Problem Set 1
September 14, 2009
Due date:
Monday, September 28 2009 at 4pm; before class.
Exercise 1: (20 points) Some years ago, greek video-club chain Seven had the following oer to their customers: every time a customer rented a DVD, he was given a ra
Solutions to Problem Set 1
October 7, 2009
Exercise 1: (20 points) Some years ago, greek video-club chain Seven had the following oer to their customers: every time a customer rented a DVD, he was given a random coupon with the title of the Academy awards
Boston University Department of Computer Science CS 565 Data Mining
Midterm Exam Solutions Date: Oct 14, 2009 Write Your University Number Here: Answer all questions. Good luck! Problem 1 [25 points] True or False: 1. Maximal frequent itemsets are sucient
Graph Clustering
Outline
Min s-t cut problem
Min cut problem
Multiway cut
Minimum k-cut
Other normalized cuts and spectral
graph partitionings
Min s-t cut
Weighted graph G(V,E)
An s-t cut C = (S,T) of a graph G = (V, E)
is a cut partition of V into S an
Problem Set 1
September 17, 2016
Due date:
Oct 10, 2016 at midnight.
Remeber: For any question you answer I do not know you get 20% of the grade associated with this
question. A totally wrong answer gets 0.
Exercise 1 (20 points)
You are given a set V con
Homework 2
October 11, 2016
Due date:
Mon, Oct 28, 2016 at 11:59pm.
Exercise 1 (25 points):
1. Consider a set of d-dimensional points X = cfw_x1 , . . . , xn and distance function
D2 (xi , xj ) =
d
X
2
(xi (`) xj (`) .
`=1
Show that the representative
X
Clustering Aggregation
References
A. Gionis, H. Mannila, P. Tsaparas: Clustering
aggregation, ICDE 2004
N. Ailon, M. Charikar, A. Newman: Aggregating
inconsistent information: Ranking and clustering,
JACM 2008
Clustering aggregation
Many different clu
Lecture outline
Classification
Decision-tree classification
What is classification?
What is classification?
Classification is the task of learning a
target function f that maps attribute set x
to one of the predefined class labels y
What is classificat
Clustering Aggregation
References
A. Gionis, H. Mannila, P. Tsaparas: Clustering
aggregation, ICDE 2004
N. Ailon, M. Charikar, A. Newman: Aggregating
inconsistent information: Ranking and clustering,
JACM 2008
Tuesday, October 15, 13
Clustering aggrega
Lecture outline
Nearest-neighbor search in low
dimensions
kd-trees
Nearest-neighbor search in high
dimensions
LSH
Applications to data mining
Wednesday, September 18, 13
Definition
Given: a set X of n points in Rd
Nearest neighbor: for any query po
Problem Set 1
September 13, 2013
Due date:
Mon, Sept 30 2013 at 4pm; before class.
Exercise 1 (20 points): You are given a set V consisting of n integers. The task is to report all n
products of the n distinct (n 1)-cardinality subsets of V . Your algorit
Hierarchical Clustering
Friday, October 4, 13
Hierarchical Clustering
Produces a set of nested clusters
organized as a hierarchical tree
Can be visualized as a dendrogram
A tree-like diagram that records the
sequences of merges or splits
Friday, Octobe
Clustering: Partition
Clustering
Wednesday, October 2, 13
Lecture outline
Distance/Similarity between data
objects
Data objects as geometric data points
Clustering problems and algorithms
K-means
K-median
K-center
Wednesday, October 2, 13
What is cl
Measuring distance/
similarity of data objects
Wednesday, September 11, 13
Multiple data types
Records of users
Graphs
Images
Videos
Text (webpages, books)
Strings (DNA sequences)
Timeseries
How do we compare them?
Wednesday, September 11, 13
Feature spac
Graph Clustering
Wednesday, October 16, 13
Why graph clustering is
useful?
