PSTAT 131 EVALUATION EXAMS ANSWERS AND
QUESTIONS SET A+
✔✔the height of a each internal node is proportional to - ✔✔the dissimilarity between its
children
✔✔What is linkage in clustering? - ✔✔Linkage measures the dissimilarity between two
clusters, measured by the Euclidean distance
✔✔Single linkage - ✔✔the minimum dissimilarity between any pair of points from two
different clusters
aka
a point from each cluster that has the smallest euclidean distance between each other
✔✔Complete linkage - ✔✔the maximum dissimilarity between any pair of points from
two different clusters
aka
a point from each cluster that has the largest Euclidean distance between each other
✔✔average linkage - ✔✔Average dissimilarity between all pairs of inter-cluster data
points
✔✔limitations of linkage - ✔✔single linkage: forms chaining, when clusters are too
spread apart but one single chain can combine everything
complete linkage: forms crowding, when points are closer to other clusters but forced to
come to its own
average linkage: strikes a balance
, ✔✔Principal Component Analysis (PCA) - ✔✔a dimension-reduction tool that can be
used to reduce a large set of variables to a small set that still contains most of the
information in the large set
helps us avoid working with high-dimensional data and removes excess noise
✔✔T/F, we can only visualize data in up to 3 dimensions? - ✔✔true
✔✔T/F, each principal component Z is a linear combination of the original features (X1,
..., Xp) - ✔✔true, linear dimension reduction
✔✔T/F, PCA finds a small number of dimensions that are as interesting as possible -
✔✔true
✔✔T/F, computing the first PC is equivalent to finding the loadings of the first PC? -
✔✔true
✔✔T/F, in PCA, loading matrix * original features (X1...Xp) = Z components - ✔✔true
✔✔T/F, the data matrix X is required to have 0 column means - ✔✔true
When the data matrix X has column means equal to 0, it means that the mean value of
each column in the dataset is 0, required for centering data
✔✔T/F, PCA requires no constraint on loadings - ✔✔False, requires pre-defined
constraint on loadings
✔✔Finding the second PC can be done similar to PC1, with an additional constraint
that... - ✔✔PC2 is uncorrelated to PC1
✔✔T/F, PC1 and PC2 are orthogonal - ✔✔true
✔✔Features need to be ________ before PCA is performed - ✔✔centered
✔✔T/F, The results from PCA depend on the feature scales? - ✔✔true
✔✔When would scaling of features not be appropriate during PCA? - ✔✔when all
features are on the same scale to begin with
✔✔Proportion of Variance Explained (PVE) - ✔✔percent of variance captured by data
= (The variance in the data explained by the m-th PC) / total variance in data
QUESTIONS SET A+
✔✔the height of a each internal node is proportional to - ✔✔the dissimilarity between its
children
✔✔What is linkage in clustering? - ✔✔Linkage measures the dissimilarity between two
clusters, measured by the Euclidean distance
✔✔Single linkage - ✔✔the minimum dissimilarity between any pair of points from two
different clusters
aka
a point from each cluster that has the smallest euclidean distance between each other
✔✔Complete linkage - ✔✔the maximum dissimilarity between any pair of points from
two different clusters
aka
a point from each cluster that has the largest Euclidean distance between each other
✔✔average linkage - ✔✔Average dissimilarity between all pairs of inter-cluster data
points
✔✔limitations of linkage - ✔✔single linkage: forms chaining, when clusters are too
spread apart but one single chain can combine everything
complete linkage: forms crowding, when points are closer to other clusters but forced to
come to its own
average linkage: strikes a balance
, ✔✔Principal Component Analysis (PCA) - ✔✔a dimension-reduction tool that can be
used to reduce a large set of variables to a small set that still contains most of the
information in the large set
helps us avoid working with high-dimensional data and removes excess noise
✔✔T/F, we can only visualize data in up to 3 dimensions? - ✔✔true
✔✔T/F, each principal component Z is a linear combination of the original features (X1,
..., Xp) - ✔✔true, linear dimension reduction
✔✔T/F, PCA finds a small number of dimensions that are as interesting as possible -
✔✔true
✔✔T/F, computing the first PC is equivalent to finding the loadings of the first PC? -
✔✔true
✔✔T/F, in PCA, loading matrix * original features (X1...Xp) = Z components - ✔✔true
✔✔T/F, the data matrix X is required to have 0 column means - ✔✔true
When the data matrix X has column means equal to 0, it means that the mean value of
each column in the dataset is 0, required for centering data
✔✔T/F, PCA requires no constraint on loadings - ✔✔False, requires pre-defined
constraint on loadings
✔✔Finding the second PC can be done similar to PC1, with an additional constraint
that... - ✔✔PC2 is uncorrelated to PC1
✔✔T/F, PC1 and PC2 are orthogonal - ✔✔true
✔✔Features need to be ________ before PCA is performed - ✔✔centered
✔✔T/F, The results from PCA depend on the feature scales? - ✔✔true
✔✔When would scaling of features not be appropriate during PCA? - ✔✔when all
features are on the same scale to begin with
✔✔Proportion of Variance Explained (PVE) - ✔✔percent of variance captured by data
= (The variance in the data explained by the m-th PC) / total variance in data
