The owner of a small grocery store wishes to understand their customers better. Specifically, they'd like to segment their customers into a small number of groups with similar purchasing characteristics so as to better target their advertising. They hire you, a data scientist, to do this. So, you do the following: (a) You identify 6 main categories of product: Bread, Fresh fruit & Veggies, Cigarettes, Milk, Canned Food, Newspapers. (b) You select 5 customers and (legally and ethically!) track their purchasing habits for a month. Specifically you record the amount that they spend on each category of product in the month, and then normalize this amount to a number between 0 and 1. This data is presented in matrix X in (8). The first column corresponds to customer 1, the second to customer 2 and so on. The rows corresponds to the product categories, in the order in which they are listed in point (a) above. Also presented in (8) is the non-negative matrix factorization of X. That is, X WH. a X= [0.735 0.179 0.079 0.698 0.307] 0.093 0.655 0.655 0.436 0.604 0.686 0.782 0.547 0.427 0.471 W 0.138 0.223 0.573 0.846 0.164 0.427 0.018 0.488 0.193 0.819 0.78 0.69 0.354 0.221 0.184 [0.162 0.449 0.696] 0.784 0.0 0.0 [0.268 0.557 0.896 0.538 0.854) 0.632 0.599 0.0 H= 0.94 0.595 0.0 0.0 0.0 0.413 0.0 0.648 0.226 0.0 0.0 0.917 0.0 0.62 0.0 0.0 0.336 0.766 0.0 (a) Recall that the columns of W represent the categories, or segments, of customers. Interpret these segments based on the products they purchase the most. (b) With which segment is Customer 1 most strongly associated? (@) With which segment is Customer 3 most strongly associated? (d) (This final question is erperimental. So it will not count towards your grade, but we will offer feedack) Write a short (less than half a page) report for the shop owner. Briefly describe your methodology and your major findings. Conclude with some actionable suggestions for the shop owner (e.g. which products to stock near each other on the shelves, potential ad campaigns and so on). The owner of a small grocery store wishes to understand their customers better. Specifically, they'd like to segment their customers into a small number of groups with similar purchasing characteristics so as to better target their advertising. They hire you, a data scientist, to do this. So, you do the following: (a) You identify 6 main categories of product: Bread, Fresh fruit & Veggies, Cigarettes, Milk, Canned Food, Newspapers. (b) You select 5 customers and (legally and ethically!) track their purchasing habits for a month. Specifically you record the amount that they spend on each category of product in the month, and then normalize this amount to a number between 0 and 1. This data is presented in matrix X in (8). The first column corresponds to customer 1, the second to customer 2 and so on. The rows corresponds to the product categories, in the order in which they are listed in point (a) above. Also presented in (8) is the non-negative matrix factorization of X. That is, X WH. a X= [0.735 0.179 0.079 0.698 0.307] 0.093 0.655 0.655 0.436 0.604 0.686 0.782 0.547 0.427 0.471 W 0.138 0.223 0.573 0.846 0.164 0.427 0.018 0.488 0.193 0.819 0.78 0.69 0.354 0.221 0.184 [0.162 0.449 0.696] 0.784 0.0 0.0 [0.268 0.557 0.896 0.538 0.854) 0.632 0.599 0.0 H= 0.94 0.595 0.0 0.0 0.0 0.413 0.0 0.648 0.226 0.0 0.0 0.917 0.0 0.62 0.0 0.0 0.336 0.766 0.0 (a) Recall that the columns of W represent the categories, or segments, of customers. Interpret these segments based on the products they purchase the most. (b) With which segment is Customer 1 most strongly associated? (@) With which segment is Customer 3 most strongly associated? (d) (This final question is erperimental. So it will not count towards your grade, but we will offer feedack) Write a short (less than half a page) report for the shop owner. Briefly describe your methodology and your major findings. Conclude with some actionable suggestions for the shop owner (e.g. which products to stock near each other on the shelves, potential ad campaigns and so on)