Demo1 - TIES445 1

28.11.2007

Demo1 - TIES445 2

Introduction

This slide set contains:

– Very easy and supervised introductory material for MATLAB

– Homework (Task 1 and Task 2 in the last two slides) If you are already expert in MATLAB then you can skip the introduction and

start to work with the homeworks By returning homeworks (a short report about the accomplished tasks) one

can get credits for the final exam (total 3 x 2points, exam max is 4x6 = 24 points)

The reports for the tasks of Demo 1 must be returned not later than 10.12.2007

The reports can be returned by e-mail (sami.ayramo@jyu.fi), or to the office room (Ag C416.2), or to mailbox (which can be found two meter away from the office door)

Some additional codes that may be useful for the homework can be found at http://users.jyu.fi/~samiayr/DM/demot

Demo1 - TIES445 3

Requirements

Basic computer skills (e.g., starting applications, opening, closing and saving files, cutting and pasting text, directory structures, …)

Know how to use a text editor, such as Windows Notepad, that you can use to write MATLAB programs (MATLAB also has its own built-in text editor which you can use)

Basic algebra and trigonometry

– Knowledge of basic linear algebra (i.e., concepts such as matrix, vector, inverse etc.) would also be very helpful

While you are following this introduction, have MATLAB running in a separate window and perform and experiment with the examples

This introduction is extracted, modified and compressed from the one available at the Mathworks Student Center:

– http://www.mathworks.com/academia/student_center/tutorials/

Demo1 - TIES445 4

Facts about MATLAB

MATLAB is a computer program

– for solving the sorts of mathematical problems frequently encountered, for example, data mining, data analysis, statistics, simulation, engineering, mathematical modelling

Built-in features of MATLAB to enables effortless solving of a wide variety of numerical problems

– from the very basic, such as a system of 2 equations with 2 unknowns: X + 2Y = 24 12X - 5Y = 10

– to the more complex, such as factoring polynomials, fitting curves to data points, making calculations using matrices, performing signal processing operations such as Fourier transforms, and building and training neural networks.

MATLAB can be used to plot many different kinds of graphs, enabling the visualization of complex mathematical functions and laboratory data

– The three images below have been created using MATLAB plotting functions

Images are taken from www.mathworks.com

Demo1 - TIES445 5

Starting MATLAB

You can start MATLAB by double-clicking on the MATLAB icon

– The MATLAB Desktop will then pop-up

Demo1 - TIES445 6

Entering commands in MATLAB

“>>” is the command prompt,

– Type a command at a command prompt and MATLAB executes the command you typed in, and then prints out the result

Ex1: Enter a simple MATLAB command date to see how it works Ex2: Try also the clc command (clear command window) Ex3: To exit MATLAB can just enter quit at the MATLAB command

prompt To get a good feel for the kinds of things you can use MATLAB for, also

many different demos are provided, all accessible from a demo window that is popped up when you type, demo, at the command prompt

Demo1 - TIES445 7

Getting help MATLAB has an extensive help system built into it, containing detailed documentation and help information on all of the commands and functions of

MATLAB To obtain help on a given function there are three main functions: help, helpwin (short for help window) or doc (short for documentation).

– help and helpwin give you the same information, but in a different window, the doc command returns an HTML page with a lot more information Ex4: Find help on the date function using the different functions Another source of help is the MATLAB help browser

– you can invoke the MATLAB help browser by

1. typing helpbrowser at the MATLAB command prompt

2. clicking on the help button “?”

