# Machine Learning

## Markov Localization Explained

In this tutorial, I explain the math and theory of robot localization and I will solve an example of Markov localization.

## Kalman Filter Explained

In this tutorial, I will explain the maths behind the Kalman Filter and I will drive the equations and their parameters.

## Density-Based Spatial Clustering (DBSCAN) with Python Code

DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a data clustering algorithm It is a density-based clustering algorithm because it finds a number of clusters starting from the estimated density distribution of corresponding nodes. It starts with an arbitrary starting point that has not been visited. This point’s epsilon-neighborhood is retrieved, and if it

## Bayes Filter Explained

In this tutorial I explain the bayes filter from scratch:

## Kernel Density Estimation (KDE) for estimating probability distribution function

There are several approaches for estimating the probability distribution function of a given data: 1)Parametric 2)Semi-parametric 3)Non-parametric A parametric one is GMM via algorithm such as expectation maximization. Here is my other post for expectation maximization. Example of Non-parametric is the histogram, where data are assigned to only one bin and depending on the number bins that fall within

## Silhouette coefficient for finding optimal number of clusters

Silhouette coefficient is another method to determine the optimal number of clusters. Here I introduced c-index earlier. The silhouette coefficient of a data measures how well data are assigned to its own cluster and how far they are from other clusters. A silhouette close to 1 means the data points are in an appropriate cluster and a silhouette

## Finding optimal number of Clusters by using Cluster validation

This module finds the optimal number of components (number of clusters) for a given dataset. In order to find the optimal number of components for, first we used k-means algorithm with a different number of clusters, starting from 1 to a fixed max number. Then we checked the cluster validity by deploying \( C-index \) algorithm and

## Octomap explanierend

In this tutorial, I explain the concept, probabilistic sensor fusion model and the sensor model used in Octomap library. related publication: OctoMap: An Efficient Probabilistic 3D Mapping Framework Based on Octrees 1)Octamap Volumetric Model 2)Probabilistic Sensor Fusion Model 3)Sensor Model for Laser Range Data

## ROS packages for Dynamic Time Warping

Dynamic Time Warping (DTW) is a method to align two sequences under certain constraints. For instance, two trajectories that are very similar but one of them performed in a longer time. The alignment should be is such way that minimizes the distance between these two sequences. Here I have done DTW between two-time series with python. I found a

## Gaussian Mixture Regression

Gaussian Mixture Regression is basically Multivariate normal distribution with Conditional distribution. The more about the theory could be found at  [1], [2], [3], [4]. For this work, I have added the functionality of adding Gaussian Mixture Regression to this project on the GitHub by forking the main project, my forked project can be download at here Github The main changes