Distance matrices are graphs
useful as any other clustering
as
Identification of communities in social
networks
Webpage clustering for better data
management of web data
Wednes
Dimensionality reduction
Monday, September 23, 13
Outline
Dimensionality Reductions or data
projections
Random projections
Singular Value Decomposition and Principal
Component Analysis (PCA)
Monday, September 23, 13
The curse of dimensionality
The eff
Hierarchical Clustering
Hierarchical Clustering
Produces a set of nested clusters
organized as a hierarchical tree
Can be visualized as a dendrogram
A tree-like diagram that records the
sequences of merges or splits
Strengths of Hierarchical
Clustering
Model Evaluation
Metrics for Performance Evaluation
How to evaluate the performance of a
model?
Methods for Performance Evaluation
How to obtain reliable estimates?
Methods for Model Comparison
How to compare the relative performance
of different mo
Epidemics and Information
Propagation in Social
Networks
Epidemic Processes
Viruses, diseases
Online viruses, worms
Fashion
Adoption of technologies
Behavior
Ideas
Example: Ebola virus
First emerged in Zaire 1976 (now
Democratic Republic of Kongo)
Very
08B-Clustering-III
October 31, 2016
1
Clustering data with k-means
Today well do an extended example showing k-means clustering in practice and in the context of
the python libraries scikit-learn.
1.1
Synthetic data
Generally, when learning about or devel
2-Pandas
September 3, 2016
1
1.1
Getting to know your data with Pandas
Pandas
Pandas is the Python Data Analysis Library.
Pandas is an extremely versatile tool for manipulating datasets.
It also produces high quality plots with matplotlib, and integrates
11-Dimensionality-Reduction-SVD-II
October 18, 2016
1
Dimensionality Reduction - SVD II
In the last lecture we learned about the SVD as a tool for constructing
low-rank matrices.
Today well look at it as a way to transform our data objects.
As a reminder,
4-Linear-Algebra-Refresher
September 20, 2016
1
Linear Algebra Refresher
Today well review the essentials of linear algebra. Given the prerequisites for
this course, I assume that you learned all of this once. What I want to do today is bring the material
CS 591 S1 Computational Audio - Spring,
2017
Wayne Snyder
Computer Science Department
Boston University
Lecture 5
Modulation synthesis: amplitude, ring, and frequency modulation
Amplitude modulation: amplitude envelope shaping based on linear
and exponent
CS 512, Spring 2017, Handout 14
Binary Decision Diagrams (BDDs)
Assaf Kfoury
February 26, 2017
Assaf Kfoury, CS 512, Spring 2017, Handout 14
page 1 of 28
background and reading material
I The last chapter, Chapter 6, in the book [LCS] is entirely devoted
CS 512, Spring 2017, Handout 34
Program Schemes and First-Order Logic
Assaf Kfoury
2 May 2017
Assaf Kfoury, CS 512, Spring 2017, Handout 34
page 1 of 22
PROGRAMS
and
PROGRAM SCHEMES
I Let P be a program in some program language
(e.g., Python, Java, Haskel
CS565
Homework 2
Leshen Sui
Problem 1
(1)
Take partial derivative w.r.t xi (l) for l [1, d]:
Pn Pd
2
l=1 (xi (l) x(l)
i=1
x
P
Well get a set of equation in the form ni=1 x(l)
(xi (l) x(l)2 for l [1, d]
And we set all d equation equal to 0, i.e:
Pn
(xi (l
1.
A.
Alpha = 0.04, E = 0.4, z = 2.054
E = z*s/n^0.5 s = 0.4 * 40^0.5/2.054 = 1.23
B. Alpha = 0.01, corresponding z = 2.576
E = 2.576*1.23/40^0.5 = 0.502
99% CI = (3 - 0.502, 3 + 0.502)
C. N = (2.054*1.23/0.1)^2 = 639 N - n = 599
So we need 599 more sampl