Computer Science Homework Help

1. Find a linear recurrence and initial conditions for the sequence an dened by the following, an

number of divisors 2 f 2;3;5g . For example a6 = 2, a7 = 0, and a30 = 3.

2. Find the following properties of the graph shown in Fig. 1 (next page). The degree distribution, the

betweeness centrality of the edge (6;1), the adjacency, degree, and laplacian matrices.

3. Consider gradient descent with learning parameter

. Suppose you have the objective function f (x ) =

x2 6x+ 10 to which you apply this algorithm for an initial point x0 = 5. For which values of is it

true that f (x1 ) f (x0 ) (assume0)?

4. A dataset has been provided with this assignment. The le is called bda-final-data.txt . Using

Python and the sklearnlibraries answer the following about the dataset. Note: this is a supervised

learning problem (binary classication) with 10 features and 1 label. Your answers to these questions

should be supported by evidence in the form of scripts and plots.

(a) Which feature has the strongest correlation with the class label?

1

(b) How many of the features provide useful information about the classication task?

(c) Which, if any, of the useful features are redundant?

(d) How many separate clusters are there in the dataset?

2