Update: the question does not require any image file for the assignment.

The following set of points represents measurements of the red and green components of pixels from a given image represented with a resolution of 4 bits per pixel where: (x_0, x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11) = ({(0, 0), (1, 0), (0, 1), (1, 1), (0, 8), (0, 9), (1, 8), (1, 9), (8, 0), (9, 0), (8, 1), (9, 1)) Assume that the points listed above represent training data. 1) Perform manual 3-means clustering on the training data assuming that the initial centers are at {(0, 0), (1, 0), (0, 1)). For reference you can use the grid below where both 'o' and 'x' are training data points and 'o' are also initial centers. Alternatively you can write your OWN k-means program and run it on the data. In any case you have to submit a detailed description of all the algorithm variables at every iteration of every stage in the algorithm. This should be like a trace of the program in which, the result of execution is recorded after every line of the code (or pseudo code). a) For termination please use the classical K-means criteria which stops when the centers stop changing. 2) Produce the lookup table (dictionary) for the training set and use it to encode the data points {(3, 3), (5, 3), (3, 5)}. Marked with P in the grid. 3) Show the reproduction value for these points. 4) Find the distortion associated with the encoding of the point at {(3, 3)} 5) Find the rate and the compression ratio for the three P's without taking into account the overhead of the dictionary. Note that the compression might be "negative." That is, compressed values require more bits than original values. The following set of points represents measurements of the red and green components of pixels from a given image represented with a resolution of 4 bits per pixel where: (x_0, x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10, x_11) = ({(0, 0), (1, 0), (0, 1), (1, 1), (0, 8), (0, 9), (1, 8), (1, 9), (8, 0), (9, 0), (8, 1), (9, 1)) Assume that the points listed above represent training data. 1) Perform manual 3-means clustering on the training data assuming that the initial centers are at {(0, 0), (1, 0), (0, 1)). For reference you can use the grid below where both 'o' and 'x' are training data points and 'o' are also initial centers. Alternatively you can write your OWN k-means program and run it on the data. In any case you have to submit a detailed description of all the algorithm variables at every iteration of every stage in the algorithm. This should be like a trace of the program in which, the result of execution is recorded after every line of the code (or pseudo code). a) For termination please use the classical K-means criteria which stops when the centers stop changing. 2) Produce the lookup table (dictionary) for the training set and use it to encode the data points {(3, 3), (5, 3), (3, 5)}. Marked with P in the grid. 3) Show the reproduction value for these points. 4) Find the distortion associated with the encoding of the point at {(3, 3)} 5) Find the rate and the compression ratio for the three P's without taking into account the overhead of the dictionary. Note that the compression might be "negative." That is, compressed values require more bits than original values