VISUAL
DATA MINING APPLICATION
IN
MATERIAL
RESEARCH
Anand M., Bharath B.N., Chaitra, Kiran Kumar
M.S., Vinay C.
* Mr.T.L.Bharatheesh*
*
P.E.S.Institute of Technology, Bangalore University
Bangalore,
India
Emails:
anand_palm@yahoo.co.in,
bharath_97@yahoo.com, chaitrabhat@mecheng.iisc.ernet.in,
kiran_k18@yahoo.com,
vinay_channakeshavarao@hotmail.com
Abstract.
The advances in manufacturing technology and proliferation of information
from research laboratories have posed the problem of information explosion. To
understand any systems behavior it would be appreciable if the process can be
visualized as a mapping from inputs to outputs. In materials research also, the
generation of hypothesis about various materials properties and the compositions
leading to such properties can be better understood by multivariate
visualization and machine learning techniques.
In this project an attempt has been made to develop a novel method for
multivariate visualization using parallel coordinate systems. The materials
classification problem is solved by using two popular methods clustering and
k-nearest neighbor technique. The prototype will allow the user to interactively
discover the hidden patterns by semiautomatic generation of hypothesis and
testing.
As a case study the developed prototype has been
tested on an Aluminium alloy database. The data for case study is taken from an
international laboratory in html format. Later it has been transformed to the
standard format for data mining. The cleaned data is later used for visual and
analytic data mining.
The preliminary application of data mining on the
aluminium alloy database indicates promising results. Few interesting
combination of materials that have wider industrial applications have been
discovered. It is hoped that the prototype with some additional features can
help knowledge discovery in materials research.
Keywords.
Data mining, knowledge discovery, visual data mining, multivariate
visualization, parallel coordinates, data mining process, manufacturing,
materials research, clustering, k- nearest neighbor..
1. Introduction.
In
manufacturing industries the constant Quest for success & progress revealed
that the problems in the industries could be fixed by the analysis of large
volumes of unorganized & scattered or raw information that may be defined as
data. Everyday there is lot of raw data that are collected and a need arises to
understand these data. The industries realized that what they really wanted was
the knowledge, trends patterns within the data- not the data itself. The
inability to discover valuable information hidden in the data prevented these
industries from transforming this data into knowledge. Hence a need arose to
extract valid, previously unknown, and comprehensible information from large
databases and uses it for the growth.
To fulfill these goals, industries need to follow the
following steps:
·
Capture
and integrate both the internal and external data into a comprehensive view that
encompasses the whole industries
·
"Mine"
the integrated data for information
·
Organize
and present the information and knowledge in ways that expedite complex
decision-making.
1.1.
Need for Data Visualization.
The
driving force behind visualizing data mining models can be broken down into key
areas: Understanding and trust. Understanding is undoubtedly the most
fundamental motivation behind visualizing the model. The more interesting way to
use a data-mining model is to get the user to actually understand what is going
on, so that action can be taken directly. Visualization will help in analyzing n
dimensions that can be selected and the evolution of the system in these
emphasized variables may be visualized directly. In order to minimize the loss
of information, where the variables can be mapped onto visual attributes like
color or texture. It helps in depicting the behavior of a dynamical system in
more than one dimension.
Other reason for data visualization is the limitation of human beings to
absorb the large amount of information. The volumes of data are overwhelming and
the human visual systems and brain are not equipped to work with the data in
this form. Using data visualization, we allow much faster processing of the data
and the ability to see the patterns in the data.
Data visualization seeks to combat the data understanding problem by
utilizing the tools of data mining. In brief data visualization is a method of
presenting the output so that the entire problem and the solution is clearly
visible to domain experts.
1.2. Different methods available for Data
Visualization.
Data visualization uses a graphical and numerical tools to reveal the
information contained in data. It is more effective approach for understanding
and communication than the use of common numerical tools. Graphical methods hold
a key for visualization. The best visualization method is one, which supports
the most insight into the phenomenon under study. There are different methods
available for visualization of the data.
Data can be:
- Univariate
- Bivariate
- Multivariate
1.2.1. Univariate Data.
Univariate data consist of samples or measurements of a single
quantitative variable. A fundamental task with this type of data is to
characterize its distribution. Other important tasks are comparing the
distributions of samples from two or more populations and comparing the data
distributions to standard distributions, especially the normal distribution.