3. by selecting Start->MATLAB->Help from the MATLAB desktop

Tutorials and documents can also be found at www.mathworks.com in large amounts

Demo1 - TIES445 8

Working with variables Variables are a fundamental concept in MATLAB and are used all the time

In its simplest mode of use, MATLAB can be used just like a pocket calculator

MATLAB supports all the basic arithmetic operations: +, -, *, /, ^, etc.; and you can group and order operations by enclosing them in parentheses

Ex5: Try the following calculator-like operations with MATLAB by typing

4 + 10

5 *10 + 6

(6 + 6) / 3

9^2

What is ans? In short ans is short for "answer", and is used in MATLAB as the default variable name when none is specified

Ex6: Check the value of ans by typing ans

Ex7: Try to change the value of ans by typing ans + 6

You can also define and use your own variables

Ex8: Create three variables, chech the value of the first one, and calculate the average. For instance, enter the following commands

a = 10

b = 20

c = 30

a

the_average = (a + b + c) / 3

Demo1 - TIES445 9

Working with variables

If you have defined a lot of different variables, you probably can't remember all the variable names you have defined. Therefore, it is nice to get a list of all the variables currently defined. Simply typing whos at the command prompt will return to you the names of all variables that are currently defined.

Ex9: Try the sequence of the following commands: clear a = 5 b = 6 whos Typing clear at the command prompt will remove all variables and values that were

stored up to that point. Ex10: For example, continue from the above example: whos clear whos

Demo1 - TIES445 10

Working with variables

If a command is followed by a semicolon (;) then MATLAB evaluates the expression and store the result internally, but will not print put the result

The user is mainly concerned only with some final result in your MATLAB sessions, which will be calculated by combining many temporary, intermediate variables and by appending a semicolon to the expressions that assign values to the temporary, intermediate variables causes their results to not be printed

Ex11: Compare the following expressions: a = 4 + 5 b = 5 + 6;

Demo1 - TIES445 11

Working with variables In MATLAB, there are some specific rules for what you can name your variables

– Only use primary alphabetic characters (i.e., "A-Z"), numbers, and the underscore character (i.e., "_") in your variable names.

– You cannot have any spaces in your variable names For example, using "this is a variable" as a variable name is not allowed, but

"this_is_a_variable" is fine

– MATLAB is case sensitive. For example, "A_VaRIAbLe", "a_variable", "A_VARIABLE", and "A_variablE" would all

be considered distinct variables in MATLAB

Using single quotes one can also assign pieces of text to variables Ex12: For example, try:

some_text = 'This is some text assigned to a variable!'; some_text

Be careful not to mix up variables that have text values with variables that have numeric values in equations

Demo1 - TIES445 12

MATLAB – the matrix laboratory

Three fundamental concepts in MATLAB, and in linear algebra, are:

– A scalar is simply just a fancy word for a number (a single value)

– A vector is an ordered list of numbers (one-dimensional) In MATLAB they can be represented as a row-vector or a column-vector

– A matrix is a rectangular array of numbers (multi-dimensional) In MATLAB, a two-dimensional matrix is defined by its number of rows and

columns

Both scalars and vectors can be considered a special type of matrix.

– A scalar is a matrix with a row and column dimension of one (1-by-1 matrix)

– A vector is a one-dimensional matrix: one row and n-number of columns or n-number of rows and one column

All calculations in MATLAB are done with "matrices". Hence the name MATrix LABoratory.

Demo1 - TIES445 13

MATLAB – the matrix laboratory

In MATLAB matricies are defined inside a pair of square braces ([]) A comma (,) and semicolon (;) are used as a row separator and

column separator, respectfully

– Note: you can also use a space as a row separator, and a carriage return (the enter key) as a column separator as well

Ex13: Try the examples to see how a scalar, and row and column vectors, can be created

– my_scalar = 3.1415

– my_vector1 = [1, 5, 7]

– my_vector2 = [1; 5; 7]

Demo1 - TIES445 14

MATLAB – the matrix laboratory

What about a two dimensional matrix?

