The data in phoneme subset, available from this book's website

consists of digitized log-periodograms for phonemes uttered by 60 speakers, each speaker having produced phonemes from each of five classes. It is appropriate to plot each vector of 256 "features" against the frequencies 0-255.

(a) Produce a separate plot of all the phoneme curves against frequency for each class.

(b) You plan to use a nearest prototype classification scheme to classify the curves into phoneme classes. In particular, you will use a K-means clustering algorithm in each class (kmeans() in R), and then classify observations to the class of the closest cluster center. The curves are high-dimensional and you have a rather small sample-size-to-variables ratio. You decide to restrict all the prototypes to be smooth functions of frequency. In particular, you decide to represent each prototype m as m = Bθ where B is a 256 × J matrix of natural spline basis functions with J knots uniformly chosen in (0, 255) and boundary knots at 0 and 255. Describe how to proceed analytically, and in particular, how to avoid costly high-dimensional fitting procedures. (Hint: It may help to restrict B to be orthogonal.)

(c) Implement your procedure on the phoneme data, and try it out. Divide the data into a training set and a test set (50-50), making sure that speakers are not split across sets (why?). Use K = 1, 3, 5, 7 centers per class, and for each use J = 5, 10, 15 knots (taking care to start the K-means procedure at the same starting values for each value of J), and compare the results.