cs2007_2026T1_Q1_NA.pdf
Machine Learning Techniques(MLT) · Quiz 1 · Jan 2026
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Question 2 MCQ · 3.0 marks
Consider a clustering problem with [[IMAGE:2e040ee5e3967d7d_3_2]] data-points and two clusters [[IMAGE:2e040ee5e3967d7d_3_3]] . As initialization, a
subset of the dataset comprising the first fifty data-points, call this [[IMAGE:2e040ee5e3967d7d_3_4]] , are assigned to cluster [[IMAGE:2e040ee5e3967d7d_3_5]]
and the remaining points, call this [[IMAGE:2e040ee5e3967d7d_3_6]] , are assigned to cluster [[IMAGE:2e040ee5e3967d7d_3_7]] . K-means is run for this
configuration and it converges after [[IMAGE:2e040ee5e3967d7d_3_8]] iterations.
Consider the following scenarios:
[[IMAGE:2e040ee5e3967d7d_3_9]] : After convergence, it is observed that all points in [[IMAGE:2e040ee5e3967d7d_3_10]] are assigned to cluster [[IMAGE:2e040ee5e3967d7d_3_11]] and
all points in [[IMAGE:2e040ee5e3967d7d_3_12]] are assigned to cluster [[IMAGE:2e040ee5e3967d7d_3_13]] .
[[IMAGE:2e040ee5e3967d7d_3_14]] : After convergence, it is observed that all points in [[IMAGE:2e040ee5e3967d7d_3_15]] are assigned to cluster [[IMAGE:2e040ee5e3967d7d_3_16]] and
all points in [[IMAGE:2e040ee5e3967d7d_3_17]] are assigned to cluster [[IMAGE:2e040ee5e3967d7d_3_18]] .
Which of the following is true?
Scenario-1 is possible, but scenario-2 is impossible.
Scenario-1 is impossible, but scenario-2 is possible.
Both scenarios are possible.
Both scenarios are impossible.
A published solution is not available for this question yet.
Question 3 MSQ · 3.0 marks
Consider a centered dataset [[IMAGE:2e040ee5e3967d7d_4_19]] in [[IMAGE:2e040ee5e3967d7d_4_20]] such that every data-point [[IMAGE:2e040ee5e3967d7d_4_21]] in [[IMAGE:2e040ee5e3967d7d_4_22]] satisfies the
equation [[IMAGE:2e040ee5e3967d7d_4_23]] . Standard PCA is performed on the dataset. Which of the
following could be the fourth principal component?
[[IMAGE:2e040ee5e3967d7d_4_24]]
[[IMAGE:2e040ee5e3967d7d_4_25]]
[[IMAGE:2e040ee5e3967d7d_4_26]]
[[IMAGE:2e040ee5e3967d7d_4_27]]
A published solution is not available for this question yet.
Question 4 NAT · 3.0 marks
Consider a polynomial kernel of degree [[IMAGE:2e040ee5e3967d7d_4_28]] on a feature space of dimension [[IMAGE:2e040ee5e3967d7d_4_29]] . How many features
will the transformed space have [[IMAGE:2e040ee5e3967d7d_4_30]]
A published solution is not available for this question yet.
Question 5 NAT · 3.0 marks
Consider the Gaussian kernel, [[IMAGE:2e040ee5e3967d7d_5_31]] with [[IMAGE:2e040ee5e3967d7d_5_32]] . Compute the value of
[[IMAGE:2e040ee5e3967d7d_5_33]] and enter your answer correct to two decimal places.
A published solution is not available for this question yet.
Question 6 NAT · 3.0 marks
Consider the following data-points in a clustering problem with five data-points and three clusters
(k = 3):
[[IMAGE:2e040ee5e3967d7d_5_34]]
K-means [[IMAGE:2e040ee5e3967d7d_5_35]] is used to initialize the three means. The first mean is chosen to be [[IMAGE:2e040ee5e3967d7d_5_36]] and
the second mean to be [[IMAGE:2e040ee5e3967d7d_5_37]] . Find the probability of choosing [[IMAGE:2e040ee5e3967d7d_5_38]] as the third mean.
That is, compute [[IMAGE:2e040ee5e3967d7d_5_39]] . Enter your answer correct to one
decimal place.
A published solution is not available for this question yet.
Question 7 NAT · 3.0 marks
Consider a cube of edge-length [[IMAGE:2e040ee5e3967d7d_6_40]] centered at the origin with its corners represented as
[[IMAGE:2e040ee5e3967d7d_6_41]] . These eight points make up a dataset [[IMAGE:2e040ee5e3967d7d_6_42]] .
Based on the above data, answer the given subquestions.
