This question aims to reproduce the ISOMAP algorithm results in the original paper for ISOMAP, J.B. Tenenbaum, V. de Silva, and J.C. Langford, Science 290 (2000) 2319-2323 that we have also seen in the lecture as an exercise (isn't this exciting to go through the process of generating results for a high-impact research paper!) The le isomap.mat (or isomap.dat) contains 698 images, corresponding to different poses of the same face. Each image is given as a 64 64 luminosity map, hence represented as a vector in R4096. This vector is stored as a row in the le. [This is one of the datasets used in the original paper] In this question, you are expected to implement the ISOMAP algorithm by coding it up yourself. You may use the provided functions in ShortestPath.zip to nd the shortest path as required by one step of the algorithm. To load data in Python, for instance, you can use from scipy.io import loadmat, images = loadmat('isomap.mat')['images']. To load data in Matlab, you can directly use load() function. Choose the Euclidean distance (i.e., in this case, a distance in R4096) to construct the nearest neighbor graph?vertices corresponding to the images. Construct a similarity graph with vertices corresponding to the images, and tune the threshold so that each node has at least K = 50 neighbors (this approach corresponds to the so-called -Isomap).

(a) (10 points) Visualize the similarity graph (you can either show the adjacency matrix, or similar to the lecture slides, visualize the graph using graph visualization packages such as Gephi (https://gephi.org) and illustrate a few images corresponds to nodes at different parts of the graph, e.g., mark them by hand or use software packages).

(20 points) Implement the ISOMAP algorithm yourself to obtain a two-dimensional low-dimensional embedding. Plot the embeddings using a scatter plot, similar to the plots in lecture slides. Find a few images in the embedding space and show what these images look like. Comment on do you see any visual similarity among them and their arrangement, similar to what you seen in the paper?

(c) (10 points) Now choose `1 distance (or Manhattan distance) between images (recall the denition from "Clustering" lecture)). Repeat the steps above. Use -ISOMAP to obtain a k = 2 dimensional embedding. Present a plot of this embedding. Do you see

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any difference by choosing a different similarity measure by comparing results in Part (b) and Part (c)?

(d) (10 points) Perform PCA (you can now use your implementation written in Question 1) on the images and project them into the top 2 principal components. Again show them on a scatter plot. Explain whether or you see a more meaningful projection using ISOMAP than PCA

Question 1 aj Jane bought 1 bottle of seaweed-based shampoo. She gave the bottle to her sister, Jill, After using the shampoo Jill discovered to her horror that her hair, which was usually healthy, was starting to fall out and that she had contracted a skin rash on her neck. Analysis reveals that the shampoo in fact contained small amounts of harmful chemicals. Advise Jill whether she can take action against the manufacturer, Tulin Products Son Bhd. 30 marks3.1 Within a lease agreement an important principle exists protecting the right of the tenant to use and enjoyment of the leased property in the event of a change in ownership. Elaborate on this principle and its implications. (10) 3.4 Itemize the types of Intellectual Property recognised in South African legislation today. (8) IEntries for Issuing par stock Instructions Chart of Accounts Journal Final Question E Instructions X On January 22, Jofferson County Flocks Inc., a marble contractor, Issued for cash 70,300 shares of $45 par common stock at $50, and on February 27, It Issued for cash 18,450 shares of preferred stock, $10 par at $15. Required: a Journalize the entries for January 22 and February 27. Aster to the Chart of Accounts for exact wording of account titles. b. What is the total amount invested (total paid-in capital) by all stockholders as of February 27?Question 24 2 pts Acyl CoA Synthetase, is an enzyme that requires ATP to function and yet it can run backwards making ATP! Why can acyl-CoA synthetase make ATP, when it consumes ATP? The thioester bond on Acyl CoA provides energy for ATP production. O The phosphate group on the CoA can provide energy for hydrolysis. O The enzyme actually favors the reverse reaction (positive AG) O There is a second enzyme that uses ATP to un-charge the acyl CoA. O None of the answers provided answers the questions