Assignment Task: Activity 1: Principal Component Analysis In this first activity, you are asked to:
1. Perform Principal Component Analysis (PCA) on the Stamps data in the 9-dimensional space of the numerical predictors ( PB_Predictors ), and show the Proportion of Variance Explained (PVE) for each of the nine resulting principal components. Plot the accumulated sum of PVE for the first components, as a function of , and discuss the result:
(a) How many components do we need to explain 90% or more of the total variance?
(b) How much of the total variance is explained by the first three components?
2. Do some research by yourself on how to render 3D plots in R, and then plot a 3D scatter-plot of the Stamps data as represented by the first three principal components computed in the previous item ( x = PC1 , y = PC2 , and z = PC3 ). You can use, for example, the function scatter3D() from the package plot3D . Use the class labels ( PB_class ) to plot inliers and outliers in different colours (for example, inliers in black and outliers in red).
Make sure you produce multiple plots from different angles (at least three). Recalling that the class labels would not be available in a practical application of unsupervised outlier detection, do the outliers (forged stamps) look easy to detect in an unsupervised way, assuming that the 3D visualisation of the data via PCA is a reasonable representation of the data in full space? How about in a supervised way? Why? Justify your answers.
Activity 2: Unsupervised outlier detection In this second activity, you are asked to perform unsupervised outlier detection on the Stamps data in the 9dimensional space of the numerical predictors ( PB_Predictors ), using KNN Outlier with different values of the parameter (at least the following three: ).
For each , produce the same 3D PCA visualisation of the data as in Activity 1 (PCA), but rather than using the class labels to colour the points, use instead the resulting KNN Outlier Scores as a continuous, diverging colour scale. Then, for each , produce a second plot where the top-31 outliers according to the KNN Outlier Scores are shown in red, while the other points are shown in black. Do these plots give you any insights on the values of that look more or less appropriate from an unsupervised perspective (ignoring the class labels)? Justify your answer.
The Final Project is a presentation based upon one of the major topics covered in the chapters of this course:
Strategic Cost Management; Activity Based Management; Strategic-Based Control; Quality and Environmental Management; Lean Accounting; Cost-Volume-Profit Analysis; Tactical Decision Making; Pricing and Profitability Analysis; Capital Investment; or Inventory Management.
Choose one of the topics for your presentation. Your presentation should be 5 minutes in length (from 4 to 6 minutes) and may be in any presentation format from a video to a narrated Power Point. The presentation is due on the last day of the finals, Tuesday, May 5.
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