Nptel Deep Learning - IIT Ropar Week 1 Assignment Answer

 

Week 1 : Assignment 1

Due date: 2025-02-05, 23:59 IST.

Assignment not submitted

Common data for questions 1,2 and 3
In the figure shown below, the blue points belong to class 1 (positive class) and the red points belong to class 0 (negative class). Suppose that we use a perceptron model, with the weight vector w as shown in the figure, to separate these data points. We define the point belongs to class 1 if wTx≥0${\text{w}}^{\text{T}}\text{x}\ge 0$ else it belongs to class 0.

1 point

The points G$G$ and C$C$ will be classified as?
Note: the notation (G,0)$(G,0)$ denotes the point G$G$ will be classified as class-0 and (C,1)$(C,1)$ denotes the point C$C$ will be classified as class-1

(C,0),(G,0)$(C,0),(G,0)$

(C,0),(G,1)$(C,0),(G,1)$

(C,1),(G,1)$(C,1),(G,1)$

(C,1),(G,0)$<b>(</b>\mathrm{<b>C</b>}<b>,</b>\mathrm{<b>1</b>}<b>)</b><b>,</b><b>(</b>\mathrm{<b>G</b>}<b>,</b>\mathrm{<b>0</b>}<b>)</b>$

1 point

The statement that “there exists more than one decision lines that could separate these data points with zero error” is,

 True

 False

1 point

Suppose that we multiply the weight vector w by −1. Then the same points G$G$ and C$C$ will be classified as?

(C,0),(G,0)$(C,0),(G,0)$

(C,0),(G,1)$(C,0),(G,1)$

(C,1),(G,1)$(C,1),(G,1)$

(C,1),(G,0)$(C,1),(G,0)$

1 point

Which of the following can be achieved using the perceptron algorithm in machine learning?

 Grouping similar data points into clusters, such as organizing customers based on purchasing behavior.

 Solving optimization problems, such as finding the maximum profit in a business scenario.

 Classifying data, such as determining whether an email is spam or not.

 Finding the shortest path in a graph, such as determining the quickest route between two cities.

1 point

Consider the following table, where x1$x_1$ and x2$x_2$ are features and y$y$ is a label.

Assume that the elements in w are initialized to zero and the perception learning algorithm is used to update the weights w. If the learning algorithm runs for long enough iterations, then

 The algorithm never converges

 The algorithm converges (i.e., no further weight updates) after some iterations

 The classification error remains greater than zero

 The classification error becomes zero eventually

1 point

We know from the lecture that the decision boundary learned by the perceptron is a line in R2${\mathbb{R}}^2$. We also observed that it divides the entire space of R2${\mathbb{R}}^2$ into two regions, suppose that the input vector x∈R4$x\in {\mathbb{R}}^4$, then the perceptron decision boundary will divide the whole R4${\mathbb{R}}^4$ space into how many regions?

 It depends on whether the data points are linearly separable or not.

 3

 4

 2

 5

1 point

Choose the correct input-output pair for the given MP Neuron.
f(x)={1,0,ifx1+x2+x3<2otherwise$f(x)=\{\begin{array}{ll}1,& \text{if}{x}_1+x_2+x_3<2\\ 0,& \text{otherwise}\end{array}$

y=1$y=1$ for (x1,x2,x3)$(x_1,x_2,x_3)$ = (0, 0, 0)

y=0$y=0$ for (x1,x2,x3)$(x_1,x_2,x_3)$ = (0, 0, 1)

y=1$y=1$ for (x1,x2,x3)$(x_1,x_2,x_3)$ = (1, 0, 0)

y=1$y=1$ for (x1,x2,x3)$(x_1,x_2,x_3)$ = (1, 1, 1)

y=0$y=0$ for (x1,x2,x3)$(x_1,x_2,x_3)$ = (1, 0, 1)

1 point

Consider the following table, where x1$x_1$ and x2$x_2$ are features (packed into a single vector x=[x1x2]$\text{x}=\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]$) and y$y$ is a label:

Suppose that the perceptron model is used to classify the data points. Suppose further that the weights w are initialized to w = [11]$\left[\begin{array}{c}1\\ 1\end{array}\right]$. The following rule is used for classification,
y={10ifwTx>0ifwTx≤0$y=\{\begin{array}{ll}1& \text{if}{\text{w}}^{\text{T}}\text{x}>0\\ 0& \text{if}{\text{w}}^{\text{T}}\text{x}\le 0\end{array}$

The perceptron learning algorithm is used to update the weight vector w. Then, how many times the weight vector w will get updated during the entire training process?

 0

 1

 2

 Not possible to determine

1 point

Which of the following threshold values of MP neuron implements AND Boolean function? Assume that the number of inputs to the neuron is 3 and the neuron does not have any inhibitory inputs.

 1

 2

 3

 4

 5

1 point

Consider points shown in the picture. The vector w = [−11]$\left[\begin{array}{c}-1\\ 1\end{array}\right]$.As per this weight vector, the Perceptron algorithm will predict which classes for the data points x1$x_1$ and x2$x_2$.
NOTE: y={10ifwTx>0ifwTx≤0$y=\{\begin{array}{ll}1& \text{if}{\text{w}}^{\text{T}}\text{x}>0\\ 0& \text{if}{\text{w}}^{\text{T}}\text{x}\le 0\end{array}$

x1$x_1$ = −1

x1$x_1$ = 1

x2$x_2$ = −1

x2$x_2$ = 1