Transformations of the data are sometimes used to achieve a more desirable
distribution.
Univariate data is represented
using the following methods.
·
Histogram
·
Pie
chart
Histogram: A histogram is the graphical representation
generally employed for a continuous distribution. A histogram is constructed by
drawing bars or rectangles on equal class intervals. The class intervals are
taken on the x-axis and the frequency on the y-axis. The bars are drawn so that
their height is proportional to the class frequency. The area of the bars will
then be proportional to the class frequency. If, however, the class intervals
are not equal, then the bars are drawn to represent frequency density. The
frequency density is obtained by dividing each frequency by the width of the
corresponding class interval .One of the best ways to summarize the data is to
provide a histogram of the data. This is the most useful way of getting a
high-level understanding of the database. Looking at the histogram, it is also
possible to build an intuition about the important factors. When there are many
values for a given predictor, the histogram begins to look smoother and
smoother.
F
= Frequency
C = Class
Figure 1 Histogram
The above Univariate graph is a histogram
representation of only one attribute with respect to its frequency.
Pie chart: A pie chart is also a pictorial representation of
the univariate data. In a pie chart or diagram a circle is drawn and it is
divided into sectors on such a way that the area of the sectors are proportional
to the magnitudes given. The angle at the center of a circle that is 3600 is
divided in the ratio of the individual data. Thus the chart is obtained.
Figure 2 Pie Chart
1.2.2. Bivariate Data
Bivariate
data consist of paired samples or measurements of two quantitative variables.
The general task with this type of data is to determine how the variables are
related. In come cases the variables are a factor (independent variable) and a
response (dependent variable). In other cases the variables are not functionally
related, but their distributions can be compared.
Bivariate data is represented
using the following methods
·
Scatter
plots
·
Line
graph
Scatter
Plots: scatter
plots have almost become a field of which research. A number of variables are
graphed to 2 to 3 axes. The simplest case is where each variable has its own
axis. Color can be used to encode additional variables. Scatter plots can use
additional visual coding. Given an m-dimensional matrix defining the data where
2 or 3 dimensions should be projected. Some objective function can be defined on
X. X = xij where xij is the ith observation or value from the jth
domain. The scatter plot is thus a projection Rm =R2 or Rm
= R3 to give (Xa,
Xb, (Xc)) where a, b,(and c)represent specific attribute types.[1]
Figure 3 Scatter Plot
Line graph: The line graph involves a method of curve fitting.
The workhorse method for curvefitting is least square regression estimating the
curve which has the minimum sum of the squares of the residuals. The most common
practice is to attempt to fit a straight line to the data. This is a case of
polynomial fitting:
Figure 4 Line Graph
This is a representation of a Bivariate graph with
only two attributes that can be represented at a time.
1.2.3. Multivariate Data:
Since
the above-mentioned techniques have multiple disadvantages we use the
multidimensional representations for visualization of the data.Multivariate data
consist of one quantitative variable, the response, and two or more categorical
variables as factors. There is a value of the response for each combination of
levels of the categorical variables. The general task with this type of data is
to determine how the response depends on the factors. N-1 points represent a
line in N dimensional space in the parallel system.
Multivariate data is
represented using the following methods
·
Dynamic
Parallel coordinate plots
·
Chernoff
faces
·
Independence
diagram
·
Parallel
coordinate plots
Dynamic Parallel coordinate system: It
is a graphic device for visual examination of large multivariate data sets. The
dynamic parallel coordinate system plot uses the novel technique of representing
a series of variables as a series of parallel axes, rather than orthogonal axes.
The dynamic plot extends the capabilities of existing versions of this graphic
device by providing a suite of interactive capabilities including brushing,
facing, color manipulation, classification scheme, customization and axis
variable reassignment. [6]
Chernoff faces: The method Chernoff faces, as the name
implies was invented by Chernoff in 1973 for representing multivariate data. The
procedure is simple bests effective. In this procedure each facial feature
denotes a particular variable. For example x1 can be associated with the size of
the mouth, x2 with the size of the nose, x3 with the size of the eyes and so on.
