{"id":1259,"date":"2013-12-25T13:31:39","date_gmt":"2013-12-25T08:01:39","guid":{"rendered":"http:\/\/ucanalytics.com\/blogs\/?p=1259"},"modified":"2016-09-12T16:02:10","modified_gmt":"2016-09-12T10:32:10","slug":"customer-segmentation-cluster-analysis-telecom-case-study-part-2","status":"publish","type":"post","link":"https:\/\/ucanalytics.com\/blogs\/customer-segmentation-cluster-analysis-telecom-case-study-part-2\/","title":{"rendered":"Customer Segmentation & Cluster Analysis \u2013 Telecom Case Study Example(Part 2)"},"content":{"rendered":"
\n

In one of\u00a0the previous articles<\/a>, we have started with a case study example from the telecom sector. We learned about cluster analysis using black holes as an analogy. In that article, we used Euclidean distance to form customer segments. Let us continue with the same case study and learn about Euclid. Additionally, we will also learn about the usefulness of data normalization to avoid spurious results while performing cluster analysis through Euclidean distance.<\/p>\n

\"Euclid<\/a>

Euclid – by Roopam<\/p><\/div>\n

Euclid<\/span><\/h2>\n

In 1440 Johannes Gutenberg invented the printing press, a device that changed the course of human history by providing an affordable source of information to the masses. One of the earliest texts to be published through this great invention was Euclid\u2019s\u00a0\u2018Elements\u2019<\/i>, published in 1482 in Venice.\u00a0\u2018Elements\u2019<\/i>\u00a0is one of the most published books in the history of mankind next only to the Bible.\u00a0\u2018Elements\u2019\u00a0<\/i>consists of 13 books that cover propositions in geometry. All the geometric theorems in\u00a0‘Elements’<\/i>\u00a0can be derived from 10 axioms or postulates. For instance, one of the famous axioms presented in \u2018Elements\u2019<\/i> is \u2013 one can only draw one straight line between two points. If one has to find a man who is known only for his work, Euclid of Alexandria is certainly a great candidate. Very little is known about Euclid as a person and he is often referred to as the \u201cFather of Geometry\u201d. It is estimated that he lived in 300 BC and taught at Alexandria in Egypt during the reign of Ptolemy I. This is all we know of Euclid, the author of one of the most influential books of all times.<\/p>\n

On the Shoulders of Giants<\/span><\/h2>\n

Isaac Newton once honored his predecessors for his contribution to physics with the following quote \u201cIf I have seen further it is by standing on the shoulders of giants\u201d. Development of human knowledge is a collective activity. Similarly Euclid\u2019s\u00a0\u2018Elements\u2019<\/i>\u00a0is a culmination of ideas and propositions from several mathematicians and a few original ideas of its author. However, as was a common practice in those days, Euclid did not give credit to several mathematicians while using their work. Pythagoras must be one of the giants on whose shoulders Euclid stood and saw further. We will use the Pythagoras theorem in the next segment to derive Euclidean distance. This will also help us understand the usefulness of data normalization in cluster analysis.<\/p>\n

\"Euclid<\/a><\/span>Euclidean Distance<\/span><\/h2>\n

Recall, in the\u00a0same article<\/a>\u00a0I mentioned above on customer segmentation and cluster analysis, we have estimated the cluster centroid using Euclidean distance. Let us try to derive the Euclidean distance formula using the famous Pythagoras theorem. We have all learned Pythagoras theorem in primary school. The simple property about right triangles makes the square of the hypotenuse (z) equal to the sum of the squares of the remaining two sides (x and y). Mathematically represented as<\/p>\n