Ex14: Create a 4-by-3 matrix called my_matrix with the numbers 8, 12, and 19 in the first row, 7, 3, 2 in the second row, 12, 4, 23 in the third row, and 8, 1, 1, in the fourth row by typing the following command:

– my_matrix = [8, 12, 19; 7, 3, 2; 12, 4, 23; 8, 1, 1]

You can also combine different vectors and matrices together to define a new matrix

– Remember that the output needs to be a valid rectangular matrix

Ex15: Construct a matrix from row vectors by typing the following lines

– row_vector1 = [1 2 3]

– row_vector2 = [3 2 1]

– matrix_from_row_vec = [row_vector1 ; row_vector2]

Ex16: Construct a matrix from column vectors by typing the following lines

– column_vector1 = [1;3]

– column_vector2 = [2;8]

– matrix_from_col_vec = [column_vector1 column_vector2]

Ex17: Construct a matrix from a 4x3 matrix by typing the following lines

– my_matrix = [8, 12, 19; 7, 3, 2; 12, 4, 23; 8, 1, 1]

– combined_matrix = [my_matrix, my_matrix]

Demo1 - TIES445 15

Indexing vectors and matrices Once a vector or a matrix is created you might needed to extract only a subset of the data, and

this is done through indexing.

– In a row vector the left most element has the index of one.

– In a column vector the top most element has the index of one.

Ex17: Create vectors “my_vector1” and “my_vector2” and try to index into its values

– my_vector1 = [1 5 7]

– my_vector2 = [1; 5; 7]

– my_vector1(1)

– my_vector2(2)

– my_vector1(3)

– my_vector2(1)

– my_vector2(2)

– my_vector2(3)

The process is much the same for a two-dimensional matrix. The only difference is that you have to specify both the row and column indices.

Ex18: Access the value of 4 in my_matrix

– my_matrix = [8, 12, 19; 7, 3, 2; 12, 4, 23; 8, 1, 1]

– my_matrix(3,2)

Note: The row number is first, followed by the column number.

Demo1 - TIES445 16

Indexing vectors and matrices

You can also extract any contiguous subset of a matrix, by referring to the row range and column range you want.

Ex19: Try the following examples:

– mat = [1 3 2 3 5 6 5; 7 4 8 1 2 3 4; 3 2 8 4 7 3 2; 3 2 3 4 1 4 2]

– mat(2:4,4:7)

– mat(1:2,[1:3 5:6]) You can change a number in a matrix by assigning to it Ex20: Try to change the value of an element by the following

commands:

– mat = [1 3 2; 2 3 4; 7 3 2; 1 4 2]

– mat(2,2) = 999

Demo1 - TIES445 17

Element-by-element operations

“Element-by-element“ operations are performed on two vectors or matrices of the same size to get the result of the same size

For example, "element-by-element multiplication" of two vectors [1 2 3] and [4 5 6] would give you [4 10 18].

The element-by-element operators in MATLAB are as follows: element-by-element multiplication: ".*" element-by-element division: "./" element-by-element addition: "+" element-by-element subtraction: "-" element-by-element exponentiation: ".^" Ex21: Try the following operations (which of these works?)

– a=[1 2 3]

– b=[4 5 6]

– c=[6; 7; 8]

– d=[6; 7; 8]

– a.*b

– a.*c

– c.*d

– c.^d

Demo1 - TIES445 18

Element-by-element operations

An additional note about element-by-element operators is that you can use them with scalars and vectors together:

Ex22: Try the following operation: a = [1 2 3 4 5 6] b = a .* 2 You can similarly use ".^", "+", and "-" with a vector and scalar. Ex23: Try some examples: c = a .^ 2 d = a + 2 e = a – 2 The reason that element-by-element multiplication and exponentiation

operators have "." appended to the front of them, while the element-by-element addition and subtraction operators do not, is that there are other kinds of multiplication, division, and exponentiation operators (denoted by "*" , "/"and "^“) for matrices, which are not element-by-element

Demo1 - TIES445 19

Matrix operations Element-by-element operations allow us to compute things on an element-by-element basis, but

matrix operations allow us to perform matrix-based computation.

