CME 250 Homework 4 Part 1

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K-means Clustering

True or false: Two runs of k-means will always produce the same clusters and assignments.

1 point

True

False

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Select all that apply. K-means clustering will NOT work well on recovering clusters that:

1 point

Have very different covariances

Are spherically shaped

Contain outliers

Are stretched out and non-convex in feature space

Hierarchical Clustering

Which of the following could result in producing different dendrograms on the same dataset? Assume we are using a bottom-up (agglomerative) algorithm.

1 point

Different distance metrics

Different linkages

Different initializations

Different features used

Select the dendrogram built using complete-linkage on the following 1-dimensional dataset.

1 point

Option 1

Option 2

Option 3

Option 4

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What is the most appropriate number of clusters for the dataset represented by the following dendrogram?

1 point

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Dimensionality Reduction

Which of the following is true about PCA?

1 point

PCA captures non-linear relationships between features.

Before performing PCA, features should be scaled to the same units.

PCA needs to be initialized.

PCA can find a bad local minimum.

Consider 3 data points in 2D space: (-1, -1), (0, 0), (1, 1). What is the first principal component of the data?

1 point

(0, 1)

(1/√ 3, √ 2/√ 3)

(√ 2 /2 , √ 2/ 2 )

(1, 0)

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Decision Trees

What is the minimum number of recursive binary splits needed to classify the following dataset of 6 samples with 100% accuracy?

1 point

Compared to a decision tree, random forests:

1 point

Are much more biased, have slightly less variance, and are less interpretable.

Are much more biased, have slightly less variance, and are more interpretable.

Are slightly more biased, have much less variance, and are less interpretable.

Are slightly more biased, have much less variance, and are more interpretable.

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You have a dataset of 1000 observations and 300 features. You train a random forest to perform binary classification and observe a training accuracy of 1.00 and a validation accuracy of 0.63. Which of the following would be a reasonable next step to improve the model?

1 point

Get more training data.

Perform feature selection or dimensionality reduction.

Decrease the minimum samples to split on in the random forest.

Increase the minimum number of samples per leaf in the random forest.

Increase maximum depth of each tree in the random forest.

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