[7]
Independence diagram:
In order to recognize the complex dependencies between attributes we use
independence diagram. In this case each attribute is divided into ranges, for
each pair of attributes, the combination of these ranges defines a
two-dimensional grid. For each cell of this grid, the number of data items is
stored in it. The grid is displayed scaling each attribute axis so that the
displayed width of a range is prepositional to the total number of data items
within the range. The brightness of a cell is proportional to the density of
data items in it.[8]
Brushing: Perhaps the most common and historically first
widely used technique explicitly identified as graphical exploratory data
analysis is brushing, an interactive method allowing one to select on screen
specific data points or subsets of data and identify their characteristics or to
examine their effects on relations between relevant variables.
2. Visualizing Multivariate Data
2.1. Parallel Coordinate plots.
The
classic scatter diagram is a fundamental tool in the construction of a model for
data. It allows us to detect structures in data as linear or non-linear
features, clustering outliners &similar things. Unfortunately, scatter
diagrams do not generalize readily beyond three dimensions, because of this
reason visualization of multivariate data is an unsolved problem.[5]
In 1985, Prof. Alfred Inselberg proposed a method to visualize a
multivariate data where instead of preserving the orthogonality of the
n-dimensions draw them parallel, that is all axes are parallel to one another
and equally spaced.
Each
data dimension is represented as a horizontal or vertical axis, and the n-axes
are organized as uniformly spaced lines. A data element is an n-dimensional
space is mapped to a polyline that traverses across all of the horizontal or
vertical axes.
A
vector (x1, x2, x3, ------------xn) is created by plotting x1 on axis one, x2 on
axis two and so on through xn on axis n. A broken line joins these points. The
figure shows 2 pints one solid and one broken plotted in parallel coordinate
representation, that agree in IV coordinate. The principal advantage of this
plotting is the each vector (x1, x2, x3, ------xn) is represented in a planar
diagram, so each vector component has essentially the same representation.
It
is important to note that the parallel coordinates are really a generalization
of the simple bar graph or one to one plots. The parallel coordinates represents
a collection of data points as y axis coordinate values arrayed along the x
axis. The name parallel coordinates are derived from the fact that a specific
point in n- dimensional Euclidean space can be represented by n y-axis values
arrayed along the x-axis.[5]
In
order to formalize the mathematical representation, there are two additional
representational features. A fixed spacing between the points arrayed along the
x-axis, a vertical line through these x-axis points results in a collection of
lines all parallel to the y-axis. Connection using straight lines between the
points arrayed along the x-axis.
Dual property:
The parallel coordinate representation enjoys some elegant duality
properties with the visual Cartesian orthogonal coordinate representation.A line
in Cartesian coordinate plane is given by y = mx + b and [(a, ma + b) and(c, mc
+ b)] are the two points lying on that line.
The
xy Cartesian axes mapped into the parallel axes as shown above. Superimpose
Cartesian coordinate axes as shown above. Superimpose Cartesian coordinate axes
tu on the xy parallel axes so that the y parallel axis has the equation u=1. The
point (a, ma + b) in the xy Cartesian system maps into the line joining (a, 0)
to (ma + b, 1) in the tu coordinate axes. Similarly(c, mc + b) maps into the
line joining (c, 0) to (mc + b, 1). It is a straightforward computation to show
that these two lines intersect at a point in the tu plane given by L=[b (1-m)-1;(1-m)-1
]. This point in parallel plot depends on m and b only. The parameters of the
original line in Cartesian plot. Thus L is the dual of L given the interesting
duality that points in Cartesian coordinates map into lines in parallel
coordinates and lines in Cartesian coordinate map into points in parallel
coordinate.
Parallel
coordinates provide a means to visualize higher order geometric in an easily
recognizable two-dimensional representation. As a tool for the exploratory data
analysis of multi dimensional systems parallel coordinates can be display the
patterns, trends, and correlation's in the data while additionally revealing
hyper dimensional geometry.
Construction of parallel coordinates:
The construction of the parallel coordinate system is fairly simple. A
single horizontal line is drawn and a series of vertical axes, each representing
a separate variable are placed equal distances along the line. The number of
vertical axes is equal to number of variables that is if there are n-variables n
vertical axes are to be drawn the spacing between each axes is typically of unit
length. The values of a given variable are represented on the vertical axes
pertaining to that variable. Line segments between successive vertical axes
connect the values on each of the n-axes that correspond to an individual point
in Euclidean space. The result is a graph of line segments connected between
axes to form polygonal lines across the entire representation. Each polygonal
line of (n-1) segments represents a distinct point in n-dimensional space. The
collection of polygonal lines share some important dualities with the Cartesian
coordinate system and these dualities provide a method of interpreting the
parallel coordinate system through a transition into Cartesian coordinates and
Euclidean space.[2], [3], [4], [5]
Advantages:
- Parallel coordinates are easy to implement and easy to comprehend.