– For example, the multiplication of two matrices, represented by "*", performs a dot product of the two matrices. What the dot product does is that it first multiplies the corresponding elements (i.e., same position elements) of the two vectors, similar to what element-by-element multiplication does, and then adds up all the results of these multiplications to get a single, final number as the answer.

Ex24: Try the following matrix multipilication:

– a = [1 2 3]

– b = [4 ; 5 ; 6]

– a * b

– To get the answer "32", what MATLAB first performs the multiplications of the corresponding elements of the two vectors: "1*4 = 4", "2*5=10", and "3*6=18". Then, to get the final answer of "32", MATLAB adds all these multiplications together: "4+10+18=32".

The length of vectors and the size of matrices can be found by length and size functions: Ex25: Try the following examples:

– a = [1 2 3]

– length(a)

– mat = [1 3 2; 2 3 4; 7 3 2; 1 4 2]

– size(mat)

Demo1 - TIES445 20

Plotting The most basic plotting command in MATLAB is the plot command. The

plot command, when called with two same-sized vectors X and Y, makes a two-dimensional line plot for each point in X and its corresponding point in Y. In other words, it will draw points at (X(1),Y(1)), (X(2),Y(2)), (X(3),Y(3)), etc., and then connect all these points together with lines.

Ex26: Try a very simple example to illustrate what the plot command does:

– simple_x_points = [1 2 3 4 5]

– simple_y_points = [25 0 20 5 15]

– plot(simple_x_points, simple_y_points); The ordering of the vectors in the plot command is important Ex27: Try the reversed order for the previous simple example: plot(simple_y_points, simple_x_points);

Demo1 - TIES445 21

Plotting To add text to a plot, you need to keep the figure window open (i.e., type the commands in the

MATLAB command window while the figure window is still open). The xlabel/ylabel command prints out a text string describing the x-axis/y-axis; The

title command prints out a title for your plot. Typing "grid on" at the command prompt, the grid lines will be added to the open figure window (typing "grid off" will get rid of the grid lines).

Ex28: Try to use these commands on the previous plot:

– simple_x_points = [1 2 3 4 5]

– simple_y_points = [25 0 20 5 15]

– plot(simple_x_points, simple_y_points);

– xlabel('this is text describing the x-axis');

– ylabel('this is text describing the y-axis');

– title('this is text giving a title for the graph');

– grid on;

Demo1 - TIES445 22

Plotting a parabola Ex29: Let's look at a more practical example of plotting. First you need to create a vector of regularly spaced points

and a vector of function values at those points for some function. Do this for the function "y = x^2" (i.e., a parabola) for x values between -5 and 5 and with regular spacing of .1:

– x_points = [-5 : .1 : 5];

– y_points = x_points .^ 2;

– % Then plot the x_points against the y_points, and get the familiar plot of a parabola

– plot(x_points,y_points);

– xlabel('x-axis'); ylabel('y-axis'); title('A Parabola');

– grid on Note: The result is very smooth: you can't really see any of the individual line segments like you could for the simple

example previously. That is because the points are so close together (at regular spacings of .1) --- MATLAB is still drawing line segments between the points, but your eye just can't see them because they are so small, and so the result seems to be a smooth curve.

Demo1 - TIES445 23

Multiple plots

Using the hold command, you can add multiple plots in the same figure window, to compare the plots for example. (Normally, when you type a plot command, any previous figure window is simply erased, and replaced by the results of the new plot.)

If you type "hold on" at the command prompt, all line plots created after that will be superimposed in the same figure window and axes. Like wise the command "hold off" will stop this behavior, and revert to the default (i.e., new plot will replace the previous plot).

