Assignment (20 Marks)
Q.1 Marks 4
In the context of machine learning, eigenvalues and eigenvectors are crucial concepts,
particularly in methods like Principal Component Analysis (PCA), Singular Value
Decomposition (SVD), and various linear transformations in feature space. These
mathematical tools help in understanding and reducing dimensionality, improving algorithm
performance, and extracting meaningful patterns from the data.
Consider a scenario where a data scientist is working on a large dataset to predict customer
churn. To simplify the predictive modeling, the scientist wants to reduce the dataset's
dimensionality without losing significant information. This is often achieved through PCA,
which requires computation of eigenvalues and eigenvectors.
To grasp the underlying concepts, the scientist starts with a simpler problem — computing the
eigenvalues of a smaller matrix. This matrix could represent a simplified transformation in a
reduced feature space. Here is the matrix in question:
A=
[
1−1 0
−1 2 1
0 1 1
]
a) Calculate Eigenvalues: The objective is to compute eigenvalues of matrix A. This will provide
insights into the variance explained by the components when matrix A is used in PCA.
b) Interpret Results: Understanding the eigenvalues helps in determining the importance of
each principal component. What is the relation between the sum of the Eigenvalues with
matrix A? What is the relation between product of the Eigenvalues with matrix A?
Q.2 Marks 4
As a senior data analyst at XYZ Corp, a leader in retail, you've been tasked with evaluating the
efficacy of a recently concluded, multifaceted campaign. This campaign, aimed at boosting the
sales of a high-profile product, spanned multiple channels including digital (emails and social
media), traditional media (TV and print), and various experimental platforms.
The primary objective is to assess the performance of a predictive model designed to identify
potential buyers among those exposed to the campaign. This assessment is crucial, as its
outcomes will guide the strategic planning for upcoming marketing efforts.
The dataset collected is extensive, including:
Engagement metrics such as number of ad impressions, clicks, and time spent on
product pages.
Viewer demographics including age, location, and previous purchase history.
Follow-up actions, specifically whether viewers purchased the product post-ad
exposure.
Additional engagement metrics unrelated to the campaign, like overall website traffic
and user interaction across non-campaign content.
Extended Data Description:
