Homework Answers
(a) K=2. Assuming that the points are uniformly distributed in the circle, how many possible ways are there (in theory) to partition the points tine 2 choices? (Again, you don’t need to provide exact centroid locations, just a qualitative description.)
Assuming the points are uniformly distributed in the circle, with K=2 theoretically circle can be partition into two half circles. When positioning the two centroids, they would be placed (as depicted in the figure below) in the center of each half circle.
(b) K=3. The distance between the edges of the circles us slightly greater that the radii of the circles.
Pertaining to figure (b) if K=3 the following figure below depicts one possible situation for the placement of the three centroids.
(c) K=3. The distance between the edges of the circles is much less than the radii of the circles.
Pertaining to figure (b) if K=3 the following figure below depicts one possible situation for the placement of the three centroids.
(d) K=2.
If K=2, the centroids would be located between the elipses as depicted below in the figure.
(e) K=3. Hint: Use the symmetry of the situation and remember that we are looking for a rough sketch of what the result would be.
If
K=3, the centroids for figure (e) would be located in the center of
each cluster. The figure below depicts the locationg of the
centroids.
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1. [10 points) For the following sets of two-dimensional points, (1) draw a sketch of how they wo...
1. [10 points) For the following sets of two-dimensional points, (1) draw a sketch of how they wo...
1. [10 points) For the following sets of two-dimensional points, (1) draw a sketch of how they would be split into clusters by K-means for the given number of clusters and (2) indicate approximately where the resulting centroids would be. Assume that we are using the squared error objective function. If you think that there is more than one possible solution, then please indicate whether each solution is a global or local minimum. Note that the label of each diagram...
For the following sets of two-dimensional points, (1) provide a sketch of how they would be split...
For the following sets of two-dimensional points, (1) provide a
sketch of how they would be split into clusters by K-means for the
given number of clusters and (2) indicate approximately where the
resulting centroids would be. Assume that we are using the squared
error objective function and random initialization of centroids. If
you think that there is more than one possible solution, then
please indicate whether each solution is a global or local minimum.
Darker areas indicate higher density....
1) For the following set of two-dimensional points, draw a sketch of how they would be split into...
1) For the following set of two-dimensional points, draw a sketch of how they would be split into two clusters by K-means (when global minimum of SSE is achieved) and by Gaussian mixture model clustering. You can assume the density of points in the darker area is much higher than the density of points in the lighter area 2) Name one other clustering method that might be able to accurately capture the two clusters.
1) For the following set of...
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Question 2 please
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1. [10 points) For the following sets of two-dimensional points, (1) draw a sketch of how they would be split into clusters by K-means for the given number of clusters and (2) indicate approximately where the resulting centroids would be. Assume that we are using the squared error objective function. If you think that there is more than one possible solution, then please indicate whether each solution is a global or local minimum. Note that the label of each diagram...
For the following sets of two-dimensional points, (1) provide a
sketch of how they would be split into clusters by K-means for the
given number of clusters and (2) indicate approximately where the
resulting centroids would be. Assume that we are using the squared
error objective function and random initialization of centroids. If
you think that there is more than one possible solution, then
please indicate whether each solution is a global or local minimum.
Darker areas indicate higher density....
1) For the following set of two-dimensional points, draw a sketch of how they would be split into two clusters by K-means (when global minimum of SSE is achieved) and by Gaussian mixture model clustering. You can assume the density of points in the darker area is much higher than the density of points in the lighter area 2) Name one other clustering method that might be able to accurately capture the two clusters.
1) For the following set of...
"A Watch t use 0.62/1.25 points 1 Prefous Anewe LaPCalc 10 B.018 Consider the follewing. x-3 cos 0 y5 sin 8 (a) Sketch the curve represented by the parametric equations (indicate the orlentation of the curve) y 10 -2 21 2 -10 21 -10 (b) Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve Adjust the domain of the resuting rectangular eqvation if necessary oed Heln? 0/1.25 points | Previous Answers LarPCalc8 10.6.042 6. Find...
Question 2 please
MATH308: Differential Equattons Problems for Chapter 7.6 (Complex-Valued Eigenvalues) 1. The following ODE systems have complex eigenvalues. Find the general solution and sketch the phase plane diagrams 3 -2 1 -A x=( x, 5 -1 1 -1*.(49) mu+ku 0 (50) where u(t) is the displacement at time t of the mass from its equilibrium position (a) Let -und show that the resulting system is 1) (51) b) Find the eigenvalues of the matrix in part (a). (c)...
1 The following questions involve the two polar curves: Sketch the curves and shade the region outside R and inside r Use a large size graph paper a l clearly indicate the points of intersection. Also indicate the values of theta that give one complete cycle for each curve b. Discuss the symmetry of each curve c. Calculate th e area for the region of overlap that you shaded and described in part a. Show all steps clearly and neatly....
3.Question for further thought Imagine the two-dimensional space {0, 1, . . . , 10).(0, 1, . . . , 10) = (0,0), (0,1),(10, 10)J. We locate a mouse on the (0,0) point and we locate a piece of cheese on the (10, 10) point. We somehow make sure that the mouse will reach the cheese with 20 steps, by either going steps 'right' (for example, from (0, 0) to (0,1)) or by going steps 'up' (for example, from (0,0)...
1 The electric field of individual point charges Question 1: (10 points) The figures above show a positive charge (left) and a negative charge (right). The circles indicate which of the dots (points in space) are at equal distances from the charge. a) At each of the points indicated by a dot, draw the electric field vector representing the field gener ated by the charge. Make sure to get both the direction and the relative magnitudes of the vectors right....
(15 points) Encounter with a semi-infinite potential "well" In this problem we will investigate one situation involving a a semi-infinite one-dimensional po- tential well (Figure 1) U=0 region 1 region 2 region 3 Figure 1: Semi-infinite potential for Problem 3 This potential is piecewise defined as follows where Uo is some positive value of energy. The three intervals in x have been labeled region 1,2 and 3 in Figure 1 Consider a particle of mass m f 0 moving in...
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