- Multi dimensional data can be viewed with a simple two-dimensional
graph.
- Potential marking of one data point by another in 3 dimensional
space is eliminated.
- Correlation patterns in multi dimensional data can be visualizes if
present.
- The number of dimensions that can be visualized is only restricted
by the horizontal resolution of the screen.
Figure 6 A five dimensional parallel coordinate
plot
2.2. Chernoff faces.
In this method each facial feature denotes a particular variable. As the
data is related to facial features in chernoff faces, they illustrate trends in
multidimensional data very effectively because it is something which we are used
to differentiate between.[7]
For example , X1 can be associated with the size of
the mouth,X2 with the size of the nose,X3 with the size of the eyes and so on.
Chernoff
faces are represented as shown above for a given data. Chernoff faces are used
for condensation of data and this avoids viewung of large tables of data and
hence helps in data digestion. In order to make use of chernoff faces the values
that the features represent must be clearly shown in addition to the plot list.
The plot itself does not contain any information on actual data values which are
plotted which is a limitation of chernoff faces. The chernoff faces can be used
where knowledge in the trends of the data determine which sections of the data
are of particular interest.
Figure 7 Chernoff Faces
Advantages of Chernoff faces:
- Trends in data are easily identified.
- Animated Chernoff faces can be used to show multiple relationship
which are more effective.
Disadvantages of Chernoff faces:
- Subjective assignment of facial expressions causes an error rate as
high as 25 for classifying faces in to groups.
- The actual values are not shown with the plot.
2.3. Independence diagrams:
In
data mining the recognition of complex dependencies between attributes is a
major issue. Earlier correlation co-efficients scatter plots and equiwidth
histograms are used to identify these attribute dependence. But these techniques
are sensitive to outliers, and often are not sufficiently informative to
identify the kind of attribute dependence present. To overcome these problems
independence diagrams are proposed.[8]
In
independence diagrams each attribute is divided into ranges and for each pair of
attributes the combination of these ranges defines a two dimensional grid. For
each cell of this grid the number of data items in it are stored. By scaling
each attribute axis the grid is displayed. So that the displayed width of a
range is proportional to the total number of data items with in that range. The
brightness of a cell is proportional to the density of data items in it.
As
a result both attributes are independently normalized by frequency ensuring
insensitivity to outliers, skew and allowing specific focus on attribute
dependencies. Independence diagrams provide quantitative
measures of the interaction between two attributes, and allow formal reasoning
about issues such as statistical significance.
Independence
diagrams enable the visual analysis of the dependence between any two attributes
of a data set this technique is not affected by data skew and outliers. It does
nit require any transformation of data to be specified by an expert. It has an
ability to focus purely on the dependence between two attributes stripping away
effects due to the respective univariate distributions. the basic idea in
independence diagrams is to divide the attributes independently into slices or
(rows or columns) such that each slice contains roughly the same number of data
items and additionally split slices having a large extension. This might be seen
as a combination of an equi-depth and equi-width histogram. Each intersection of
row or column defines a two-dimensional bucket, with which count is stored. This
kind of two-dimensional histogram is called as an equi-slice histogram. This
equi-slice histogram is maped to the screen in such a way that the width of data
items in the slice. Finally the brightness of a bucket is proportional to the
count of the bucket divided by its area.
This
kind of visualization is amenable to interpreting dimension dependence effects,
because the one- dimensional distributions have already been “normalized"
by depicting the slices in an equi-depth fashion. Equally populated slices
occupy equal space in the image, meaning that resolution is spent in proportion
to the data population, and that the image is not sensitive to outliers.
Given
d attributes there are (d2-d)
/ 2 images. These images could be shown together as thumbnails, lining up the
images along the same attributes.
There are three steps to generate an independence
diagrams
- Determine the boundaries of the slices used in each dimension and
count the number of data items in each grid cell and size.
- Scale each dimension and obtain a mapping from buckets to pixels.
- Determine the brightness for the pixels in each grid cell.
