Random Walk in R
- Autonomous Driving – Car detection with YOLO Model with Keras in Python
- Deep Learning with TensorFlow in Python
- Fourier Series and Differential Equations with some applications in R (Part 1)
- Some Social Network Analysis with Python
- Implementing Lucas-Kanade Optical Flow algorithm in Python

- Data (2)
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- Python (2)
- Analysis (1)
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- Chain (1)
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- Deep (1)
- Differential (1)
- Equation (1)
- Exploratory (1)
- Fourier (1)
- Machine (1)
- Markov (1)
- Math (1)
- Mathematical (1)
- Modeling (1)
- R (1)
- Science (1)
- Semisupervised (1)
- Tensorflow (1)
- Transform (1)
- Visualization (1)

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