\"z^{2}=x^{2}+y^{2}<\/pre>\n
\"Euclidean<\/a>Now, let us make an attempt to find the distance between two points (A & B) in the two-dimensional plane (x & y-axis). The positions of the first point are 4 on the x-axis and 10 on the y this can also be written as (4,10). Similarly, the position of the second point is (7,6) as shown in the above diagram.<\/p>\n
Now to measure the distance between these two points, let us create a right triangle as shown in the adjacent diagram. Notice that the coordinates for the point C (4, 6) is taken from x coordinate of A and y coordinate of B. Now the length of the line AC is y1<\/sub>-y2<\/sub>\u00a0i.e. (10-6 = 4) since the x coordinate is fixed on this line. Similarly, the length of the line BC is x2<\/sub>-x1<\/sub>\u00a0i.e. (7-4 =3). Finally, using Pythagoras theorem we can find the value of length of the line AB i.e.<\/p>\n
\"\mathbf{AB}=\sqrt{(x_{1}-x_{2})^{^{2}}+(y_{1}-y_{2})^{^{2}}}<\/pre>\n
\"=>\mathbf{AB}=\sqrt{(7-4)^{^{2}}+(10-6)^{^{2}}}=5<\/pre>\n
The shortest distance between two points is the length of the unique line drawn between them. Hence the shortest distance between two points A and B is 5.<\/p>\n
Telecom case study Example \u2013 Cluster Analysis<\/span><\/h2>\n
\"Euclid<\/a>Keeping the above in mind, let us come back to the telecom case study. This time as the head of customer insights and marketing at a telecom company, ConnectFast Inc,\u00a0you want to perform cluster analysis for customer segmentation using two variables: age and income. There are two customers with the following ages 37 years and 44 years and their annual income are $90,000 and $62,000. Now if you have to find the Euclidean distance between (37, 90000) and (44, 62000), we will form a right triangle similar to the one shown adjacent. Note, this plot is not drawn\u00a0according to scale otherwise, it will show just a straight line.<\/p>\n
In this case, it is easy to notice that the income variable is dominating the distance by a large margin of 28000 to 7. This is certainly a highly skewed picture. We need to think of a strategy to counter this problem otherwise our cluster analysis will give spurious results. The strategy will involve bringing both the variables on comparable scales. Data normalization presents a solution to our problem.<\/p>\n
Data Normalization \u00a0\u00a0<\/span><\/h2>\n
There are various ways of data normalization. The one we are going to use here is called min-max normalization. \u00a0The normalization is performed using the following formula<\/p>\n
\u00a0\"X^{^{*}}=\frac{X-min(X)}{max(X)-min(X)}<\/pre>\n
Here,<\/p>\n
X*\u00a0<\/sup>is the normalized value of the variable<\/p>\n
min(X) is the minimum value in the dataset for the variable<\/p>\n
max(X) is the maximum value\u00a0in the dataset for the variable<\/p>\n
Now for our example, let us assume in our base of customers we have the maximum income of $130000 and the minimum income of $45000. The normalized value of income for the customer A is<\/p>\n
\"Y^{^{*}}=\frac{(90000-45000)}{(130000-45000)}=0.529<\/pre>\n
\"Euclidean<\/a><\/p>\n
We will perform the same exercise for all the data points for all the variables. T<\/span>he income for the second customer i.e. 62000 will become 0.2 after performing the same normalization. Additionally, the \u00a0minimum\u00a0and\u00a0<\/span>maximum<\/span>\u00a0<\/span>age of customer base are 23 and 58 years. \u00a0This will make normalized ages of two customers equal to 0.4\u00a0<\/span><\/span>and\u00a00.6.<\/span><\/span><\/p>\n
In this case, it is easy to see that all the normalized value will fall between the range of 0 and 1. \u00a0Hence we have created a normalized data set that is on a comparable scale. The normalized plot, as shown\u00a0adjacent, is not as skewed as the original plot. We have rectified the problem.<\/p>\n
It is always advisable to perform normalization before cluster analysis since most data sets suffer from the problem described above.<\/p>\n
Sign-off Note<\/span><\/h4>\n
I have started measuring the Euclidean distance between the frequency of posting of articles on YOU CANalytics. Of late there is a little variation in the posting of articles because of my busy schedule. I prefer to post an article every week or fortnight and would like to stick to this schedule. However, as a statistician, I know that every data set has a variation and I cannot avoid the variation in time of posting the articles on the site. I also know, as a reader you are extremely forgiving and won’t mind a little bit of variation. See you soon with the next post!<\/p>\n","protected":false},"excerpt":{"rendered":"
In one of\u00a0the previous articles, we have started with a case study example from the telecom sector. We learned about cluster analysis using black holes as an analogy. In that article, we used Euclidean distance to form customer segments. Let us continue with the same case study and learn about Euclid. Additionally, we will also<\/p>\n