Figure
8
3. Visual Data Mining in Material Science.
This
phase deals with the implementation of the techniques and functions of data
mining for material classification, which involves different stages that are
discussed below.
3.1. System architecture
The system architecture consists of five
stages, they are
·
Data
collection
·
Data
modeling
·
Data
transformation
·
Data
visualization
·
Data
analysis
Data visualization is done using Parallel coordinate
system (for multivariate visualization) and histogram (for univariate
visualization), where as data analysis is done using Clustering and k-Nearest
Neighbor techniques.
Figure 9 System Architecture
3.1.1. Data collection
The prime most tasks involved is the collection of the data. The aluminum
alloys are chosen for the purpose. The data containing the information of
Aluminum alloys and their properties are considered. 1000 Series, 2000 series,
3000 series, 4000 series and 5000 series of Aluminum are taken from the
matweb.com. An example of the exact form of data available on the web and in
which the data was collected is as shown below:
Table.2
Aluminum 1060-H12
Subcategory: Aluminum Alloy; Nonferrous Metal; 1000
Series Aluminum
Close Analogs: Four Other Tempers
Key Words: Aluminium 1060-H12; UNS A91060;
AA1060-H12;
Composition:
[11]
3.1.2. Data modeling
After the data has been collected the data has to be modeled, that is
cleaning of the data is necessary. This is an important stage in knowledge
discovery. The Aluminum alloys contain a number of other materials in them. The
materials are taken and their statuses are being determined as per the data
available and are incorporated in a table as shown below. This involves the
stage of modeling the data. There are mainly two variables available the
predicator and the descriptor variables. The properties of the material
contribute to the descriptor variable and the materials themselves form the
predictor. All the properties are not considered. Only three properties are
taken into account. The table given below gives the complete details of the data
being collected.
Table.3
3.1.3. Data
transformation.
The data that is being modeled and cleaned has to be transferred into a
database that can be used for the development of the software. The cleaned data
hence is taken and is put into the database with all the compositions and the
values of the properties. Thus a database of the material is generated. The
database of materials as an example is exactly as shown below: This is the data
transformation stage.
Table.4
3.1.3.1. Statistics
The statistical tables for all the materials are tabulated. The table
gives the computed values of maximum and minimum values of the variables.
Table.5
3.1.4.
Visualization.
3.1.4.1. Parallel coordinates.
The multivariate visualization is achieved by parallel coordinate
representation. The plot involves vertical planes equal to number of variables
drawn parallel to each other. The planes are equi-spaced on the screen at a
distance
X = screen width / n, where n = number of variables +1.
Vertical coordinates of the planes Starts at
Ystart = (screen height) /10
Ends
at Yend = 8 *
(screen height) / 10
Each plane represents a variable, the Ystart point
represents the maximum value and the Yend point represents the minimum value of
that variable in the training dataset. Other values are mapped on the line using
a scaling factor.
Scaling factor = (Yend – Ystart)/ (Range)
One record is retrieved at a time from the dataset
and values of all the variables are mapped using the scaling factor, all these
points are then joined with straight lines. All the records are mapped in the
similar way to obtain a raw plot as shown in figure 10.
In
order to generate hypothesis and to answer the user's query the statistical
analysis is necessary. The calculation of mean and mode is given by the
following formula:
Calculation of mean :
Xi = sum of all values/number of occurrence
Calculation of mode :
M= Lm +((Fm-Fp)/(2Fm-Fp-Fp))*w
Where Lm = lower limit of the modal class
Fm = frequency of the modal class
Fp = frequency of the modal
preceding class
Fs = frequency of the successor class
W = width of the class
3.1.5. Data analysis.
3.1.5.1.
Clustering.
Clustering
is used for segmenting the dataset into groups of like data. Clusters are
observed in the raw plot in all the attributes. Using this technique a
relationship between clusters of one attribute with other attributes can be
seen. The number of clusters k, as seen in the raw plot for any attribute is
entered. K, number of records starting from the first record is chosen as
arbitrary cluster centers.
