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Clustering is a form of unsupervised learning (learning with unlabeled data) that involves grouping data points according to features and attributes. Clustering algorithms are unsupervised algorithms which means that there is no labelled data available. The clustering algorithms come from the machine learning literature. As the name implies, the basic idea is to try to identify natural clusters of data points within some large set of data. This method is used to identify different classes or clusters in the given data based on how similar the data is. Data points in the same group are more similar to other data points in that same group than those in other groups. Clustering uncovers patterns and structures within data, leading to valuable insights across various domains.

The most common kind of clustering is K-means clustering, which involves representing each cluster by a variable “k” and then defining the centroid of those clusters. Some other applications of clustering in machine learning are:

1. Genetic Research: 

   Clustering can be used to identify patterns and relationships within genetic data. It helps in grouping genes or sequences with similar characteristics, which can be valuable in understanding genetic variations and their implications. 

2. Image Segmentation: 

   In image processing, clustering is employed to segment images into distinct regions based on similarities in pixel values. This is useful in computer vision applications, such as object recognition, where identifying different parts of an image is crucial. 

3. Market Research: 

   Clustering aids in market segmentation by grouping similar customers based on their purchasing behavior, preferences, or demographics. This information is valuable for targeted marketing strategies and personalized product recommendations. 

4. Medical Imaging: 

   Clustering is used in medical imaging to identify patterns or anomalies in patient data. It helps in categorizing medical images, detecting abnormalities, and assisting healthcare professionals in diagnosis and treatment planning. 

5. Social Network Analysis: 

   Clustering is applied to analyze relationships and patterns in social networks. It helps identify communities or groups of individuals with similar connections or interactions, providing insights into the structure and dynamics of social systems. 

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Denoising with OpenCV. code:
         
Input:         
         
Output at odd_int = 7:         
         
Output at odd_int = 57:         
         
Output at odd_int = 67:         
         
Output at odd_int = 207 (errors are generated):