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 definition 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

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

3. Assume that the US resident uses his 112,000 JPY to purchase a camera from a store in Japan and then brings it back to the US. The transaction can be recorded by noting the foowing (for the US): (a) +$1.000 Financial account, $1.000 Capital account. (b) +$1.000 Financial account, $1.000 Current account. (c) +$1.000 Current account, $1.000 Financial account. ) l (d +$1.000 Financial account, $1.000 Financial account. [e +$1.000 Capital account, ~$1.000 Financial account. Question 34 (1 point) Saved Which statement is false? ) The discounted value of a loan is similar to the present value of an investment Compound interest investments can be modelled with exponential functions. O Increasing the frequency of the compounding increases the final value of an investment A compound interest investment always gives a greater future value than a simple interest investmentQuestion 41 (2 points) Select the correct statement regarding managerial and financial accounting. O A) Financial accounting is more highly regulated than managerial accounting. ( B) Users of managerial accounting information desire greater aggregation than do users of financial accounting information. O C) Both managerial and financial accounting use economic and physical data in addition to financial data. O D) Timeliness is more important in financial accounting than in managerial accounting. SaveQUESTION 12 Ordering decision making process for managers - T Follow up Identify problem Analyze the allomativos Implement the decision Determine alternative courses of action Select the best alternative QUESTION 13 What is correct explanation about first step for analzing the alternatives in decision making process? 8. Select an appropriate, measurable criterion O b. Carry out the chosen analysis * Select a method of analysis " Determine alternative courses of action