eigenvec= eigen vectors of
B W
1 −
7 VI.
Sort eigenvec with respect to eigenval in descending order and choose K greater of them. So
the eigenvec will be a matrix of MK dimensional is chosen heuristically through experiments, such that
the first K largest eigenvalues are conspicuously greater than the rest of other. Fig.1 is a typical
example of an eigenvalue distribution.
VII. Use the eigenvec to project training sample to new
domain
K M
old
eigenvec X
X =
8
Assumptions This algorithm makes the following assumptions
about the data in X:
• The populations for each group are normally
distributed. •
The variance-covariance matrix is the same for each population.
• All observations are mutually independent.
Figure 1.Typical Eigenvalue distribution
3. User Identification
Output of prior section is eigenvec matrix that will be used to project new instances with M feature to
new domain with K dimensions .suppose
x
be the feature vector of new user, we have
K M
1 1
eigenvec
M K
x x
=
Now we should determine the class that this instance belongs to. To do this we used nearest neighbor
algorithm; In the other hand we classify the new sample as a member of the known class if its position
is near the locus of that training sample set else if this distance is greater than a threshold, the user is
identified as unknown. Below figures shows that the first two canonical
variables produce more separation between groups than any pair of original variables.
Figure 2. Two original variables
Figure 3. First two canonical variables
4. Experiments and Results
Experiments were done using the keystroke pattern from eight users gathered in ten weeks time. We asked
users to type a constant text “This is a Test”. This process has been done at least twice a day with hours of delay
between them. Using this method it seems that the mental effects of users in different situation will be included in
the gathered typing pattern. Users were able to enter the sentence in each time as many as they want.
There are two points that must be attended. First, because of the typed sentence is similar for all users,
getting a low error classification results seems difficult. Second, in normal typing case, a user presses one key,
releases it, and then presses another key and continues this cycle. But in abnormal case, a user presses a key
before releasing another key.
Int’l Symposium on Telecommunications IST2003 , 16 -18 August, 2003 Isfahan-Iran
393
The users typed the sentence totally 1509 times. To achieve more accurate classifier, we studied the result
of the nearest neighbor classifier under following conditions. We have used 10, 25 and 50 percent of
samples as the test set and the rest of data as the training samples.
1-
The Mahalanobis distance is calculated in a 1-nearest neighbor scheme. The results of classifier
are shown in table 1.
2-
The Euclidean distance is calculated in a 1- nearest neighbor scheme. The results are shown in
table 2.
3-
The Euclidean distance is calculated between each sample and the gravity center of the
classes in a 1-nearest neighbor scheme. The results are shown in table 3.
Test set T
A B
C 10
0.0861 0.053
0.0066 0.0265
25 0.1114
0.045 0.0106
0.0557 50
0.1391 0.065
0.0172 0.0570
Table 1 Mahal. distance Test set
T A
B C
10 0.0927
0.0795 0.0066
0.0066 25
0.1088 0.0398
0.0371 0.0318
50 0.1285
0.0583 0.0344
0.0358 Table 2 Euclidean distance
Test set T
A B
C 10
0.0927 0.0464
0.0199 0.0265
25 0.1088
0.0424 0.0345
0.0318 50
0.1245 0.0477
0.0318 0.045
Table 3 Gravity The nomenclature we used is as follows:
T= Total error rate A= Error rate that a good user identified as other
good user. B= Error rate that a good user identified as bad user
C= Error rate that a bad user identified as good user 10 means TR=1358
Tst=151 25 means TR=1132
Tst=377 50 means TR=754
Tst=755 The resulting tables show that using different distance
metrics has no effect on the total error rate but the distribution of error type is affected. We have observed
that the performance of the Mahalanobis distance is enhanced more then the other distances when the size of
the training set is concerned. We used quarter of training samples of each class
which were not used in feature enhancement to calculate the threshold level by measuring distance between them
and the samples of other classes.
5. Conclusion
