cluster analysis

olU] /NNE Va \ R T (https://ucanalytics.com/blogs) Customer Segmentation & Cluster Analysis — Telecom Case Study Example (Part 1) (https://ucanalytics.com/blogs/customer-{{; segmentation-cluster-analysis- telecom-case-study-example/) i (https://ucanalytics g case-study-example/) - Roopam Upadhyay (https://ucanalytics /blogs/author/roopam/) 15 Comments (https://ucanalytics.com/blogs/ -cluster-analysis-telecom- -cluster-analysis-telecom- b= o 144, case-study Galaxies and Cluster Analysis | live in Mumbai (Bombay), the financial capital of India and one of the largest cities in the world. One of the problems of living in a large city is that you rarely see stars 2. L4 in the night sky. (https://i0.wp.com/ucanalytics.com/blogs/wp- . content/uploads/2013/11/sky-1.jpg) The Ilmlted Sky The Night Sky & Cluster Analysis- by Roopam one can see through the skyscrapers is smeared with light pollution and it is difficult to sight stars if any. One of the best night skies | have ever seen in my life was at Saint George Island on Gulf of Mexico, Florida. On a pitch-dark night during Floridian winters, one could see more than a million stars in the gorgeous night sky. It is a wonderful sight! My fascination for sky and stars is a possible reason for my fascination for physics. As | have mentioned earlier | have done L AMIL vl IBilvE R YA V'Aw] JI T 15Ut |4 £/ 3 ‘1‘ i ucAnalytics.com is an effort for you to gain deeper and intuitive understanding of data science, predictive analytics, and big data Roopam Upadhyay YOU CANalytics SUBSCRIBE TO BLOG Provide your email address to receive notifications of new posts Email Address Search ... MUST READ ead Articles (https://lucanalytics.com/blogs/category/d: science- career/) my masters in physics and am ever curious about astrophysics and the origin of the universe. Let us try to understand the enormousness of the universe we can only fractionally see in the night sky. Our planet, the earth, may seem like everything to us. However, we know it is just one of the nine (now eight) revolving planets around the sun. The sun is yet another star among around 200 billion stars in the galaxy Milky Way — the place where the sun and the earth reside. This is already enormous but to make it unfathomable, the universe has more than 200 billion galaxies. Using this one could approximate the number of stars in the universe i.e. ~ 4X1022 (from 200 billion X 200 billion, obviously these numbers are a gross approximation). | am happy we can see more than a million stars in a clear night sky, even if it is just a tiny fraction of the actual number of stars. Now, we have the following two questions to answer 1) What are galaxies? 2) What is the relationship between galaxies and the title of this post (cluster analysis / customer segmentation)? Galaxies are clusters of stars, gas, dust, .planets and (https://iO.wp.com/ucanalytics.com_/blogs/wp- analytics/retail- interstellar clouds. content/uploads/2013/11/Galaxy.jpg) case-study- UsuaIIy, galaxies are Galaxies & Cluster Analysis example/) spiral or elliptical in - Marketing shape (shown in the M:naar:::::t_ picture from Wikipedia). The galaxies are separated from neighboring galaxies in three-dimensional space. Enormous black holes are often at the center of most galaxies. These black holes are the binding force providing distinct shapes to the galaxies. As we will discuss cluster analysis in the next section, you will find striking similarities between galaxies and cluster analysis. As the galaxies are formed in three-dimensional space, cluster analysis is a multivariate analysis performed in n-dimensional space. Note — keep the concept of black holes at the center of the galaxies in mind. We will use a similar concept of the centroid for cluster analysis really soon. Cluster Analysis — Telecom Case Study Example You are head of customer insights and marketing at a telecom company, ConnectFast Inc. You realize that not every customer is similar and you need to have different strategies to attract different customers. You appreciate the power of customer Career in Data Science - Interview Preparation - Best Practices LEaRn Pyiton & R fi @Click Here to Read Articles (https://ucanalytics.com/blogs/category/p and-r/) Free Books - Machine Learning - Data Science - Artificial Intelligence CASE- STUDIES ONLINE REtalL CasEe Stuny /\ jy Click Here to Read Articles (https:/lucanalytics.com/blogs/category/m Revenue Estimation & Optimization TELECOM Caske Stuny Click Here to Read Articles (https://lucanalytics.com/blogs/category/m analytics/telecom- case-study- example/) Customer Segmentation - Cluster Analysis - Segment wise Business Strategy

