Enhancing the performance of Naive Bayesian(NB) using the attributes with have highest Information Gain

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2.  Abstract of the work
 Why we need it?
 Naïve Bayesian Classifier
 Definition
 Algorithm
 Gaussian Distribution
 Decision Tree
 Definition
 Algorithm
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3.  Information Gain
 My Algorithm
 Experimental Design
 Experimental Result
 Remarks
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4.  Apply Naïve Bayesian.
 Based on information gain create decision tree
& select attributes.
 Apply Naïve Bayesian with the selected
attributes.
 Minimize the time & space need to analysis.
 Can work with continuous data stream.
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5. 1. Now-a-days data volume of internet
user is getting larger.
2. Machine learning is getting harder
day by day.
3. Pre-processing of data may be a
solution for it.
4. Using the necessary data only can
make the learning process faster
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6. 5. A better technique can make the process more
organized using only necessary data
6. Cut off all un-important attributes from data set.
7. Dataset become compact in terms of attributes
and calculation becomes fast.
8. Get better performance than past on behalf of
time and space.
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7.  Naïve Bayesian Classifier
 Gaussian Distribution
 Decision Tree
 Information Gain
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8.  The Naïve Bayesian classifier(NB) is a
straightforward and frequently used method
for supervised learning.
 It provides a flexible way for dealing with any
number of attributes or classes
 It’s based on statistical probability theory.
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9.  It is the asymptotically fastest learning
algorithm that examines all its training input.
 It has been demonstrated to perform
surprisingly well in a very wide variety of
problems in spite of the simplistic nature of the
model.
 Furthermore, small amounts of bad data, or
“noise,” do not perturb the results by much.
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10.  There are classes, say Ck for the data to be
classified into.
 Each class has a probability P(Ck) that
represents the prior probability of classifying
an attribute into Ck.
 For n attribute values, vj, the goal of
classification is clearly to find the conditional
probability P(Ck | v1 ∧ v2 ∧ … ∧ vn).
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11.  By Bayes’ rule, this probability is equivalent to
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12.  The mathematical function for calculating the
probability density of Gaussian distribution at a
particular point X is:
where µ is the mean and σ is the standard deviation of
the continues-valued attribute X
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13.  1. Decision trees are one of the most
popular methods used for inductive
inference.
 2. The basic algorithm for decision tree
induction is a greedy algorithm that
constructs decision trees in a top-down
recursive divide-and-conquer manner.
 3. The main concept of selecting an
attribute and constructing a decision tree
is Information Gain(IG)
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14.  The basic idea behind any decision tree
algorithm is as follows:
 Choose the best attribute(s) to split the remaining
instances and make that attribute a decision node
using Information Gain
 Repeat this process for recursively for each child
 Stop when:
 All the instances have the same target attribute value
 There are no more attributes
 There are no more instances
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15. Leave At
Stall? Accident?
10 AM 9 AM
8 AM
Long
Long
Short Medium Long
No Yes No Yes
If we leave at
9 AM and
there is no
accident
happened on
the road, what
will our
commute time
be?

16.  The critical step in decision trees is the selection of
the best test attribute.
 The information gain measure is used to select the
test attribute at each node in the tree.
 The expected information needed to classify a
given sample is given by
where pk is the probability that an arbitrary sample
belongs to class Ck and is estimated by sk / s.
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17. 1. Run Naïve Bayesian classifier on the training
data set
2. Run C4.5 on data from step 1.
3. Select a set of attributes that appear only in
the simplified decision tree as relevant features.
4. Run Naïve Bayesian classifier on the training
data using only the final attributes selected in
step 3.
5. Compare the result of step 4 with step 1.
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18.  Each dataset is shuffled randomly.
 Produce disjoint training and test sets as
follows.
 80% training & 20% test data
 70% training & 30% test data
 60% training & 40% test data
 For each set of training and test data, run
 Naïve Bayesian Classifier (NBC)
 C4.5
 Selective Bayesian Classifier(SBC)
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19. Dataset # of instances # of attributes # of attributes
selected
Iris 150 4 2
Diabetes 768 8 6
Ionosphere 351 34 14
Breast Cancer 286 9 6
Ecoli 336 8 7
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 Number of instances and attributes before &
after Decision Tree

