Intro to MATLAB and K-mean algorithm

 MATLAB (Matrix Laboratory) [1]
 MATLAB(matrix laboratory) is a multi-paradigm
numerical computing environment and fourth-generation
programming language.
 Developed by Math Works, MATLAB allows matrix
manipulations, plotting of functions and data,
implementation of algorithms, creation of user interfaces,
and interfacing with programs written in other
languages, including C, C++, Java and Fortran.
MATLAB

 MATLAB (Matrix Laboratory) [2]
 Although MATLAB is intended primarily for numerical
computing, an option al toolbox uses the MuPAD
symbolic engine, allowing access to symbolic computing
capabilities. An additional package, Simulink, adds
graphical multi-domain simulation and Model-Based
Design for dynamic and embedded systems.
 In 2004, MATLAB had around one million users across
industry and academia. MATLAB users come from
various backgrounds of engineering, science, and
economics. MATLAB is widely used in academic and
research institutions as well as industrial enterprises.
MATLAB

 Commands
 >>433.12*15.7
 ans=6.8000e+003
 MATLAB spits out the answer to our query conveniently
named ans.
 This is a variable or symbolic name that can be used to
represent the value later.
 >>x=5*6
 X=30
MATLAB

 Commands
 To write the multiplication ab, in MATLAB we type a*b
 For division, the quantity a÷b is typed as a/b. This type
of division is referred to as right division.
 MATLAB also allows another way to enter division,
called left division. We can enter the quantity by a
typing the slash mark used for division in the opposite
way, that is, we use a back slash instead of a forward
slash ab
MATLAB

 Commands
 Exponentiation a to the power b is entered in the
following way a ^ b
 Finally, addition and subtraction are entered in the
usual way
 a + b
 a –b
MATLAB

 Commands
 Individual matrix and vector entries can be referenced
with indices inside parentheses. For example, A(2,3)
denotes the entry in the second row, third column of
matrix A.
 A=[123;456;-179]
 A(2,3)
 Create a column vector, x, with:
 x=[321]’
 Or equivalently:
 x=[3;2;1]
MATLAB

 Commands
 The relational operators in MATLAB are:
 < less than
 > greater than
 <= less than or equal
 >= greater than or equal
 == equal
 ~= not equal
 Note that = is used in an assignment statement whereas
== is a relational operator.
MATLAB

 Commands
 Logical operators:
 Relational operators may be connected by logical
operators:
 & and
 | or
 ~ not
 && short-circuit and
 || short-circuit or
MATLAB

 Commands
 Inner product or dot product
 .* Array multiply:
 X.*Y denotes element-by-element multiplication. X and
Y must have the same dimensions unless one is a
scalar.
 * Matrix multiply:
 X*Y is the matrix product of X and Y. Any scalar (a 1-by-
1 matrix) may multiply anything. Otherwise, the number
of columns of X must equal the number of rows of Y.
MATLAB

 Commands
 /Slash or right matrix divide:
 A/B is the matrix division of B into A, which is roughly the
same as A*INV(B), except it is computed in a different
way. More precisely, A/B = (B'A')'.
 Backslash or left matrix divide:
 AB is the matrix division of A into B, which is roughly the
same as INV(A)*B, except it is computed in a different
way. If A is an N-by-N matrix and B is a column vector
with N components, or a matrix with several such
columns, then X=AB is the solution to the equation
singular
MATLAB

 Commands
 To divide Matrices, element-by-element, the following
formula is useful A./B
 A = [2 4 6 8]; B = [2 2 3 1];
 C = A./B
 % C = [1 2 2 8]
 Array left division is indicated by writing C = A.B (this
is the same as C = B./A):
 C = A.B
 % C = [1.0000 0.5000 0.5000 0.125]
MATLAB

 Commands
 fix()
 fix(X) rounds the elements of X to the nearest integers
towards zero.
 >> fix(5.5)
 ans =
 5
 >> fix(5.9)
 ans =
 5
MATLAB

 Commands
 rand()
 rand():returns an n-by-n matrix containing pseudo
random values drawn from the standard uniform
distribution on the open interval(0,1).
 >> n = rand(1,10)
 n =0.1576 0.9706 0.9572 0.4854 0.8003 0.1419
0.4218 0.9157 0.7922 0.9595
 >> n = fix(10*rand(1,10))
 n =8 9 1 9 6 0 2 5 9 9
MATLAB

 Commands
 Question: Simulate the outcomes of 1000 biased coin
tosses with p[Head] = 0.3
 Solution:
 n = 1000;
 randomNumber= rand(n,1);
 Heads = randomNumber<= 0.3;
 totalNumberOfHeads= sum(Heads);
 probabilityOfHeads= totalNumberOfHeads/n;
MATLAB

 Commands
 Plot(x,y) plot the graph between x and y.
 X and y are the vectors of same lengths.
 >>X=1:10
 >>y=11:20
 >> plot(x,y)
MATLAB

 Commands
 Two or more than two graphs plot on at same time with
hold on function
 x=-5:5
 y=x.*x
 plot(x,y)
 hold on
 a=1:5
 b=1:5
 plot(a,b)
MATLAB

INTRODUCTION-
What is clustering?
 Clustering is the classification of objects into
different groups, or more precisely, the
partitioning of a data set into subsets
(clusters), so that the data in each subset
(ideally) share some common trait - often
according to some defined distance measure.

Common Distance measures:
 Distance measure will determine how the similarity of two
elements is calculated and it will influence the shape of the
clusters.
They include:
1. The Euclidean distance (also called 2-norm distance) is
given by:
2. The Manhattan distance (also called taxicab norm or 1-
norm) is given by:

K-MEANS CLUSTERING
 The k-means algorithm is an algorithm to cluster
n objects based on attributes into k partitions,
where k < n.

K-MEANS CLUSTERING
 Simply speaking k-means clustering is an
algorithm to classify or to group the objects
based on attributes/features into K number of
group.
 K is positive integer number.
 The grouping is done by minimizing the sum
of squares of distances between data and the
corresponding cluster centroid.

How the K-Mean Clustering
algorithm works?

 Step 1: Begin with a decision on the value of k =
number of clusters .
 Step 2: Put any initial partition that classifies the
data into k clusters. You may assign the
training samples randomly,or systematically
as the following:
1.Take the first k training sample as single-
element clusters
2. Assign each of the remaining (N-k) training
sample to the cluster with the nearest
centroid. After each assignment, recompute the
centroid of the gaining cluster.

 Step 3: Take each sample in sequence and
compute its distance from the centroid of
each of the clusters. If a sample is not
currently in the cluster with the closest
centroid, switch this sample to that cluster
and update the centroid of the cluster
gaining the new sample and the cluster
losing the sample.
 Step 4 . Repeat step 3 until convergence is
achieved, that is until a pass through the
training sample causes no new assignments.

Applications of K-Mean
Clustering
 It is relatively efficient and fast. It computes result
at O(tkn), where n is number of objects or points, k
is number of clusters and t is number of iterations.
 k-means clustering can be applied to machine
learning or data mining
 Used on acoustic data in speech understanding to
convert waveforms into one of k categories (known
as Vector Quantization or Image Segmentation).
 Also used for choosing color palettes on old
fashioned graphical display devices and Image
Quantization.

Intro to MATLAB and K-mean algorithm

Intro to MATLAB and K-mean algorithm

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