Ac1 = [ X111, X121,X131……..X1n1
]……… ack = [ Xk11, Xk21,……..Xkn1
]
From
each of the cluster centers, distances of all the records are calculated using
the distance formula
dij = | Xk11 – X1 | + | Xk21
– X2 | +..…+ | Xkn1 – Xn |
A record is grouped into that
cluster with which it has the minimum distance.New cluster centers are
calculated based on allocated clusters. The average of the allocated clusters
forms new cluster centers. The distances of all the records from the new
calculated cluster centers are calculated and the new clusters are assigned
again. If the new clusters assigned match with the previous clusters, the
clusters are accepted and visualized. Otherwise, the process is repeated again
by calculating new cluster centers and the distances and clusters until these
clusters match the previously assigned clusters.
Finally
the clusters thus formed are visualized with different colors for different
clusters (As shown in figure 14). This helps in ease of visualization and
verification for further analysis.
3.1.5.2.
k-Nearest Neighbor.
In k-NN, the predictors are used to find the descriptors. The predictors
here are the composition of the alloy and the descriptors are mechanical
properties namely Hardness, Tensile Strength and Shear Strength.
The known composition of the material (predictors) [ X11,
X21, X31, X41,…Xn1
] and
number of closest cases required (k) are entered. The distance of this given
composition with available training dataset is calculated.
Distance i
= | Xi1 – X11| + | Xi2 -
X21 | + …….. + | Xin – Xn1|
i = number of records.
n = number of attributes
Descriptors
of k number of nearest records are listed in an ascending order of the distance.
4. Results.
The
process of obtaining the results in this project is divided into a three-stage
procedure.
The three stages are
- Generation
of hypothesis using visual information (Histogram – a univariate
visualization tool) available.
- Testing
of the generated hypothesis on the experimental data
collected (This is accomplished by querying).
- Verification
of the hypothesis for augmented or rejection by
analyzing
the parallel coordinate plot obtained in response to the
input
query.
Among
the results obtained a few are interesting and which depict novel properties are
explained.
Result 1.
Ho:
Increase in Bismuth concentration increases Tensile strength.
H1:
Increase in Bismuth concentration has no effect on Tensile strength.
In result
1 the null hypothesis Ho states increase in Bismuth concentration increases
tensile strength and the alternate hypothesis H1 states increase in Bismuth has
no effect on tensile strength. For generation of the above stated hypothesis a
univariate visualization tool, histogram (figure 11a) is used. When this
hypothesis was tested on the experimental data, two plots were obtained which
are as shown in figure 11b and figure11c.
In
figure 11b it can be seen that when the Bismuth ranges from 0.2 to 0.3%, the
tensile strength ranges from 262 to 270Mpa. In figure 11c, it can be seen that
when Bismuth concentration ranges from 0.4 to 0.6%, the tensile strength ranges
from 276 to 310Mpa. This is rather a simple result showing one to one relation
between the concentration of Bismuth and the tensile strength involving only two
variables.
- Concentration
of Bismuth a predictor variable.
- Tensile
strength a descriptive variable.
By
verifying the plot null hypothesis is augmented.
Result 2.
Ho:
Increase in concentrations of Lithium and Zirconium increases values of
mechanical properties like hardness, tensile strength, and shear strength.
H1:
Increase in concentration of Lithium and Zirconium has no effect on hardness,
tensile strength, and shear strength.
In this
result the null hypothesis states increase in concentrations of Lithium and
Zirconium increases values of mechanical properties and alternate hypothesis
states that increase in concentration of Lithium and Zirconium have no effect on
the mechanical properties. For generation of the above stated hypothesis a
univariate visualization tool, histograms (figure12a and 12b) is used.
This
hypothesis involves 5 variables of which 2 are predictor variables and 3
descriptor variables. Testing this hypothesis and verifying the plot obtained
can appreciate the real powers of parallel coordinate system.
When
this hypothesis was tested on the experimental data, the corresponding plot
obtained is shown in figure12c. From the plot it can be seen that when the
concentration of Lithium and Zirconium are between (2 to 2.2%) and (0.08 to
0.1%) respectively, the hardness value ranges from 57 to 86 BHN, the tensile
strength ranges from 190 to 210MPa and the shear strength ranges from 130 to
190MPa respectively. Whereas when the concentration of Lithium and zirconium are
between (2.4 to 2.6%) and (0.13 to 0.16%) respectively, the hardness ranges from
140 to 150 BHN, the tensile strength ranges from 470 to 520MPa and the shear
strength being a maximum of 320MPa.
For
a small increase on the concentration of Lithium and Zirconium more than a 100%
increase in the properties are observed and it follows that null hypothesis is
augmented.
