# Finding cluster density

1.

In CLIQUE, the threshold used to find cluster density remains constant,

even as the number of dimensions increases. This is a potential problem

since density drops as dimensionality increases; i.e., to find clusters in higher

dimensions the threshold has to be set at a level that may well result in the

merging of low-dimensional clusters. Comment on whether you feel this is

truly a problem and, if so, how you might modify CLIQUE to address this

problem.

### 2. QUESTION 2

Name at least one situation in which you would not want to use clustering based on SNN similarity or density.

### QUESTION 3

Give an example of a set of clusters in which merging based on the closeness

of clusters leads to a more natural set of clusters than merging based on the

strength of connection (interconnectedness) of clusters.

### QUESTION 4

We take a sample of adults and measure their heights. If we record the gender of each person, we can calculate the average height and the variance of the height, separately, for men and women. Suppose, however, that this information was not recorded. Would it be possible to still obtain this information? Explain.

### QUESTION 5

1. Explain the difference between likelihood and probability.

### QUESTION 6

1. Traditional K-means has a number of limitations, such as sensitivity to outliers and difficulty in handling clusters of different sizes and densities, or with non-globular shapes. Comment on the ability of fuzzy c-means to handle these situations.

### QUESTION 7

1. Clusters of documents can be summarized by finding the top terms (words) for the documents in the cluster, e.g., by taking the most frequent k terms, where k is a constant, say 10, or by taking all terms that occur more frequently than a specified threshold. Suppose that K-means is used to find clusters of both documents and words for a document data set.

(a) How might a set of term clusters defined by the top terms in a document cluster differ from the word clusters found by clustering the terms with K-means?

(b) How could term clustering be used to define clusters of documents?

### QUESTION 8

1. Suppose we find K clusters using Ward’s method, bisecting K-means, and ordinary K-means. Which of these solutions represents a local or global minimum? Explain.

### QUESTION 9

1. You are given a data set with 100 records and are asked to cluster the data. You use K-means to cluster the data, but for all values of K, 1 ≤ K ≤ 100, the K-means algorithm returns only one non-empty cluster. You then apply an incremental version of K-means, but obtain exactly the same result. How is this possible? How would single link or DBSCAN handle such data?

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