Data Mining and Neural Networks Homework 1

Project 1. Condensed Nearest Neighbour for data reduction in Nearest Neighbour classifier 

Go to web-page

https://github.com/Mirkes/Data_Mining_Softbook/wiki/KNN-and-potential-eneRead

text. Download application

https://github.com/Mirkes/Data_Mining_Softbook/blob/master/knn/knn.jar

Task 1. Study how the number of prototypes depends on the number of points for two convex well-separated classes.
Task 2. Prepare a series of examples with more sophisticated non-convex shapes of
well-separated classes. Study how the number of prototypes depends on the number of points in these classes.
Task 3. Study how the number of prototypes and outliers depends on the number of points for two well-separated classes with added background uniformly distributed noise (option “random”).
Task 4. In conclusion, discuss the results and propose a hypothesis for further study.
Do not forget to save and submit the configurations of the classes and prototypes as figures! 1

Project 2. Dynamics of k-means clustering

Go to web-page

https://github.com/Mirkes/Data_Mining_Softbook/wiki/k-means-and-k-medoidsRead

text. Download application

https://github.com/Mirkes/Data_Mining_Softbook/blob/master/kmeans/KMeansKMedoids.jar

Task 1. (Exploration) Find the final k-means configurations for a series of datasets and various initial generations of centroids. How many different configuration did you observe?
How frequently did they appear? How many iterations were required?
Task 2. Formulate a hypothesis about a number of different final k-means configurations and their frequencies. Analyse, how they depend on the number of data points. Check this hypothesis on the random sets of equidistributed points.
Task 3. Formulate a hypothesis about the convergence rate of k-means and its dependence on the number of data points. Check this hypothesis on the random sets of equidistributed points (use the same series of experiments as in question 2).
Task 4. In conclusion, discuss the results and propose a hypothesis for further study.
Do not forget to save and submit the configurations of the classes and prototypes as figures!

Theoretical background 

• Give a description of classification and clustering problems.
• What is the difference between them? 
• Describe KNN approach and Hart’s algorithm for data reduction.
• Describe the K-means algorithm.