segmentation to deliver superior results with optimized cost. You are also aware of unsupervised learning techniques such as cluster analysis to create customer segments. To brush up your skills with cluster analysis, you have selected a sample of eight customers with their average call duration (both locally and internationally). The following is the data: Customer# | Av. Local Call Duration | Av. International Call Duration 1 2 2 2 1 2 3 1 3 4 3 2 5 4 5 6 4 4 7 5 5 g 6 ] (https://i0.wp.com/ucanalytics.com/blogs/wp- content/uploads/2013/11/T1.jpg) To get a feel for this, you have plotted the data with average international call duration on the x-axis and average local call duration on the y-axis. The following is the plot: 6 - a e o @ @ Av. Local Call Duration [ s] w [ £ & = 0 1 2 3 4 ) 6 7 Ay. Internation Call Duration (https://i0.wp.com/ucanalytics.com/blogs/wp- content/uploads/2013/11/T1-Copy.jpg) Note — this is similar to the cluster of stars in the night sky (here, stars are replaced with customers). Additionally, instead of a three-dimensional space we have a two-dimensional plane with average local and international call duration on the x-axis and y- axis. Now, like galaxies the task is to find the location of black holes; in cluster analysis, they are called centroids. To locate the centroids, we start with assigning random points for the location of centroids. Euclidian Distance to find Cluster Centroids In this case, two centroids (C1 & C5) are randomly placed at the coordinates (1, 1) and (3, 4). Why did we choose two centroids? For this problem, visual estimation of scattered plot above informs us that are two clusters. However, we will notice in a later part of this series, this question may not have such a straightforward answer for larger data sets. Caske Stuny s Click Here t é/ R;:dA:in.:s (https://ucanalytics.com/blogs/category/ris analytics/banking- risk-case- study- example/) - Risk Management - Credit Scorecards ManuFactuRing Case Stuny Click Here to Read Articles (https://ucanalytics.com/blogs/category/m case-study- example/) - Sales Forecasting - Time Series Models CREDIT | must thank my wife, Swati Patankar, for being the editor of this blog. PAGES Blog- Navigation (https://ucanalytics.com/blogs/navigation/) Art (https://ucanalytics.com/blogs/art- gallery/) About (https://ucanalytics.com/blogs/about- me/) Contact (https://ucanalytics.com/blogs/contact/) Now, we will measure the distance between two centroids (C1 & C-,) and all the data points on the above-scattered plot using Euclidean measure. Euclidean distance is measured through the following formula y VD — £ = 4 4 D"Sf(l‘"“ = \/(‘\(-cnfroid('l - ‘\‘_)2 + (}ccntroid c, - }E)Q Columns 3 and 4 (i.e. Distance from C4 and C,) are measured using the same formula. For instance, for the first customer Distance from €'y = \/(1 224+ (1-2)2=2= 141 You could measure all the other values similarly. Additionally, cluster membership (last column) is assigned using the closeness to clusters (C4 and C»). The first customer is closer to centroid 1 (1.41 in comparison to 2.24) hence is assigned membership C. Av. Local Call | Av. International | Distance | Distance | Cluster Duration Call Duration from C; from G Membership 2 2 1.41 2.24 Ci 1 2 1.00 2.83 Ci 1 3 2.00 2.24 Cy 3 2 2.24 2.00 C, 4 3 5.00 1.41 Gz 4 4 4,24 1.00 Ca 3 3 5.66 2.24 C3 6 3 6.40 3.16 C; (https://i0.wp.com/ucanalytics.com/blogs/wp- content/uploads/2013/11/T2.jpg) The following is the scatter plot with cluster centroids C4 and C, (displayed with blue and orange diamond shapes). The customers are have marked with the color of centroids basis their closeness to the centroids. 6 5 ® ® @ B ‘e o - a . 2 F3 O % = %4 w ) 59 O © i: @ 13 O 0 .. e i} 1 2 3 4 5 6 7 Av. Internation Call Duration (https://i0.wp.com/ucanalytics.com/blogs/wp- content/uploads/2013/11/T2-Copy.jpg) As we have randomly assigned the centroids, the second step is to move them iteratively. The new position of the centroid is measured by taking the average of member points for the centroid. For the first centroid, customers 1, 2 and 3 are members. Hence, the new x-axis position for the centroid C4 is