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.
Homework Answers
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For the following sets of two-dimensional points, (1) provide a sketch of how they would be split...
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...
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...
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...
Hierarchical clustering is sometimes used to generate K clusters, K > 1 by taking the clusters...
Hierarchical clustering is sometimes used to generate K clusters, K > 1 by taking the clusters at the Kth level of the dendrogram. (Root is at level 1.) By looking at the clusters produced in this way, we can evaluate the behavior of hierarchical clustering on different types of data and clusters, and also compare hierarchical approaches to K-means. The following is a set of one-dimensional points: {6, 12, 18, 24, 30, 42, 48}. (a) For each of the following...
Implement the following update centers function in Python def _update_centers(self, old_centers, cluster_idx, points): np.random.seed(1) Args: old_centers:...
Implement the following update centers function in Python
def _update_centers(self, old_centers, cluster_idx, points): np.random.seed(1) Args: old_centers: old centers KxD numpy array, where K is the number of clusters, and D is the dimension cluster_idx: numpy array of length N, the cluster assignment for each point points: NxD numpy array, the observations Return: centers: new centers, KxD numpy array, where K is the number of clusters, and D is the dimension. call_(self, points, K, max_iters=100, abs_tol=1e-16, rel_tol=1e-16, verbose=False, **kwargs): Args: points:...
1. Thermodynamics and acid solutions a) The following reaction occurs when HCl is bubbled into water...
1. Thermodynamics and acid solutions a) The following reaction occurs when HCl is bubbled into water at 25°C and latm pressure: HCl(g) -> H+(aq) + Cl (aq) Calculate AS rxn for this reaction. b) Sketch two possible structures of the hydronium ion in water. Circle the hydronium ion in each case. Also sketch the local structures of water surrounding the hydronium and chloride ions in aqueous solution. Include the important water molecules in both sets of sketches. c) Draw a...
QUESTION 13 Which of the following would occur if a mutation caused Kinase 1 to be...
QUESTION 13
Which of the following would occur if a mutation caused Kinase 1
to be unable to be phosphorylated? (Select all)
RTK would bind VEGF
RTK would phosphorylate itself
RAS would become active
The phosphorylation cascade would occur
The endothelial cell would divide
0.2 points
QUESTION 14
Imagine that an endothelial cell has a mutation in several of
the enzymes that perform mismatch repair. The endothelial cell
replicates its DNA and then divides into two cells. The resulting...
(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 regio...
(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...
Requirements: 1. You are not allowed to use global variables. 2. Must declare the following two...
Requirements: 1. You are not allowed to use global variables. 2. Must declare the following two constants public static final int POINTS = 30; public static final int FORFEIT_POINTS = 20; 3. You can implement your own solution but you are required to break down the problem into smaller pieces. 4. You must provide the output for two rounds of game minimum. 5. Since we are using the Random number generator your output will not be exactly like mine. However,...
specifically on finite i pmu r the number of objøcts or ways. Leave your answers in fornsiala form, such as C(3, 2) nporkan?(2) Are repeats poasib Two points each imal digits will have at le...
specifically on finite
i pmu r the number of objøcts or ways. Leave your answers in fornsiala form, such as C(3, 2) nporkan?(2) Are repeats poasib Two points each imal digits will have at least one xpeated digin? I. This is the oounting problem Al ancmher so ask yourelr (1) ls onder ipo n How many strings of four bexadeci ) A Compuir Science indtructor has a stack of blue can this i For parts c, d. and e, suppose...
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...
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...
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...
Implement the following update centers function in Python
def _update_centers(self, old_centers, cluster_idx, points): np.random.seed(1) Args: old_centers: old centers KxD numpy array, where K is the number of clusters, and D is the dimension cluster_idx: numpy array of length N, the cluster assignment for each point points: NxD numpy array, the observations Return: centers: new centers, KxD numpy array, where K is the number of clusters, and D is the dimension. call_(self, points, K, max_iters=100, abs_tol=1e-16, rel_tol=1e-16, verbose=False, **kwargs): Args: points:...
1. Thermodynamics and acid solutions a) The following reaction occurs when HCl is bubbled into water at 25°C and latm pressure: HCl(g) -> H+(aq) + Cl (aq) Calculate AS rxn for this reaction. b) Sketch two possible structures of the hydronium ion in water. Circle the hydronium ion in each case. Also sketch the local structures of water surrounding the hydronium and chloride ions in aqueous solution. Include the important water molecules in both sets of sketches. c) Draw a...
QUESTION 13
Which of the following would occur if a mutation caused Kinase 1
to be unable to be phosphorylated? (Select all)
RTK would bind VEGF
RTK would phosphorylate itself
RAS would become active
The phosphorylation cascade would occur
The endothelial cell would divide
0.2 points
QUESTION 14
Imagine that an endothelial cell has a mutation in several of
the enzymes that perform mismatch repair. The endothelial cell
replicates its DNA and then divides into two cells. The resulting...
(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...
specifically on finite
i pmu r the number of objøcts or ways. Leave your answers in fornsiala form, such as C(3, 2) nporkan?(2) Are repeats poasib Two points each imal digits will have at least one xpeated digin? I. This is the oounting problem Al ancmher so ask yourelr (1) ls onder ipo n How many strings of four bexadeci ) A Compuir Science indtructor has a stack of blue can this i For parts c, d. and e, suppose...
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