利用matlab编程实现以下问题：This assignment is about resource planning A hospital intends to purchase a fleet of cordless wireless infusion pumps for a single floor of their building Recharge stations must also

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Part 1:

Q1.1. Load the infusion pump location data.

• Load the data from the InfusionPumpLocations.xlsx file using the xlsread() function.
• Store the x and y coordinates in separate variables.

Q1.2. Use MATLAB’s inbuilt k-means function, kmeans, to determine the minimal cost arrangement.

• Use the kmeans() function to cluster the infusion pump locations into the optimal number of clusters.
• Calculate the cost for each cluster, taking into account the distance between the pumps and their assigned recharge station.
• Determine the optimal number and locations of the recharge stations and plot them on the same graph as the pump locations, coloring the pumps according to their recharge station assignments.
• Plot the cost versus the number of recharge stations.

Q1.3. What are the three primary assumptions made for k-means to work?

• The number of clusters is known in advance.
• The clusters are spherical and have equal variance.
• The data points are independent and identically distributed. Is each of these satisfied for the infusion pump data?
• The number of clusters is not known in advance.
• The clusters may not be spherical or have equal variance.
• The data points may not be independent and identically distributed. Justify your answer and explain the effect it has on the clustering performance.
• The assumptions may affect the accuracy of the clustering results, as k-means may not be able to find the optimal clusters for the infusion pump data.

Part 2:

Q2.1. Use MATLAB’s inbuilt agglomerative clustering function, linkage, to implement agglomerative hierarchical clustering.

• Use the linkage() function with the specified linkage type and distance metric to cluster the infusion pump locations into the optimal number of clusters.
• Calculate the cost for each cluster, taking into account the distance between the pumps and their assigned recharge station.
• Determine the optimal number and locations of the recharge stations and plot them on the same graph as the pump locations, coloring the pumps according to their recharge station assignments.
• Plot the cost versus the number of recharge stations.

Q2.2. Repeat using average linkage.

Q2.3. Repeat using single linkage.

Q2.4. Which linkage gives the same result as k-means? Why?

• The complete linkage gives the same result as k-means, as it minimizes the maximum distance between the points in a cluster.

Q2.5. Explain why single linkage gives such poor results.

• Single linkage tends to create long chains of points, as it only considers the minimum distance between points in different clusters. This can lead to clusters that are not compact or well-separated