Question: Here, we further explore the cosine and correlation measures. (a) What is the range of values that are possible for the cosine measure? (b) If

Here, we further explore the cosine and correlation measures.
(a) What is the range of values that are possible for the cosine measure?
(b) If two objects have a cosine measure of 1, are they identical? Explain.
(c) What is the relationship of the cosine measure to correlation, if any?
(d) Figure 2.1(a) shows the relationship of the cosine measure to Euclidean distance for 100,000 randomly generated points that have been normalized to have an L2 length of 1. What general observation can you make about the relationship between Euclidean distance and cosine similarity when vectors have an L2 norm of 1?
(e) Figure 2.1(b) shows the relationship of correlation to Euclidean distance for 100,000 randomly generated points that have been standardized to have a mean of 0 and a standard deviation of 1. What general observation can you make about the relationship between Euclidean distance and correlation when the vectors have been standardized to have a mean of 0 and a standard deviation of 1?
(f) Derive the mathematical relationship between cosine similarity and Euclidean distance when each data object has an L2 length of 1.
(g) Derive the mathematical relationship between correlation and Euclidean distance when each data point has been been standardized by subtracting its mean and dividing by its standard deviation.

Step by Step Solution

★★★★★

3.46 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a 1 1 Many times the data has only positive entries and in that case the range is 0 1 b Not necessar... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

908-M-S-D-A (8576).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

In this exercise we will further explore the ARE of the median to the mean, ARE(Mn, ). (a) Verify the three AREs given in Example 10.2.4. (b) Show that ARE(Mn, ) is unaffected by scale changes. That...

A car leaves four skid marks each 50 feet in length. The drag factor for the road is 0.9. Let x represent the braking efficiency. a. What is the range of values that can be substituted for x? b. Let...

List all pairs (rank(h), nullity(h)) that are possible for linear maps from R5 to R3.

please answer this subject data mining with clearly. thank you this is the real answer, i need tu solution for number 2 2. Here, we further explore the cosine and correlation measures. a. What is the...

7. Select the sentence or sentences that are correct about cosine and correlation measures. The range of values that are possible for the cosine measure is [0, 1 if two objects have a cosine...

// Question 7: Which of the following is correct regarding cosine and correlation measures? (select all that apply) (1)The range of values for cosine similarity measure is [0, 1]\ (2)Correlation is...

I need to see the SPSS output. You need to have all z-scores, all charts, all descriptives data from SPSS, everything you used to answer the questions. I am sending you what the previous tutor sent...

413-432_CH18_Nachmias.qxd 1/17/07 3:47 PM Page 413 Chapter Index Construction and Scaling Methods INDEX CONSTRUCTION The Purpose of the Index The Sources of the Data The Base of Comparison Methods of...

Describing Data Once we have collected data from surveys or experiments, we need to summarize and present the data in a way that will be meaningful to the reader. We will begin with graphical...

1. Calculate the sample size needed given these factors: one-tailed t-test with two independent groups of equal size small effect size (see Piasta, S.B., & Justice, L.M., 2010) alpha =.05 beta = .2...

Below is information related to the stockholders' equity of Brookdale Corporation as of December 31, 2018: 11% cumulative preferred stock, $130 par, 100,000 shares authorized, 10,000 shares issued...

DGK Company maintains a lockbox account to facilitate the collection of its accounts receivable. All of the companys cash receipts from credit sales are sent directly to a post office box held in the...

The subject matter of an ERISA audit is most likely to be: Multiple Choice corporate income statements. employee benefits. engineering research results. financial forecasts.

58. Asian immigrants 2012 Below are data on immigration to Canada from countries in Asia: a) We want to predict the percentage of total immigrants who are from Asia based on the year. You may use two...

What step should precede the deriving of a new numerical variable representing the mean of two other numerical variables?

Why is binning based on predictive value considered to be somewhat of an art?

Explain the objective and the method of binning based on predictive value.

You own $7,000. The dollar rate in Tokyo is 216.2463 Y/$. The Yen rate in New York is given in the following table: COUNTRY-CURRENCY CONTRACT $/FOREIGN CURRENCY Canadadollar Spot .8432 30-day .8415...

Please refer to the following passage for question 3. The following is an excerpt from Toifail et. al The Lancet 2018: Background: Poor nutrition and hygiene make children vulnerable to delays in...

Question 1 Blue Demon Bank expects that the Mexican peso will depreciate against the dollar from its spot rate of $0.15 to $0.14 in 10 days. The following interbank lending and borrowing rates exist:...