Questions and Topics Review Dec. 10, 2013 - PowerPoint Presentation

Slide1

Questions and Topics Review Dec. 10, 2013

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AGNES /Hierarchical clustering with K-means; what are the main

differences?

2. K-means

has a runtime complexity of O

(t*k*n*d)

, where

t

is the number of iterations,

d

is the dimensionality of the datasets,

k

is the number of clusters in the dataset, and

n

is the number of objects in the dataset

.

Explain! In general, is K-means an efficient clustering algorithm; give a reason for this answer, by discussing its runtime by referring to its runtime complexity formula! [5]

The number of attributes an object has

!

3.

Assume

the

Apriori

-style sequence mining algorithm described at pages 429-435 is used and the algorithm generated 3-sequences listed

below (see 2007 Final Exam!):

Frequent 3-sequences Candidate Generation Candidates that survived pruning

<(1) (2) (3)>

<(1 2 3)>

<(1) (2) (4)>

<(1) (3) (4)>

<(1 2) (3)>

<(2 3) (4)>

<(

2) (3) (4)>

<(3) (4 5

)>

 Slide2

Answers Question 1

a.

AGNES creates set of clustering/a

dendrogram; K-Means creates a single clusteringK-means forms cluster by using an iteration procedure which minimizes an objective functions, AGNES forms the dendrogram by merging the closest 2 clusters until a single cluster is obtained…Slide3

Answers Questions 2&3

Answer Question 2

:

t: #iteration k: number of clusters n: #objects-to-be-clustered d:#attributes In each iteration, all the n points are compared to k centroids to assign them to nearest centroid, which is O(k*n), each distance computations complexity is O(d). Therefore, O(t*k*n*d). Slide4

Questions and Topics Review Dec. 10, 2013

4.

Gaussian

Kernel Density Estimation and DENCLUEAssume we have a 2D dataset X containing 4 objects : X={(1,0), (0,1), (1,2) (3,4)}; moreover, we use the Gaussian kernel density function to measure the density of X. Assume we want to compute the density at point (1,1) and you can also assume h=1 (=1) and that we use Manhattan distance as the distance function!. Give a sketch how the Gaussian Kernel Density Estimation approach determines the density for point (1, 1). Be specific! What is a density attractor?. How does DENCLUE form clusters.?5) PageRank [8]a) What does the PageRank compute? What are the challenges in using the PageRank algorithm in practice? [3]b) Give the equation system that PAGERANK would use for the webpage structure given below. Give a sketch of an approach that determines the page rank of the 4 pages from this equation system! [5]  

P1

P2

P3

P4Slide5

Answer Question4

4.

Gaussian

Kernel Density Estimation and DENCLUEAssume we have a 2D dataset X containing 4 objects : X={(1,0), (0,1), (1,2) (3,4)}; moreover, we use the Gaussian kernel density function to measure the density of X. Assume we want to compute the density at point (1,1) and you can also assume h=1 (=1) and that we use Manhattan distance as the distance function!. Give a sketch how the Gaussian Kernel Density Estimation approach determines the density for point (1, 1). Be specific! What is a density attractor?. How does DENCLUE form clusters.?a. The density of (1,1) is computed as follows:fX((1,1))= e-1/2 + e-1/2 + e-1/2 + e-25/2b. A density attractor is a local maximum of a density function. DENCLUE iterates over the objects in the dataset and uses hill climbing to associate each point with a density attractor.

Next,

if forms clusters such that each cluster contains objects in the dataset that are associated with the same clusters; objects who belong to a cluster whose

density (of its attractor)

is below a user defined threshold are considered as outliers.

 Slide6

Answers Questions 5 and 6

5a

) What does the PageRank compute? What are the challenges in using the PageRank algorithm in practice? [3]

It computes the probability of a webpage to be assessed. [1]As there are a lot of webpage and links finding an efficient scalable algorithm is a major challenge [2]5b) Give the equation system that PAGERANK would use for the webpage structure given below. Give a sketch of an approach that determines the page rank of the 4 pages from this equation system! [5]PR(P1)= (1-d) + d * (PR(P3)/2 + PR(P4)/3)PR(P2)= (1-d) + d * (PR(P3)/2 + PR(P4)/3 + PR(P1))PR(P3)= (1-d) + d*PR(P4)/3PR(P4)=1-d[One solution: Initial all page ranks with 1 [0.5] and then update the PageRank of each page using the above 4 equations until there is some convergence[1].6) A Delaunay triangulation for a set P of points in a plane is a triangulation DT(P) such that no point in P is inside the

circumcircle

of any

triangle

in DT(

P

).  Slide7

Questions and Topics Review Dec. 10, 2013

What is a Delaunay triangulation?

SVM

The soft margin support vector machine solves the following optimization problem:What does the second term minimize? Depict all non-zero i in the figure below! What is the advantage of the soft margin approach over the linear SVM approach? [5]b) Referring to the figure above, explain how examples are classified by SVMs! What is the relationship between i and example i

being classified correctly? [4]

 Slide8

Answer Question 7

a.

Minimizes

the error which is measured as the distance to the class’ hyperplane for points that are on the wrong side of the hyperplane [1.5]Depict [2]; distances to wrong hyperplane at most 1 point]. Can deal with classification problems in which the examples are not linearly separable[1.5].b.The middle hyperplane is used to classify the examples[1.5]. If i less equal to half of the width of the hyperplane the example is classified correctly.

The length of the arrow for point

i

is the value of



i

; for points

i

without arrow



i

=0.