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 :1 point: Semistrong form efficiency implies: I a] All historical market information, including prices and volume. is included in the price. I b] All information, both public and private is already incorporated in the price. I c} Superior returns may be obtained by the analysis of past prices and volumes. d] All public information is already incorporated in the price. Question 211 point]- Which ofthe following is NOT an empirical challenge to market efficiency? I a] small stocks tend to outperform large stocks I b] value stocks tend to outperform growth stocks I c] investors appear to react slowly to earnings announcements di stocks sometimes return more than their expected return s, and at othertimes return less than their expected returns Question 3 [1 point]- Which ofthe following should not lead to an increase in market efciency? I a] Information is available faster I b] Infon'nation is available at a lower cost cjl There are more assets {for example, number of stocks) in the market for the same number of market participants I d] There are more participants in the markets for the same number ofassets Question 411 polnt] An exchange rate regime is one under which rates of exchange are determined in the market on the basis of predominantly private transactions is called: Determine the category of financial benefits or costs for each scenario given in the following table. The category available: tangible benefit, intangible benefit. one-time-cost, and recurring cost. Reminder: Please separate each answer into a different line and include relevant label in front of your answer Example: a. Intangible benefit b. Intangible benefit C. Intangible benefit d. Intangible benefit No. Scenario Category Example Increased organizational flexibility Intangible benefit A. New hardware and software purchases b. Application software maintenance C. Cost and error reduction d. Faster decision makingQUESTION 23 An overheating economy is one where O A. Workers' job performance lags due to slow changes in technology. O B. Actual real GDP is below the full employment level of GDP. O C. The full employment level of GDP is almost equal to actual real GDP. OD. Actual real GDP is above the full employment level of GDP. QUESTION 24 The long-run aggregate supply curve is A. Upward sloping because of the effects of price level changes on real GDP. O B. The same as the short-run aggregate supply curve. O C. Vertical at the full-employment level of real GDP. O D. Horizontal at the full employment price level.Question 2 Complete the following table for a given country and show how can you determine if the country faces an inflation in 2018? Nominal GOP2017 Nominal GDP 2014 Real GDPXD18 P P Q P C 2 A I 3 3 3 R GOP Question 3 - What is the purchasing power of (1000) Rails after (7) years if the inflation rate is (4%) per year? What are the similarity and difference between "Minimum Wage Laws" and "Theory Of Efficiency Wages"? Question 4 A theatre that sells a ticket for a comedy show. The ticket price is 3 Rials to have a seat and watch the show. There is a snack to be given to each ticket buyer that cost 1 Rial. Now, consider this scenario: There are about 50 seats that are not sold and the show is few minutes to start and there is a standby customer willing to buy the ticket by price less than 3. What is the minimum price the theater can offer? Explain the logic about your answer. Question 5 A government is trying to reduce inflation but this has led to higher unemployment. Explain the role of the prices stickiness in causing this tradeoffs