[SOLVED] CS412-Homework 5

Description

Question 1

Suppose we want to predict whether a restaurant is popular based on its price, delivery, and cuisine, and we collected the training data as shown in table 1. Answer the following questions.

Table 1: Training dataset (P – popular, NP – not popular)

1a. Based on the training data, we want to construct a Naive Bayes classifier. (No smoothing is required.) Please estimate the following terms: 1a(i). [4] Pr(Popularity = ‘P’)

1a(ii). [4] Pr(Popularity = ‘NP’)

1a(iii). [4] Pr(Price = ‘$’, Delivery = ‘Yes’ , Cuisine = ‘Korean’ | Popularity = ‘P’)

1a(iv). [4] Pr(Price = ‘$’, Delivery = ‘Yes’ , Cuisine = ‘Korean’ | Popularity = ‘NP’)

1b.[6] Suppose a restaurant has the values: Price = ‘$’, Delivery = ‘Yes’ , Cuisine = ‘Korean’. Based on the calculation in part (1a.), is this restaurant classified as popular?

1c. [4] Design an ensemble method for Naive Bayes to further improve the accuracy and briefly describe the steps.

1d. [4] Describe the metrics that can effectively evaluate the classification of data with rare positive examples.

2                    Question 2

We have eight training points, which are plotted in figure 1.

Table 2: Dataset                                            Figure 1: 2-D scatterplot of the Dataset

Also, we have four test points with their true labels. Please answer following questions.

Table 3: Test Dataset

2a.[10] Perform k-nearest neighbor classification with K = 1. What’s the testing error? (Please use Euclidean distance. Show your reasoning.)

2b. [10] Do the same thing as question 2a with K = 2.

2c. [10] A linear classifier f(x) = a ∗ x₁ + b ∗ x₂ + c works as follows: if f(x) >= 0 , predict x as +1; otherwise, predict x as −1. Design a reasonable linear classifier(i.e. choose proper a, b, c). What’s the training error? What about the testing error? Show your reasoning(Your design doesn’t need to be optimal).

2d. [10] Compare KNN and linear classification method(e.g. SVM). You may draw conclusions based on your experience with question 2a-2c.

3                    Question 3

Suppose we want to cluster the following 13 points:

Table 4: Dataset                                            Figure 2: 2-D scatterplot of the Dataset

3a. [10] Cluster above points using K-means algorithm with k = 2. Please use (0, 3) and (6, 4) as the initial center points for the two clusters. Show your reasoning.

3b. [10] Now we want to use DBSCAN, a density-based algorithm, with MinPts = 2, and Eps = 1.5. Outline your clustering process.

3c. [10] Please perform AGNES, a hierarchical clustering algorithm on above points. Please use single link method and adopt Euclidean distance as the dissimilarity measure.