Find the covariance matrix [[IMAGE:2e040ee5e3967d7d_6_43]] of the dataset. Enter the sum of all the entries of [[IMAGE:2e040ee5e3967d7d_6_44]] as the answer.
A published solution is not available for this question yet.
Question 8 NAT · 2.0 marks
Consider a cube of edge-length [[IMAGE:2e040ee5e3967d7d_6_40]] centered at the origin with its corners represented as
[[IMAGE:2e040ee5e3967d7d_6_41]] . These eight points make up a dataset [[IMAGE:2e040ee5e3967d7d_6_42]] .
Based on the above data, answer the given subquestions.
Let [[IMAGE:2e040ee5e3967d7d_6_45]] be some unit vector. Find the variance of the dataset along the direction [[IMAGE:2e040ee5e3967d7d_6_46]] .
A published solution is not available for this question yet.
Question 9 NAT · 2.0 marks
Standard PCA is performed on a centered dataset in [[IMAGE:2e040ee5e3967d7d_7_47]] . The first three principal components are:
[[IMAGE:2e040ee5e3967d7d_7_48]]
The first two principal components are retained and the third is discarded. The coordinate
representation of the data-point [[IMAGE:2e040ee5e3967d7d_7_49]] after projection onto the first two principal components
is [[IMAGE:2e040ee5e3967d7d_7_50]] .
Based on the above data, answer the given subquestions.
Find [[IMAGE:2e040ee5e3967d7d_7_51]] . Enter your answer correct to three decimal places.
A published solution is not available for this question yet.
Question 10 NAT · 2.0 marks
Standard PCA is performed on a centered dataset in [[IMAGE:2e040ee5e3967d7d_7_47]] . The first three principal components are:
[[IMAGE:2e040ee5e3967d7d_7_48]]
The first two principal components are retained and the third is discarded. The coordinate
representation of the data-point [[IMAGE:2e040ee5e3967d7d_7_49]] after projection onto the first two principal components
is [[IMAGE:2e040ee5e3967d7d_7_50]] .
Based on the above data, answer the given subquestions.
Find [[IMAGE:2e040ee5e3967d7d_7_52]] . Enter your answer correct to three decimal places.
A published solution is not available for this question yet.
Question 11 MCQ · 2.0 marks
Answer true or false for the given subquestions.
If [[IMAGE:2e040ee5e3967d7d_8_53]] and [[IMAGE:2e040ee5e3967d7d_8_54]] are valid kernels, then [[IMAGE:2e040ee5e3967d7d_8_55]] is also a valid
kernel.
True
False
A published solution is not available for this question yet.
Question 12 MCQ · 2.0 marks
Answer true or false for the given subquestions.
If [[IMAGE:2e040ee5e3967d7d_8_56]] is a data-matrix of shape [[IMAGE:2e040ee5e3967d7d_8_57]] , then [[IMAGE:2e040ee5e3967d7d_8_58]] and [[IMAGE:2e040ee5e3967d7d_8_59]] have the same eigenvectors.
True
False
A published solution is not available for this question yet.
Question 13 MCQ · 2.0 marks
Consider a dataset in [[IMAGE:2e040ee5e3967d7d_8_60]] for a clustering problem with two clusters [[IMAGE:2e040ee5e3967d7d_8_61]] . The [[IMAGE:2e040ee5e3967d7d_8_62]] data-point is
represented as [[IMAGE:2e040ee5e3967d7d_8_63]] .
[[IMAGE:2e040ee5e3967d7d_9_64]]
[[IMAGE:2e040ee5e3967d7d_9_65]] indicates the cluster assignment vector at the end of time-step [[IMAGE:2e040ee5e3967d7d_9_66]] . [[IMAGE:2e040ee5e3967d7d_9_67]]
indicates the initial assignment. The cluster indices are represented by [[IMAGE:2e040ee5e3967d7d_9_68]] and [[IMAGE:2e040ee5e3967d7d_9_69]] , that is,
[[IMAGE:2e040ee5e3967d7d_9_70]] .
Based on the above data, answer the given subquestions.
If [[IMAGE:2e040ee5e3967d7d_9_71]] , which of the following is the final cluster assignment after running K-means
on this dataset with this initial configuration?
[[IMAGE:2e040ee5e3967d7d_9_72]]
[[IMAGE:2e040ee5e3967d7d_9_73]]
[[IMAGE:2e040ee5e3967d7d_9_74]]
[[IMAGE:2e040ee5e3967d7d_9_75]]
[[IMAGE:2e040ee5e3967d7d_9_76]]
A published solution is not available for this question yet.