Ex30: Try the following example of how to plot several different exponential functions in the same axes (you need to define the points on x-axis only once):

– x_points = [-10 : .05 : 10];

– plot(x_points, exp(x_points));

– grid on

– hold on

– plot(x_points, exp(.95 .* x_points));

– plot(x_points, exp(.85 .* x_points));

– plot(x_points, exp(.75 .* x_points));

– xlabel('x-axis'); ylabel('y-axis');

– title('Comparing Exponential Functions');

Demo1 - TIES445 24

Subplots In order to have multiple plots in the same window, but each in a separate part of the window (i.e., each

with their own axes), you use the subplot command. If you type subplot(M,N,P) at the command prompt, MATLAB will divide the plot window into a bunch of rectangles --- there will be M rows and N columns of rectangles --- and MATLAB will place the result of the next "plot" command in the Pth rectangle (where the first rectangle is in the upper left).

Ex31: Try this example of a line plot, a parabola, an exponential, and the absolute value function into four rectangles in the same figure window

– x_points = [-10 : .05 : 10];

– line = 5 .* x_points;

– parabola = x_points .^ 2;

– exponential = exp(x_points);

– absolute_value = abs(x_points);

– subplot(2,2,1);plot(x_points,line);

– title('Here is the line');

– subplot(2,2,2);plot(x_points,parabola);

– title('Here is the parabola');

– subplot(2,2,3);plot(x_points,exponential);

– title('Here is the exponential');

– subplot(2,2,4);plot(x_points,absolute_value);

– title('Here is the absolute value');

Demo1 - TIES445 25

Line Plots in Three Dimensions

MATLAB cover two different kinds of three-dimensional plots you can do in MATLAB, 1) three-dimensional line plots and 2) surface mesh plots.

The three-dimensional line plots are analagous to the two-dimensional line plots created with the plot command. The only difference is that the command has a "3" added to it, plot3, and that it requires an extra input, Z, for the third dimension.

Ex32: A simple example of using the plot3 command, and the resulting output figure window (notice that you can also here use hold and subplot in the same way too):

X = [10 20 30 40]; Y = [10 20 30 40]; Z = [0 210 70 500]; plot3(X,Y,Z); grid on; xlabel('x-axis'); ylabel('y-axis'); zlabel('z-axis'); title('Pretty simple');

Demo1 - TIES445 26

Three-Dimensional Surface Mesh Plots

The mesh and meshgrid commands can be used to create surface mesh plots, which show the surface of three-dimensional functions, such as "z = x^2 + y^2"

The way it works is that:

1. Generate a grid of points in the xy-plane using the meshgrid command

2. Evaluate the three-dimensional function at these points

3. Create the surface plot with the mesh command Ex33: Try to generate the meshgrid and generate the surface mesh plot : x_points = [-10 : 1 : 10]; y_points = [-10 : 4 : 10]; [X, Y] = meshgrid(x_points,y_points); Z = X.^2 + Y.^2; mesh(X,Y,Z); xlabel('x-axis'); ylabel('y-axis'); zlabel('z-axis');

Demo1 - TIES445 27

MATLAB scripts

A MATLAB script is an ASCII text file that contains a sequence of MATLAB commands

– the commands contained in a script file can be run, in order, in the MATLAB command window simply by typing the name of the file at the command prompt

Any text editor, such as Microsoft Windows Notepad, or wordprocessor, such as Microsoft Word, can used to create scripts, but the scripts must always be saved as simple text documents (i.e., in the "Save As" dialogue box, choose "Text Document" or its equivalent for "Save as type:").

It is easiest to create scripts using MATLAB's built-in text editor, which automatically just saves files as ASCII text files for you.

When naming script files, you need to append the suffix ".m" to the filename, for example "my_script.m".

Scripts in MATLAB are also called "M-files" because of this, and the ".m" suffix tells MATLAB that the file is associated with MATLAB.

Demo1 - TIES445 28

Creating MATLAB script Ex34: Create a simple script that calculates the average of five numbers that are stored in variables.

Start with typing “edit average_script.m” after the command prompt. Then add the following contents of the script file "average_script.m" in the MATLAB's built-in text editor:

– % a simple MATLAB m-file to calculate the average of 5 numbers.

