21 High-Temperature Creep Damage Evolution of C/SiC …
239
2. Calculate the distance from the sample points which are undefined as the centerto-center of each category (the distance being the Euclidean distance), obtaining
the minimum value, and putting it in the category where the shortest center is
located.
All samples are classified according to the method above, and the number
of samples in all categories is recorded. Then each new cluster center is
re-calculated.
C i1 =
1
n
n
j=1
x j i = 1, 2, . . . , K
(n is the number of samples belonging to class i),
Then all the data points are divided into K classes, and the cluster centers were
settled as the average of each cluster data.
3. By comparing the new category center and the old cluster center, if all the category
centers are equal, namely C im = C i(m+1) , i = 1,2, …, K, then the clustering
process is finished, otherwise step (2) is repeated, the samples are reclassified until
condition (3) is satisfied. When this occurs the clustering process is complete,
with m representing the number of iterations.
4. When the best results are obtained, the entire iterative process is complete and
the squares of the errors for all cluster categories are calculated.
21.2.2 The Voting and Evaluation Criterion
The key step in unsupervised analysis is to evaluate the validity of the reducing-order
algorithm. We give three independent similarity criteria to evaluate the clustering.
Then we use a voting rule to find the optimal value of the binary variable (H, I), with
the rule given in Table 21.1.
It is important to note that the optimal value of the DB indicator is small, while
the optimal value of the Dunn index and the Silhouette index is large. After the three
votes were independently completed, the final total voting score Z is the sum of them:
Z = V _D B(Z 1 ) + V _Dunn(Z 2 ) + V _Slih(Z 3 )
The above formula is the final score function expression; the optimal feature
combination and optimal clustering number are obtained as a function of the binary
variable H and I.
Table 21.1 Voting criterion
Rank
I
II
III
IV
Score
30
15
10
5
239
2. Calculate the distance from the sample points which are undefined as the centerto-center of each category (the distance being the Euclidean distance), obtaining
the minimum value, and putting it in the category where the shortest center is
located.
All samples are classified according to the method above, and the number
of samples in all categories is recorded. Then each new cluster center is
re-calculated.
C i1 =
1
n
n
j=1
x j i = 1, 2, . . . , K
(n is the number of samples belonging to class i),
Then all the data points are divided into K classes, and the cluster centers were
settled as the average of each cluster data.
3. By comparing the new category center and the old cluster center, if all the category
centers are equal, namely C im = C i(m+1) , i = 1,2, …, K, then the clustering
process is finished, otherwise step (2) is repeated, the samples are reclassified until
condition (3) is satisfied. When this occurs the clustering process is complete,
with m representing the number of iterations.
4. When the best results are obtained, the entire iterative process is complete and
the squares of the errors for all cluster categories are calculated.
21.2.2 The Voting and Evaluation Criterion
The key step in unsupervised analysis is to evaluate the validity of the reducing-order
algorithm. We give three independent similarity criteria to evaluate the clustering.
Then we use a voting rule to find the optimal value of the binary variable (H, I), with
the rule given in Table 21.1.
It is important to note that the optimal value of the DB indicator is small, while
the optimal value of the Dunn index and the Silhouette index is large. After the three
votes were independently completed, the final total voting score Z is the sum of them:
Z = V _D B(Z 1 ) + V _Dunn(Z 2 ) + V _Slih(Z 3 )
The above formula is the final score function expression; the optimal feature
combination and optimal clustering number are obtained as a function of the binary
variable H and I.
Table 21.1 Voting criterion
Rank
I
II
III
IV
Score
30
15
10
5