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
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
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
Problem Set 1
September 19, 2012
Due date:
Wed, October 3 2012 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 algor
Problem Set 3
November 15, 2013
Due date:
Mon, Dec 2, 2013 at 4pm.
Exercise 1 (30 points)
Assume a binary classification problem, where every data instance can belong to one of two possible
classes: class A and class B.
1. Assume a meta-classifier that cl
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
Problem Set 3
November 24, 2014
Due date:
Wed, Dec 10, 2014 at 2pm.
Exercise 1 (30 points)
Assume a binary classification problem, where every data instance can belong to one of two possible
classes: class A and class B.
1. Assume a meta-classifier that c
Problem Set 2
October 16, 2012
Due date:
Mon, October 29 2012 at 4pm.
Exercise 1: (20 points) Assume two d-dimensional real vectors x and y. And denote by xi (yi ) the value
in the i-th coordinate of x (y). Prove or disprove the following statements:
1. D
Problem Set 3
November 23, 2012
Due date:
Wed, Dec 12, 2012 at 4pm.
Exercise 1 (30 points)
Assume a binary classification problem, where every data instance can belong to one of two possible
classes: class A and class B.
1. Assume a meta-classifier that c
Problem Set 1
September 15, 2014
Due date:
Wed, Oct 1 2014 at 1pm; before class.
Instructions: Return your answers to the teaching assistant, Natali Ruchansky by email natalir@bu.edu.
You can either hand your paper in person or send it by email.
Discussin
Problem Set 2
October 9, 2014
Due date:
Wed, Oct 24, 2014 at 1pm; before class.
Exercise 1 (20 points): The aglomerative hierarchical clustering produces a hierarchical clustering of n
points by starting with all points being in separate clusters and merg
Lecture outline
Classification
Decision-tree classification
Wednesday, October 23, 13
What is classification?
Wednesday, October 23, 13
What is classification?
Classification is the task of learning a
target function f that maps attribute set x
to one
Co-clustering or Biclustering
References:
A. Anagnostopoulos, A. Dasgupta and R. Kumar:
Approximation Algorithms for co-clustering, PODS 2008.
K. Puolamaki. S. Hanhijarvi and G. Garriga: An
approximation ratio for biclustering, Information
Processing L
Recommendation
Systems
Thanks to: Anand Rajaraman, Jeffrey D. Ullman
Sunday, December 8, 13
Items
Sunday, December 8, 13
Products, web sites, blogs, news items,
Search
Items
Sunday, December 8, 13
Products, web sites, blogs, news items,
Search
Recommend
/* File: Haiku.java
* Author: Gijung Kim (tkixi@bu.edu)
* Date: 1/27/16
* Purpose: This is a solution to Problem One of Lab 1.
*/
public class Haiku cfw_
public static void main(String[] args) cfw_
String x = "Jack Kerouac";
int y = 1968;
System.out.print
TUESDAY, 20 JANUARY
What is a computer?
Just about anything that takes input and provides output
A computer is a device that receives, stores, and processes information
Different types of computers have different characteristics
- supercomputers: power
HW5 CS132
Total: 18 points
1) (10 pts) Are the following T: 2 2 transformations linear? If yes find the corresponding
1
matrices A and check that: T(1,2) = A[ ].
2
a. T(x,y)=( 2x-4y, 3x+10y)
b. T(x,y)=( 4xy, 4x+3y)
c. T(x,y)=( 4|x+y|, 4x+y)
d. T(x,y)=( x+
import numpy as np
import warnings
def swapRows(A, i, j):
"
interchange rows i and j of A
operates on A in place
"
tmp = A[i].copy()
A[i] = ?
A[j] = ?
def relError(a, b):
"
compute the relative error of a and b
"
with warnings.catch_warnings():
warnings.s
CS 132 Practice Midterm Exam
Prof. Olga Lepsky
Students Name:
Students Score:
1. Indicate whether the following statements are True or False. (Capital letters
indicate matrices.) (1 pt per question)
1) AB=BA for any square matrices A and B
2) A+B=B+A for
HW4 CS132
Total: 9 points
5 3
4
1) (3 pts) Find L and U matrices in LU decomposition of A = [ 10 8 9], following an
15 1
2
algorithm discussed at the lecture. Verify that LU = A (by hand). Show your work.
2) (3 pts) Write the 2x2 matrix A of linear transf
CS132 Homework #1 (10 pts)
Write the linear equations describing each problem. Solve the linear equations for problems 25, following the Gaussian elimination algorithm.
1)
(2 pts) Find all the unknowns in the traffic flow described by the roundabout below
CS132 Homework #2 (40 pts)
1. (30 pts) For numbers 1-5 from HW1, do the following
a. write a coefficient matrix,
b. an augmented matrix (with a right-hand side),
c. compute an echelon form of an augmented matrix (show your intermediate steps and
the resul
CS132 Homework #3 (8 pts)
1) (2 pts) How long would it take for a PC computer with a performance of 50 gigaflops (giga = 109) to
solve a linear system of 2 million unknowns and equations via Gaussian elimination? How long
would it take with LU method, ass