– % first define variables for the 5 numbers:

– a = 5;

– b = 10;

– c = 15;

– d = 20;

– e = 25;

– % now calculate the average of these and print it out:

– five_number_average = (a + b + c + d + e) / 5;

– five_number_average

NOTE! Save the above script for the later use! The text in green (i.e., the lines starting with % --- all comment lines must start with %) are

comments.

Demo1 - TIES445 29

Running MATLAB script

If you saved the above script "average_script.m" into the present working directory, then it can be run simply by typing average_script at the MATLAB command prompt.

Ex35: Try to run it using the following sequence of commands in the command prompt:

– clear

– whos

– pwd

– dir

– average_script

– whos

Demo1 - TIES445 30

Saving variables 1

The save command can be used to save all or only some of your variables into a MATLAB data file type called MAT-file

If you want to choose the name of the file yourself, you can type save followed by the filename you want to use.

– MATLAB will then save all currently defined variables in a file named with the name you chose followed by the suffix ".mat" (for example, if you chose the name my_variables MATLAB would save as "my_variables.mat" in your present working directory).

– Before saving you should change your present working directory to one of your own directories (such as some directory on your floppy diskette), or specify the complete path to where you want MATLAB to save your variables (for example "a:\my_variables\my_vars").

Ex36: Try this example of using save:

clear

who

cd c:\my_variables %(replace this with your own folder)

pwd % present working directory

a = 10;

b = 20;

c = 30;

d = sqrt((a + b + c)/pi)

who

save my_chosen_filename %(replace this with your own filename)

dir

clear

who

Demo1 - TIES445 31

Saving variables 2

The above use of the save command saved all the MATLAB workspace defined variables. If you just want to save some of your variables, you simply list the variables you want to save after typing, save and the filename.

Ex37: Try to save only the variables a and c:

– clear

– who

– a = 10;

– b = 20;

– c = 30;

– who

– pwd

– save some_of_my_variables a c %(replace this with your own filename)

– dir

– clear

– who

Demo1 - TIES445 32

Loading variables 1

The load command is used for loading variables back in later to use them again. Typing load followed by a filename (without the ".mat" suffix) will search the MATLAB path (refer to the next lesson regarding the MATLAB path) for the file, "filename.mat", and load all the variables saved in that file (for example, typing load my_vars would cause MATLAB to search for "my_vars.mat" and load the variables saved in it).

Ex38: Try this example of loading variables back into MATLAB

– clear

– who

– cd c:\my_variables %(replace this with your own folder)

– dir

– load my_chosen_filename %(replace this with your own filename)

– who

– a

– clear

– who

– load some_of_my_variables %(replace this with your own filename)

– who

– c

Demo1 - TIES445 33

Loading variables 2

You can also choose to load in only some of the variables that are saved in a MATLAB data file (MAT-file). To load only some of the variables saved in a file back into MATLAB, just type the names of the variables you want loaded back in after typing load and the filename (without ".mat") at the command prompt.

Ex39: Assuming that variables "a", "ans", "b", "c", and "d" are all saved in a file, you can use the load command to load only "a" and "c" back in:

– who

– dir

– whos -file my_chosen_filename %(replace this with your own filename)

– load my_chosen_filename a c %(replace this with your own filename)

– who

– a

Demo1 - TIES445 34

Working with Files, Directories and Paths

In general, files are managed, organized, and accessed in MATLAB in the same way as in Microsoft Windows, that is, in a hierarchical file system.

How MATLAB Finds Files?

1. MATLAB always look inside your present working directory (type pwd at the MATLAB command prompt to see your present working directory)

2. If the file is not located in the present working directory MATLAB will also search in other directories that are stored in the MATLAB path (The present working directory can also be thought of as part of the MATLAB path)

Ex40: To print out the current MATLAB path type, matlabpath or path, at the command prompt:

If you want to store your MATLAB files in some directory that does not exist in the matlabpath, add the complete path to your directory to the MATLAB path.