20.  Number of test instance(s) classified properly
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Trainin
g : Test
Number
of
instance
Naïve
Bayesia
n
Accurac
y(%)
Selectiv
e Naïve
Bayesia
n
Accurac
y(%)
80 : 20 30 27 90% 29 96.67%
Iris 70 : 30 45 42 93.33% 43 95.56%
60 : 40 60 56 93.33% 57 95%
Trainin
g : Test
Number
of
instance
Naïve
Bayesia
n(NB)
Accurac
y(%)
Selectiv
e Naïve
Bayesia
n
Accurac
y(%)
80 : 20 154 119 77.27% 126 81.81%
Diabetes 70 : 30 231 173 76.20% 181 78.35%
60 :40 308 239 77.60% 246 79.87%

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Training
: Test
Number
of
instance
Naïve
Bayesian
(NB)
Accuracy
(%)
Selective
Naïve
Bayesian
Accuracy
(%)
80 : 20 137 134 97.81% 135 98.54%
Breast
Cancer
70 : 30 205 200 97.56% 202 98.54%
60 : 40 274 261 95.26% 264 96.35%
Training
: Test
Number
of
instance
Naïve
Bayesian
(NB)
Accuracy
(%)
Selective
Naïve
Bayesian
Accuracy
(%)
80 : 20 68 56 82.35% 58 85.29%
Ecoli 70 : 30 101 81 80.20% 82 81.19%
60 :40 135 110 81.48% 110 81.48%

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Trainin
g : Test
Number
of
instance
Naïve
Bayesian
Accuracy
(%)
Selective
Naïve
Bayesian
Accuracy
(%)
80 : 20 81 74 91.36% 78 96.30%
Ionospher
e
70 : 30 106 97 91.51% 100 94.34%
60 : 40 141 131 92.91% 134 95.04%

23.  Result of Cross Validation(10 fold)
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Naïve Bayesian Selective Naïve
Bayesian
Number of
instances
15 16 16
16 16 16
14 14 16
16 16 16
Iris 13 13 16
16 16 16
15 15 16
15 16 16
15 16 16
15 15 15

24.  Result of Cross Validation(10 fold)
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Naïve Bayesian Selective Naïve
Bayesian
Number of
instances
65 63 69
68 68 69
68 68 69
66 65 69
Breast Cancer 65 65 69
66 66 69
68 69 69
67 68 69
65 66 69
67 69 69

25.  Result of Cross Validation(10 fold)
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Naïve Bayesian Selective Naïve
Bayesian
Number of
instances
69 68 77
53 56 77
56 57 77
61 62 77
Diabetes 65 64 77
56 56 77
56 57 77
60 59 77
52 54 77
59 60 77

26.  Result of Cross Validation(10 fold)
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Naïve Bayesian Selective Naïve
Bayesian
Number of
instances
21 21 34
31 31 34
31 31 34
26 26 34
Ecoli 25 25 34
23 23 34
24 24 34
27 27 34
29 29 34
30 30 34

27.  Result of Cross Validation(10 fold)
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Naïve Bayesian Selective Naïve
Bayesian
Number of
instances
35 33 36
33 33 36
31 32 36
33 34 36
Ionosphere 33 35 36
30 31 36
30 31 36
32 33 36
31 31 36
33 34 36

28.  Dataset:
 UCI Machine Learning Repository
 Weka provided datasets
 Software & Tools:
 Weka 3.6.9
 Python Data Mining libraries
 sklearn
 numpy
 pylab
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29. Thank You
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