1. These slides are additional material for TIES4451 Lecture 5 TIES445 Data mining Nov-Dec 2007 Sami Äyrämö

2. These slides are additional material for TIES4452 l An abundance of instrumentation enables to measure dozens of system variables l When this happens, you can take advantage of redundancy of information l In data sets with many variables, groups of variables often move together l A data set can be simplified by replacing a group of variables with a single new variable, called principal component Principal component analysis

3. These slides are additional material for TIES4453 Principal component analysis l Principal component is a linear combination of the original variables l All the principal components are orthogonal to each other, so there is no redundant information l The principal components as a whole form an orthogonal basis for the space of the data l There are an infinite number of ways to construct an orthogonal basis for several columns of data

4. These slides are additional material for TIES4454 Principal component analysis l The first principal component –possesses the maximum variance among all possible choices of the first axis

5. These slides are additional material for TIES4455 Principal component analysis l The second principal component –is another axis in space, orthogonal to the first PC

6. These slides are additional material for TIES4456 Principal component analysis l Usually the sum of the variances of the first few principal components to exceed 80% of the total variance of the original data l By examining plots of these few new variables, researchers often develop a deeper understanding of the driving forces that generated the original data