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In: Statistics and Probability

Question 1. What is k-means clustering? How does it work? Give a few examples that you...

Question 1.

What is k-means clustering? How does it work? Give a few examples that you would use this algorithm.

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Question 2.

What is k-nearest neighbor? How does it work? Give a few examples that you would use this algorithm.

Expert Solution

SOLUTION1:

K Means Clustering

K means is an iterative clustering algorithm that aims to find local maxima in each iteration. This algorithm works in these 5 steps :

Specify the desired number of clusters K : Let us choose k=2 for these 5 data points in 2-D space.

Randomly assign each data point to a cluster : Let’s assign three points in cluster 1 shown using red color and two points in cluster 2 shown using grey color.

Compute cluster centroids : The centroid of data points in the red cluster is shown using red cross and those in grey cluster using grey cross.

Re-assign each point to the closest cluster centroid : Note that only the data point at the bottom is assigned to the red cluster even though its closer to the centroid of grey cluster. Thus, we assign that data point into grey cluster

Re-compute cluster centroids : Now, re-computing the centroids for both the clusters.

Repeat steps 4 and 5 until no improvements are possible : Similarly, we’ll repeat the 4^th and 5^th steps until we’ll reach global optima. When there will be no further switching of data points between two clusters for two successive repeats. It will mark the termination of the algorithm if not explicitly mentioned.

. Applications of Clustering

Clustering has a large no. of applications spread across various domains. Some of the most popular applications of clustering are:

Recommendation engines
Market segmentation
Social network analysis
Search result grouping
Medical imaging
Image segmentation
Anomaly detection

Solution2:

KNN can be used for both classification and regression predictive problems. However, it is more widely used in classification problems in the industry. To evaluate any technique we generally look at 3 important aspects:

1. Ease to interpret output

2. Calculation time

3. Predictive Power

We were unable to transcribe this image

Applications of KNN Classifier Used in classification Used to get missing values . Used in pattern recognition Used in gene expression Used in protein-protein prediction Used to get 3D structure of protein . Used to measure document similarity

orchestra answered 1 year ago

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