Ex41: There are two ways you can append your own paths to the MATLAB path:

– use the addpath command - type addpath followed by the complete path to your directory

– use the path tool of MATLAB - type pathtool at the command prompt, or select File->Set Path…

– addpath a:\my_stuff\letters

– matlabpath

Demo1 - TIES445 35

Useful functions pwd - present working directory dir, or ls - List directory what - List MATLAB-specific files in directory cd - Change current working directory

path, or matlabpath - List the MATLAB search path addpath - Add directory to search path pathtool - Invoke the path tool interface

help general - List of general MATLAB commands

Demo1 - TIES445 36

Exercises…1. Download the well-known Iris data to your working directory from

http://www.ics.uci.edu/~mlearn/MLSummary.html

2. Import the data into MATLAB by choosing from menu: File->Import data->…

3. Perform some explorative DM for the Iris data set.

1. Make a global summarization for the Iris data (for example, compute the mean, median, variance and range of the variables)

2. Explore data by plotting 2-dimensional scatter plots for each pair of variables (e.g., plotmatrix)

3. Find the two most correlating variables in the data (corrcoef)

4. Plot histogram (using, for example, 10 bins) for each variable (hist)

5. Compute attribute means and medians for each class

6. Compute the variance of all the variables (var)

7. Compute the covariance matrix of the whole data (cov)

8. Construct histograms of 10 bins for each Iris variable

9. Make 2-dimensional scatter plots for each pair of variables on Iris data. Use different markers with different colors for different classes

Use help commands and documentation at http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.html!!!

Demo1 - TIES445 37

Task 11. Load the Iris data set from UCI repository http://www.ics.uci.edu/~mlearn/MLSummary.html

– A short description of the data is found from the lecture slides, Tan et al. Chapter 3: Exploring data, slide number 4.

2. Expect that you do not know the class names, the number of classes etc. of the Iris data set. What you know is that you have some data about flowers and the attribute names. Then, ”without prior assumptions and knowledge”, analyse the data set using the available (or self-implemented) explorative and summarizing MATLAB tools. Document and explain all you can learn from the data by exploring. The documentation should contain figures and interpretation of useful and interesting visual views (different plots, colors, histograms,... see the techniques in the lecture slides Tan et al. Chapter 3: Exploring data). For example:

1. Can you determine the number of classes by exploring (assumed to be unknown)? How?

2. Behavior of attributes (correlations, scatters (variance/MAD/covariance), ranges,… ). What kind of preprocessing might be needed? Are there redundant attributes? Outliers? And so on..

3. …other findings?

3. Explain what you can learn about data (that represents the three flower types). Describe carefully your findings and compare your results with respect to the known class labels of the flowers. Did you find the classes from the data?

Demo1 - TIES445 38

Task 21. Load the synthetic cluster data set from the file clusterdata1.data. The data set contains a set of

generated 7-dimensional clusters. Try to find the best possible prototypes for the clusters using the MATLAB implementation of the dckmeans.m. Before this, exploring and preprocessing the data set (see Task 1), try to find all possible information for the clustering step (for example, data may contain errors, noise, redundancies, moreover, you must determine the number of clusters and so on). You may also modify the dckmeans code (e.g., replace the sample mean estimate wih a more robust one such as median). Remember that K-means is a local seach method (results depend on the initial prototypes, you may find the good ones). You can also utilize the PCA code in exploration and/or clustering.

2. Document and explain all the steps and all the significant facts you can learn from the data by exploring, summarization, visualization, clustering etc. The documentation should contain plots, histograms, etc. with interpretations. If you do some prepocessing, transformations, scaling for data, report and explain them carefully. The most important thing is to document the final clustering results (prototypes and clusterlabels) that is your refinement for the data set.

3. Remember not to only report the findings, but also how did you proceed (your mining process)!

Exploit frequently the help commands and documentation at http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.html!!!