(5/5)

write 3 python programs with explaining every line as required to understand[100 points] K-Mean++. Implement K-Mean++ clustering algorithm in python as

follows:

- Read input file ‘as4_1.txt’ given in the Canvas course website. The file is

composed of X and Y values in the first and second columns and label in the third

column.

- Create myInit() that places the initial k centroids far away from each other in the

4 steps as shown below:

1. Randomly select the first centroid from the data points

2. For each data point compute its distance from the nearest, previously chosen

centroid

Use following Euclidean distance function:

import numpy as np

def euclidean2D(point1, point2):

x1 = point1[0]

x2 = point2[0]

y1 = point1[1]

y2 = point2[1]

return np.sqrt((x1 - x2)**2 + (y1 - y2)**2)

3. Select the point having maximum distance from the nearest centroid as the next

centroid

4. Repeat steps 2 and 3 until k centroids have been sampled

- Create myAssign() that assigns each example to the nearest centroid, �(�)

, � ∈

{1, ... , �} where for every x(i), label[x(i)] = J which is arg minj||x(i)

-µ(j)

||

#

.

- Create myCentroid() that calculates a new centroid of all points that are assigned

to the same centroid.

- Create myUpdateCentroid() that moves the centroids to the center of the

examples that were assigned to it

- Create myKmeanPlusPlus() that initially calls myInit(), and then repeats to

call myAssign(), myCentroid(), and myUpdateCentroids() until the cluster

assignments do not change or a user-defined tolerance or maximum number of

iteration is reached. myKmeanPlusPlus() should ask user to receive the

following arguments and use the same variable name in the parenthesis:

1. The number of clusters (k)

2. Tolerance (myTol)

3. Maximum number of iterations (myMax)

myKmeanPlusPlus()returns a list of new labels.

- Create myPlot() that visualizes plot of clustering result in different colors and

markers. You can use any plot method.

2. [100 points] DBSCAN. Implement DBSCAN (Density-Based Spatial Clustering of

Applications with Noise) algorithm in python as follows:

- Read input file named as ‘as4_2.csv’ using numpy. The file is composed of X and Y

values in the first and second columns and label in the third column.

- Create ‘getLabel()’ that receives true labels from the read file.

- Create ‘getData()’ that returns vectors from the read file.

- Create ‘getDBSCAN()’ that receives vectors, epsilon, and minPoints and returns

predicted label. This function finds the points in the epsilon neighborhood of every

point, and identifies the core points with more than minPoints neighbors. Secondly,

this function finds the connected components of core points on the neighbor graph.

Lastly, this function assigns each non-core point to a nearby cluster if the cluster is

an epsilon neighbor, otherwise assign it to noise. getDBSCAN() returns a list of

new labels.

For the more detailed algorithm for DBSCAN, you can check out at the

https://en.wikipedia.org/wiki/DBSCAN

- Create ‘getAccuracy()’ that receives predicted label and true label and returns

accuracy.

- Create ‘plotDBSCAN()’ that visualizes plot of clustering result in different colors

and markers. You can use any plot method.

3. [Bonus 50 points] Improved DBSCAN. Implement improved DBSCAN method using

one of existing algorithms introduced in the paper “S. Li, An Improved DBSCAN

Algorithm Based on the Neighbor Similarity and Fast Nearest Neighbor Query, IEEE

Access, 2020”. This paper introduces many previous methods enhancing performance

and accuracy. You can use any suggested methods in Section II, RELATED WORK as well

as the method that the paper mainly suggests. Show the enhanced accuracy comparing

to what you will be obtaining in the previous problem 2 (DBSCAN). You can use the

same functions that you have implemented and dataset in problem 2. You can use

different dataset from problem 2 to show better accuracy but when you compare the

accuracy, the chosen dataset should be equally and additionally used in problem 2.

Write your 3 python programs in each cell of jupyter notebook and save into your shared

directory as a name, ‘assignment4_your_first_name.ipynb’ where ‘your_first_name should

be your real first name. Attach the file at the Assignment 4 in the Canvas

(5/5)

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