- Download all files (2 Python programs and 1 PNG image)
- To see the answers to the questions, run the respective python program
- Run recolor.py to implement the k-means clustering algorithm and apply it to color a given image
- Run original_color.py to implement the k-means clustering algorithm and reconstruct the coloring of a given image (k determines the number of clusters/colors of the image)
Implement k-means clustering algorithm and apply it to color a given image (image.png).
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Step 1: First, load the image, which will give you a handle (i.e., img) of a (244, 198, 3) numpy.ndarray. The first two dimensions represent the height andwidth of the image. The last dimension represents the 3 color channels (RGB) for eachpixel of the image.
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Step 2: Next implement the k-means algorithm to partition the 244×198 pixels into k clustersbased on their RGB values and the Euclidean distance measure. The k-means max iteration is 50. Run your experimentwith k = 2, 3, 6, 10 with the following given starting centroids: k = 2: (0, 0, 0), (0.1, 0.1, 0.1) k = 3: (0, 0, 0), (0.1, 0.1, 0.1), (0.2, 0.2, 0.2) k = 6: (0, 0, 0), (0.1, 0.1, 0.1), (0.2, 0.2, 0.2), (0.3, 0.3, 0.3), (0.4, 0.4, 0.4), (0.5, 0.5,0.5) k = 10: (0, 0, 0), (0.1, 0.1, 0.1), (0.2, 0.2, 0.2), (0.3, 0.3, 0.3), (0.4, 0.4, 0.4), (0.5, 0.5,0.5), (0.6, 0.6, 0.6), (0.7, 0.7, 0.7), (0.8, 0.8, 0.8), (0.9, 0.9, 0.9)
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Step 3: For each k = 2, 3, 6, 10, report the final SSE and re-color the pixels in each clusterusing the following color scheme: Cluster 1. SpringGreen: (60, 179, 113) Cluster 2. DeepSkyBlue: (0, 191, 255) Cluster 3. Yellow: (255, 255, 0) Cluster 4. Red: (255, 0, 0) Cluster 5. Black: (0, 0, 0) Cluster 6. DarkGray: (169, 169, 169) Cluster 7. DarkOrange: (255, 140, 0) Cluster 8. Purple: (128, 0, 128) Cluster 9. Pink: (255, 192, 203) Cluster 10. White: (255, 255, 255)
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Step 4: Calculate and record the SSE values and colored images for each k. You can find the SSE values on 'sse_values.csv'.
Consider the following dataset: { 0, 4, 5, 20, 25, 39, 43, 44 }
- a) Build a dendrogram for this dataset using the single-link, bottom-up approach.Show your work.
- b) Suppose we want the two top-level clusters. List the data points in each cluster
- Answers included in the written answers PDF
Given two clusters C1 = {(1, 1), (2, 2), (3, 3)} and C2 = {(5, 2), (6, 2), (7, 2), (8, 2), (9, 2)} compute the values in (a) - (f). Use the definition for scattering criteria presented inclass. Note that tr in the scattering criterion is referring to the trace of the matrix.
- a) The mean vectors m1 and m2
- b) The total mean vector m
- c) The scatter matrices S1 and S2
- d) The within-cluster scatter matrix SW
- e) The between-cluster scatter matrix SB
- f) The scatter criterion tr(SB)/tr(SW)
- Answers included in the written answers PDF
A Naive Bayes classifier gives the predicted probability of each data pointbelonging to the positive class, sorted in a descending order:
Instance # | True Class Label | Predicted Probability of Positive Class 1 | P | 0.95 2 | N | 0.85 3 | P | 0.78 4 | P | 0.66 5 | N | 0.60 6 | P | 0.55 7 | N | 0.43 8 | N | 0.42 9 | N | 0.41 10 | P | 0.4
Suppose we use 0.5 as the threshold to assign the predicted class label to each datapoint, i.e., if the predicted probability ≥ 0.5, the data point is assigned to positive class; otherwise, it is assigned to negative class. Calculate the Confusion Matrix, Accuracy, Precision, Recall, F1 Score and Specificity of the classifier.
- Answers included in the written answers PDF