Read More…<\/a><\/p>\n","protected":false},"author":1,"featured_media":1261,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_newsletter_tier_id":0,"jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[1,58],"tags":[7,71,6,10],"jetpack_publicize_connections":[],"yoast_head":"\nCluster Analysis & Segmentation : Case Study Example (2)<\/title>\n<meta name=\"description\" content=\"This is a case study example to find customer segments through cluster analysis. 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One of the problems of living in a large city is that you rarely see stars in the night sky. The limited sky one can see through\u2026","rel":"","context":"In "Marketing Analytics"","block_context":{"text":"Marketing Analytics","link":"https:\/\/ucanalytics.com\/blogs\/category\/marketing-analytics\/"},"img":{"alt_text":"The Night Sky - by Roopam","src":"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2013\/11\/sky-1.jpg?fit=768%2C1024&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2013\/11\/sky-1.jpg?fit=768%2C1024&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2013\/11\/sky-1.jpg?fit=768%2C1024&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2013\/11\/sky-1.jpg?fit=768%2C1024&ssl=1&resize=700%2C400 2x"},"classes":[]},{"id":1385,"url":"https:\/\/ucanalytics.com\/blogs\/customer-segmentation-outliers-telecom-case-study-part-3\/","url_meta":{"origin":1259,"position":1},"title":"Cluster Analysis and Outliers \u2013 Telecom Case Study Example (Part 3)","author":"Roopam Upadhyay","date":false,"format":false,"excerpt":"Outliers \"I refuse to join any club that would have me as a member.\" - Groucho Marx This witty statement came from (according to me) one of the funniest men in the history of American cinema \u2013 Julius Henry Marx better known as Groucho Marx. Groucho was certainly a very\u2026","rel":"","context":"In "Marketing Analytics"","block_context":{"text":"Marketing Analytics","link":"https:\/\/ucanalytics.com\/blogs\/category\/marketing-analytics\/"},"img":{"alt_text":"Groucho - by Roopam","src":"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/01\/photo.jpg?fit=768%2C1024&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/01\/photo.jpg?fit=768%2C1024&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/01\/photo.jpg?fit=768%2C1024&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/01\/photo.jpg?fit=768%2C1024&ssl=1&resize=700%2C400 2x"},"classes":[]},{"id":1532,"url":"https:\/\/ucanalytics.com\/blogs\/customer-segmentation\/","url_meta":{"origin":1259,"position":2},"title":"Telecom Case (Part 4) – Customer Segmentation and Application","author":"Roopam Upadhyay","date":false,"format":false,"excerpt":"Telecom Case Study \u2013 Customer Segmentation For the last few articles we have been working on a telecom case study to create customer segments (Part 1, Part 2 and Part 3). In this case, you are the head of customer insights and marketing at a telecom company, ConnectFast Inc. Recall,\u2026","rel":"","context":"In "Marketing Analytics"","block_context":{"text":"Marketing Analytics","link":"https:\/\/ucanalytics.com\/blogs\/category\/marketing-analytics\/"},"img":{"alt_text":"Customer Segmentation - by Roopam","src":"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/02\/photo1.jpg?fit=742%2C1024&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/02\/photo1.jpg?fit=742%2C1024&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/02\/photo1.jpg?fit=742%2C1024&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/02\/photo1.jpg?fit=742%2C1024&ssl=1&resize=700%2C400 2x"},"classes":[]},{"id":9519,"url":"https:\/\/ucanalytics.com\/blogs\/cluster-analysis-learn-by-doing-analytics-challenge-part-1\/","url_meta":{"origin":1259,"position":3},"title":"Cluster Analysis Puzzle – Learn by Doing! (Part 1)","author":"Roopam Upadhyay","date":false,"format":false,"excerpt":"Cluster analysis is a powerful analytical technique to group or segment identical elements i.e. customers, products etc. In this series of articles, you will explore nuances of cluster analysis and its applications. Analytics challenges, on YOU CANalytics, are designed like puzzles where your participation is extremely important to move things\u2026","rel":"","context":"In "Analytics Challenge"","block_context":{"text":"Analytics Challenge","link":"https:\/\/ucanalytics.com\/blogs\/category\/analytics-challenge\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2017\/01\/Twins-and-Cluster-Analysis-1.jpg?fit=427%2C233&ssl=1&resize=350%2C200","width":350,"height":200},"classes":[]},{"id":1474,"url":"https:\/\/ucanalytics.com\/blogs\/the-beauty-of-%cf%80-iterative-calculation\/","url_meta":{"origin":1259,"position":4},"title":"The Beauty of \u03c0 (Pi) – Iterative Calculation","author":"Roopam Upadhyay","date":false,"format":false,"excerpt":"Let us continue with our inadvertently started tradition of separating the articles on cluster analysis with a different topic to make them form perfect clusters. This time, I am going to discuss iterative calculation in between articles on our running series on cluster analysis and customer segmentation for telecom.\u00a0 Though\u2026","rel":"","context":"In "Analytics Graffiti"","block_context":{"text":"Analytics Graffiti","link":"https:\/\/ucanalytics.com\/blogs\/category\/analytics-graffiti\/"},"img":{"alt_text":"Archimedes - by Roopam","src":"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/01\/photo1.jpg?fit=1109%2C1200&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/01\/photo1.jpg?fit=1109%2C1200&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/01\/photo1.jpg?fit=1109%2C1200&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/01\/photo1.jpg?fit=1109%2C1200&ssl=1&resize=700%2C400 2x, https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2014\/01\/photo1.jpg?fit=1109%2C1200&ssl=1&resize=1050%2C600 3x"},"classes":[]},{"id":1251,"url":"https:\/\/ucanalytics.com\/blogs\/murder-cases-evidence-and-logical-rigor-addendum\/","url_meta":{"origin":1259,"position":5},"title":"Murder Cases, Evidence and Logical Rigor – Addendum","author":"Roopam Upadhyay","date":false,"format":false,"excerpt":"I know this article should be a continuation of our telecom case study on customer segmentation and cluster analysis. Though it\u2019s not intended, but possibly is apt that the articles on cluster analysis are separated by articles on other topics \u2013 forming them into perfect clusters. 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