The
novel properties observed in this result is very useful in aeronautical, space
research and such other fields which demand for materials with high tensile
strength & high shear strength with the weight of the material being light.
Result 3.
Ho:
Increase in Vanadium concentration improves tensile strength, hardness and
shear strength.
H1:
Increase in Vanadium concentration has no effect on tensile strength, hardness
and shear strength.
In result
3, the null hypothesis states that increase in vanadium concentration improves
tensile strength, hardness and shear strength and the alternate hypothesis
states that increase in vanadium concentration has no effect on tensile
strength, hardness and shear strength. For generation of the above stated
hypothesis a univariate visualization tool, histogram (figure13a) is used.
When
this hypothesis has tested on the experimental data, two plots were obtained as
shown in the figure 13b and figure 13c. From parallel coordinate plot (figure
13b) it can be seen that when the concentration of Vanadium ranges from 0.01 to
0.03%, hardness ranges from 17 to 50 BHN tensile strength ranges from 30 to
165MPa and shear strength ranges from 26 to 105MPa. Whereas from figure 13c, it
can be seen that when the concentration of vanadium is increased from 0.03 to
0.05%, no significant change in the values of the properties is observed. By
this verification, null hypothesis is rejected that means vanadium hardly
affects the properties.
Figure
10 Parallel
coordinates plot showing all records.
Figure 11a Histogram for Bismuth Concentration
Figure 11b Plot for increasing Bi concentration from 0.2 to 0.3 %
Figure
11c Plot for increasing Bi concentration from 0.4 to 0.6 %
Figure 12a Histogram for Lithium
Figure 12b Histogram for Zirconium
Figure
12c Plot for increasing Li and Zr concentration.
Figure
13a Histogram for Vanadium
Figure
13b Plot for increasing V concentration from 0.04 to 0.05 %
Figure
13c Plot for increasing V concentration from 0.01 to 0.03 %
Figure
14 Parallel Plot showing different clusters in Shear Strength
5.
Conclusions.
In
this project software prototype has been developed for Visual and Analytic Data
Mining. For the development of the prototype, Parallel Coordinate System is used
for multivariate data visualization. K-NN technique is used for classification
of the specified composition of Al alloy to the class that it belongs to and
also to predict the properties of the specified alloy composition. Clustering
technique is used for grouping of different compositions & properties of
those alloys in different syndicates/groups. The k-NN technique & clustering
technique together constitute the Analytic Data Mining.
The
developed prototype has been tested on the standard data collected from an
International Material Research Lab. Some of the Novel properties, which are
interesting but not explicitly available, are discovered. These are explained in
Results.
6.
Scope for further work.
The following points can enumerate the road ahead for
further improvement of this project.
-
The variables
can be generalized so that wider material data set can be mined.
-
Parallel
Coordinate System can be complimented by the use of Independence
Diagrams.
-
Techniques
like Decision Trees & k – Medoids can be used in place of k -NN
& Clustering techniques.
References.
[1] Datatool.com/dvt/dataviz
[2] Alfred Inselberg, The plane with parallel
coordinates, Visual Computer, 1 (1985), pp 69-97
[3] Alfred Inselberg and B.Dimsdale, Multidimensional
Lines I and II, SIAM J. Appl. Math., 54 (1993),
pp. 559-596.
[4] Alfred Inselberg, Visual Data Mining with
Parallel Coordinates *multidimensional graph Ltd.
(1981), Computer Science dept. TelAviv University, Israel.
[5] E. Wegman, Hyper dimensional data analysis
using parallel coordinates, J. Amer. Statist. Assoc.,
85 (1990), pp. 664-675.
[6] Robert .M. Edsall, Dynamic parallel
coordinate plot for visualizing multivariate data, Dept of Geography,
Penn State University.
[7] H. Chernoff, The use of faces to represent
points in k-dimensional space graphically, J. Amer. Statist. Assoc., 68 (1973), pp. 361-368.
[8] Stephen Berchtold, H.V. Jagadish (AT&T
Laboratories) and Kenneth Ross (Columbia University)
Independence diagram - A technique for
Visual Data Mining.
[9] Tim McLean (1995), www.islandnet.com
[10] Alex Berson, Stephen Smith and Kurt
Thearling - Building Data Mining Application for CRM.
[11] www.Matweb.com