Question 14 MCQ · 2.0 marks
Consider a dataset in [[IMAGE:2e040ee5e3967d7d_8_60]] for a clustering problem with two clusters [[IMAGE:2e040ee5e3967d7d_8_61]] . The [[IMAGE:2e040ee5e3967d7d_8_62]] data-point is
represented as [[IMAGE:2e040ee5e3967d7d_8_63]] .
[[IMAGE:2e040ee5e3967d7d_9_64]]
[[IMAGE:2e040ee5e3967d7d_9_65]] indicates the cluster assignment vector at the end of time-step [[IMAGE:2e040ee5e3967d7d_9_66]] . [[IMAGE:2e040ee5e3967d7d_9_67]]
indicates the initial assignment. The cluster indices are represented by [[IMAGE:2e040ee5e3967d7d_9_68]] and [[IMAGE:2e040ee5e3967d7d_9_69]] , that is,
[[IMAGE:2e040ee5e3967d7d_9_70]] .
Based on the above data, answer the given subquestions.
If [[IMAGE:2e040ee5e3967d7d_9_77]] , which of the following is the final cluster assignment after running K-means
on this dataset with this initial configuration?
[[IMAGE:2e040ee5e3967d7d_10_78]]
[[IMAGE:2e040ee5e3967d7d_10_79]]
[[IMAGE:2e040ee5e3967d7d_10_80]]
[[IMAGE:2e040ee5e3967d7d_10_81]]
[[IMAGE:2e040ee5e3967d7d_10_82]]
A published solution is not available for this question yet.
Question 15 MCQ · 2.0 marks
Let [[IMAGE:2e040ee5e3967d7d_10_83]] be i.i.d. observations from the mixture distribution
[[IMAGE:2e040ee5e3967d7d_10_84]]
where
[[IMAGE:2e040ee5e3967d7d_10_85]]
The observed data are
[[IMAGE:2e040ee5e3967d7d_10_86]]
Assume that the initial estimate of the mixing parameter is
[[IMAGE:2e040ee5e3967d7d_10_87]]
Based on the above data, answer the given subquestions.
Which of the following expressions correctly represents the log-likelihood function [[IMAGE:2e040ee5e3967d7d_11_88]] for the
given data?
[[IMAGE:2e040ee5e3967d7d_11_89]]
[[IMAGE:2e040ee5e3967d7d_11_90]]
[[IMAGE:2e040ee5e3967d7d_11_91]]
[[IMAGE:2e040ee5e3967d7d_11_92]]
A published solution is not available for this question yet.
Question 16 NAT · 3.0 marks
Let [[IMAGE:2e040ee5e3967d7d_10_83]] be i.i.d. observations from the mixture distribution
[[IMAGE:2e040ee5e3967d7d_10_84]]
where
[[IMAGE:2e040ee5e3967d7d_10_85]]
The observed data are
[[IMAGE:2e040ee5e3967d7d_10_86]]
Assume that the initial estimate of the mixing parameter is
[[IMAGE:2e040ee5e3967d7d_10_87]]
Based on the above data, answer the given subquestions.
Consider the E-step of the EM algorithm. Introduce latent variables [[IMAGE:2e040ee5e3967d7d_11_93]] such that [[IMAGE:2e040ee5e3967d7d_11_94]] if
[[IMAGE:2e040ee5e3967d7d_11_95]] is generated from [[IMAGE:2e040ee5e3967d7d_11_96]] . Compute the posterior responsibility
[[IMAGE:2e040ee5e3967d7d_11_97]]
for each observation [[IMAGE:2e040ee5e3967d7d_11_98]] . Write down [[IMAGE:2e040ee5e3967d7d_11_99]] as your answer. Enter the answer correct to two
decimal places.
A published solution is not available for this question yet.
Question 17 MCQ · 3.0 marks
Let [[IMAGE:2e040ee5e3967d7d_10_83]] be i.i.d. observations from the mixture distribution
[[IMAGE:2e040ee5e3967d7d_10_84]]
where
[[IMAGE:2e040ee5e3967d7d_10_85]]
The observed data are
[[IMAGE:2e040ee5e3967d7d_10_86]]
Assume that the initial estimate of the mixing parameter is
[[IMAGE:2e040ee5e3967d7d_10_87]]
Based on the above data, answer the given subquestions.
Using a Maximum A Posteriori (MAP) decision rule, a data point [[IMAGE:2e040ee5e3967d7d_12_100]] is assigned to mixture 2 if the
posterior responsibility [[IMAGE:2e040ee5e3967d7d_12_101]] . Based on the values calculated in the E-step, which data
point(s) are classified as belonging to Component 2?
[[IMAGE:2e040ee5e3967d7d_12_102]]
[[IMAGE:2e040ee5e3967d7d_12_103]]
[[IMAGE:2e040ee5e3967d7d_12_104]]
All four points
A published solution is not available for this question yet.