In this task the idea is to study the behaviour of extreme distances and relative contrast...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
In this task the idea is to study the behaviour of extreme distances and relative contrast with different Lp norm based distance measures when the dimensionality of data increases. The relative contrast for data vector x; is defined as Ci = 2 Dmax — Dmin Dmin 2 where Dmax and Dmin are the maximum and minimum distances from vector x; to any other vector in the data, calculated with a given distance function. In the experiment, vary the dimensionality as d = 1, 2, 3, 4, 5, 10, 20,..., 100. For each d, simulate random data with n = 100 data points x; E Rd, where each component has uniform distribution in the range [0, 1]. For each x; € {x₁,...,Xn}, find the minimum, average and maximum distances from it to all other vectors. Then calculate the difference between the maximum and minimum distances and the relative contrast value. Finally compute the averages of all these five measures over all xi. Plot the average values and their logarithms as functions of increasing d. (Place all distance values in one plot and the contrast values in another plot. Similarly, do not mix the original and the logarithmic values in the same plot. You should thus have in total four plots.) Repeat the experiment four times with the following Lp measures as the distance function: L0.5, L₁, L2, and L3. a) What happens to each one of the distance values and the difference between the maxi- mum and minimum distances when d increases? Explain, how you use the original and logarithmic plots to draw these conclusions. b) What happens to the relative contrast measure when d increases? How can this finding be explained based on the distance plots? c) What kind of an effect does the p value have on the bahavior of the relative contrast measure as a function of d? d) How do you interpret the results with respect to so called "curse of dimensionality"? In this task the idea is to study the behaviour of extreme distances and relative contrast with different Lp norm based distance measures when the dimensionality of data increases. The relative contrast for data vector x; is defined as Ci = 2 Dmax — Dmin Dmin 2 where Dmax and Dmin are the maximum and minimum distances from vector x; to any other vector in the data, calculated with a given distance function. In the experiment, vary the dimensionality as d = 1, 2, 3, 4, 5, 10, 20,..., 100. For each d, simulate random data with n = 100 data points x; E Rd, where each component has uniform distribution in the range [0, 1]. For each x; € {x₁,...,Xn}, find the minimum, average and maximum distances from it to all other vectors. Then calculate the difference between the maximum and minimum distances and the relative contrast value. Finally compute the averages of all these five measures over all xi. Plot the average values and their logarithms as functions of increasing d. (Place all distance values in one plot and the contrast values in another plot. Similarly, do not mix the original and the logarithmic values in the same plot. You should thus have in total four plots.) Repeat the experiment four times with the following Lp measures as the distance function: L0.5, L₁, L2, and L3. a) What happens to each one of the distance values and the difference between the maxi- mum and minimum distances when d increases? Explain, how you use the original and logarithmic plots to draw these conclusions. b) What happens to the relative contrast measure when d increases? How can this finding be explained based on the distance plots? c) What kind of an effect does the p value have on the bahavior of the relative contrast measure as a function of d? d) How do you interpret the results with respect to so called "curse of dimensionality"?
Expert Answer:
Answer rating: 100% (QA)
The image contains text describing a task for studying the behavior of extreme distances and relative contrast with increasing dimensionality of data The task involves conducting experiments with vary... View the full answer
Related Book For
Posted Date:
Students also viewed these programming questions
-
A concentric tube heat exchanger having an area of 100 m2 is used to heat 5 kg/s of water that enters the heat exchanger at 50oC. The heating fluid is oil having a specific heat of 2.1 kJ/kg and a...
-
What are the problems with the company/individual/concepts mentioned in the case study article The Secrets of Great? Why are the problems important? In what way does the problem impact the...
-
"I'm not sure we should lay out $300,000 for that automated welding machine," said Jim Alder, president of the Superior Equipment Company. "That's a lot of money, and it would cost us $84,000 for...
-
Terminology Key: Key Word List Describe Explain What to do In bulleted, numbered or paragraph form, provide a number of consecutive items-if paragraph form, use commas (,) to separate items In...
-
What distinguishes zero-based budgeting from other types of budgeting?
-
At the start of 2022, Santana Rey is considering adding a partner to her business. She envisions the new partner taking the lead in generating sales of both services and merchandise for Business...
-
Discuss the main recognition and measurement issues that must be considered when preparing the income statement.
-
(a) A sinusoidal signal, with amplitude of 3.25 volts, is applied to a uniform quantizer of the mid-tread type whose output takes on the values 0, 1, 2, 3 volts. Sketch the waveform of the resulting...
-
The following facts pertain to a non-cancelable lease agreement between Shamrock Leasing Company and Pharoah Company, a lessee. Commencement date May 1, 2025 Annual lease payment due at the beginning...
-
Given this, answer the following questions: 1. Draw a diagram of the process using the format in Exhibit 7.3. 2. Consider a base case where a customer arrives every 40 seconds and the Customer...
-
On June 1, 2020, the Alma Corp. acquired a piece of land with a building on it for $1,400,000. The land was worth $250,000, and the building was worth $1,150,000. Alma paid for this purchase by...
-
Using a program trace or otherwise, find out what operation the following Java method performs. Show its operation using the following example inputs: N = 17, and N = 25. public static Boolean...
-
Suppose you are the financial manager of a manufacturing company that is facing significant market risk due to fluctuations in raw material prices. Design a comprehensive risk management strategy to...
-
The figure below shows three small, charged beads, all lying along the horizontal axis. Bead A, at left, has a 5.90 nC charge. Bead B has a 1.60 nC charge and is 3.00 cm to the right of A. Bead C has...
-
This is a question I failed and I need help on how to go about it with a proper explanation please I will appreciate if you can stick to the terms we have covered and nothing outside of it. ("...
-
Bold Ltd purchased machinery on 1 January 2 0 2 1 at a cost of R 1 2 0 0 0 0 0 . A major inspection has to be carried out on the machinery every three years. The last inspection performed on the...
-
2. On the basis of magnetic moment data the complex [Co(NH)]+ is found to be diamagnetic what can you say about the hybridisation of complex. (a) spd (b) dsp (c) pd (d) pd
-
A number of years ago the United Food and Commercial Workers Union organized 800 workers of the 1035 employees at one of the Wilson Brothers food operations in Toronto, Ontario. The employees include...
-
Find a basis of solutions. Try to identify the series as expansions of known functions. Show the details of your work. x 2 y" + 2x 3 y' + (x 2 - 2)y = 0
-
What property of the Laplace transform is crucial in solving ODEs?
-
Using (1) or (2), find L(f) if f(t) if equals: sin 4 t. Use Prob. 19. Data from Prob. 19 sin 2 t
-
How might the three categories of management assertions provide a powerful tool for the financial statement auditor?
-
Summarize the major changes made in ISO 9000-2015.
-
1. E-Z Open Manufacturing Company is a leading maker of manual can openers. In the year just closed, E-Z Open controlled 17.2% of the manual can opener market in North America. That placed the...
Study smarter with the SolutionInn App