Draw the graphic for the healthy set

Assignment Help Data Structure & Algorithms
Reference no: EM13873046

Problem 1: K-means clustering

For this question you need to refer to the k-means clustering algorithm in the Course Slides posted on Blackboard.

Point

x

y

1

1.0

1.0

2

1.5

2.0

3

3.0

4.0

4

5.0

7.0

5

3.5

5.0

6

4.5

5.0

7

3.5

4.5

Assume we have the above dataset that shows 7 points in a 2-dimensional space, with x coordinates shown in the x column, and y coordinates shown in the y column. Assuming the number of clusters is set to 2 (i.e., k=2), and distances among points are measured by Euclidean distance. Based on observation, a good choice of the initial centroids (cluster centers) are point 1 (1.0, 1.0) and point 4 (5.0, 7.0) (these two points are relatively further away from each other). Your job is to run the k-means algorithm and answer the following questions.

(i) After the initial centroids are assigned (shown above), the first step in a clustering process is to check the rest of the points and assign them to one of the two clusters. Here we assume that the centroid remain unchanged during the first round (iteration).

Determine cluster memberships (which points belong to Cluster 1 and which belong to Cluster 2) for each of these 7 points after the first iteration. Show intermediate results how you obtain the solution.

(ii) Based on the results obtained from step (i), recalculate centroids (the mean vectors) for the two clusters. Then recalculate the distance from each point to its centroid. Show your results. Are there any points need to change their cluster memberships? If so, what are these points?

(iii) Continue the process shown in step (ii) for another iteration. Do you observe any changes in cluster memberships? If so, what are these points? If not, will there be further changes if we continue the process with more iterations?

Notes:
• It would be easier to solve the problem if you can draw a picture and show changes of centroids on a 2-dimensional system.
• Since this is a tiny dataset, the entire process can be computed by hand.

Problem 2: Logic

(i) Look at the following sentences written in first-order logic. Explain these sentences in plain English. Based on the definitions on validity and satisfiability, are these statements valid? If not, are they satisfiable? [20 points]

∀x ∃y Loves(x, y) ⇔∃x ∀y Loves(x, y)
∀x Loves(x, movie) ⇔ ¬∃x ¬Loves(x, movie)
∃x Loves(x, movie) ⇔ ¬∀x ¬Loves(x, movie)
¬∀x ¬ Loves(x, movie) ⇔ ∀x Loves(x, movie)

(ii) Based on our discussion on refutation resolution, given the following premises:

Father(A, B) Alive(A)
∀x∀y Father(x, y) ⇒ Parent(x, y)
∀x∀y (Parent(x, y) ∧ Alive(x)) ⇒ Older(x, y) Prove the following: Older(A, B)
Note: this simple question can also be proved by forward/backward reasoning. However you are required to use refutation resolution. [20 points]

Problem 3: Fuzzy Logic

The following fuzzy function was used to calculate membership values for the set healthy. A membership value of 1 is healthy; a membership value of 0 is not healthy; a membership value between 0 and 1 is the degree of membership in the healthy set.

158_Fuzzy Logic.png

BMI values that range from 20 to 25 are members of the healthy set (1). BMI values greater than 27 or less than 18 are not members of the healthy set (0). BMI values close to the healthy range (20 to 25) are a value between 0 and 1. For example, a BMI of 19.6 is 0.8 degree of membership in the healthy set.

(i) Draw the graphic for the healthy set, representing the values, healthy and unhealthy.

(ii) What is the degree of membership to the fuzzy set healthy of person B who has a BMI of 26.2? And to the fuzzy set unhealthy?

(iii) In this example, is it possible that the total degree of membership (summation of degrees of membership in different sets) exceeds 1? Why or why not?

Reference no: EM13873046

Previous Q& A

  Examine the key factors that influence the supply and demand

examine the key factors that influence the supply and demand

  Mcdonalds social responsibility

From the e-Activity, evaluate McDonald's level of responsiveness to social responsibility concerns. Include an example from your observation of your local McDonald's to support your response

  Items are likely to be reported on southern sporting goods

Which of the above items are likely to be reported on Southern Sporting Goods' external financial statements, and which items will be combined behind the scenes? Prepare the journal entries that Southern Sporting Goods would record and show any comp..

  Person returned to the cave

Question 1 According to Plato, what would the people in the cave do to the person who had been outside the cave after this person returned to the cave?

  Write paper on-pros and cons of being a veetarian

Write paper on "Pros and cons of being a veetarian".

  Rigorous scientific methodology standards

Examine the key reasons why so many people might seem to be attracted to more pseudoscience-type claims. Describe at least two (2) such claims that you have heard people make, and analyze the main reasons why such claims do or do not meet rigorous sc..

  Describe porter five forces model of industry competition

From the first e-Activity, describe Porter's Five Forces Model of industry competition. Give your opinion on how the various barriers to entry are relevant to global marketing

  The company''s return on assets

The Habicht Company was formed in 2009 to produce a single product. The production and sales for the next four years were as follows:

  Significant causal role in subsequent re-birth of science

Question 1. The 9 Crusades from 1099 -1300AD had a significant causal role in the subsequent re-birth of science and humanism in Western, with the Renaissance, Reformation and the Scientific Revolution of the 15th, 16th and 17th Centuries, respective..

  Creating different kinds of engagement opportunities

From the e-Activity, Ms. Helstab said. "We've taken a leading position in creating different kinds of engagement opportunities." Assess the degree to which the main types of engagement opportunities based on the available digital opportunities wou..

Reviews

Write a Review

 

Similar Q& A

  How two types of assets are valued for balance sheet purpose

Explain how the 2-types of assets are valued for balance sheet purposes, using the following assets owned by a corporation that writes and sells software packages

  Question about indexed strategy

Think about a file system on a disk that has both logical and physical block sizes of 512 bytes. Suppose that the data about each file is already in memory.

  Writing a c program

Create a C program that has a declaration in main() to store the following numbers into an array named channels: 2, 4, 5, 7, 9, 11, 13. There should be a function call to display().

  Determine the objective of a query simplifier describe the

question 1 what is the objective of a query simplifier? what are the idempotence rules used by query simplifier? give

  Inventory tracking database

Construct a relational database of your choice. The DB should contain no more than six tables. Define three business requirements that this database will provide.

  Implement and test a generic binary search

Implement and test a generic binary search. Note that your test program must use at least 2 types of data to prove that bsearch is generic

  Define the data structure array

Define the data structure array. Include uses; what represent the name of the array; importance of the index value; naming of the variables bundle within the array.

  Draw the hierarchy chart and then plan logic for a program

Draw the hierarchy chart and then plan the logic for a program for the sales manager of The Couch Potato Furniture Company. The manager needs a program to determine the profit on any item sold

  Determine the impedances of elements in laplace domain

Redraw the schematics with the impedance of each of the element shown in Laplace domain. Then determine the overall impedance of the entire circuit between the two ends of the shown circuit and express it in Laplace domain as a ratio of two polyno..

  Describe the key components in requirements elicitation

Analyze and describe functional and nonfunctional requirements in software engineering and describe the key components in requirements elicitation and analysis and use technology and information resources to research issues in software engineering.

  Object oriented approach versus the relational database

Supporters of object oriented databases list many benefits for using the object oriented approach versus the relational one.

  Complications in a time sharing system

Determine what complications could happen in a time-sharing system if two processes need access to the same file at the same time?

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd