n
m
ij ¼
1; F
m
ðd i Þ ¼ F
m
ðd j Þ
0; F
m
ðd i Þ 6 ¼ F
m
ðd j Þ
&
ð11Þ
In the base clusters, each cluster can be treated as a local region, so the reliability of
clusters should be considered, while weighting term x
m
i is incorporated to assign
weights to clusters via the ROC measure. So the ROC-CA matrix not only considers the
reliability of base clusters but also considers the locally diversity.
The final consistency method adopted in this paper is a hierarchical clustering
algorithm combined with ROC-CA matrix. Hierarchical agglomerative clustering is a
typically used clustering method, which always takes a similarity matrix as input and
performs region merging iteratively to achieve a dendrogram, i.e., a hierarchical representation of clusterings. The input is ROC-CA matrix, which can denote as:
Q
ð0Þ
¼ fQ
ð0Þ
ij g NÂN , where Q
ð0Þ
ij ¼ a ij . The N original data are treated as the N regions,
denoted as: R
ð0Þ
¼ fR
ð0Þ
1 ; . . .; R
ð0Þ
N g. According to the given initial region and similarity
matrix, the region merging iteration begins, and two regions with the highest similarity
are selected for merging each time. The region in the tth is denoted as:
R
ðtÞ
¼ fR
ðtÞ
1 ; . . .; R
ðtÞ
R ðtÞ
j j
g, the similarity matrix is denoted as: Q
ðtÞ
¼ fQ
ðtÞ
ij g R ðtÞ
j jÂR ðtÞ
j j ,
where Q
ðtÞ
ij ¼
1
R
ðtÞ
i
j j R
ðtÞ
j
j j
P
d k 2R
ðtÞ
i ;d l 2R
ðtÞ
j
a kl .
Algorithm 4: Locally Weighted Consensus Function
Input: P: Ensemble of base clusterings; k: number of clusters;
Method:
1: C_{i} in P;
2: compute the ROC measure of the clusters in P;
3: formulate the ROC-CA matrix;
4: initialize the set of regions R
ð0Þ and the similarity matrix Q
ð0Þ ;
5: construct the dendrogram iteratively:
for t = 1, 2, …, N−1
merge the two most similar regions in R
ðtÀ1Þ
obtain the new set of regions R
ðtÞ
obtain the new similarity matrix Q
ðtÞ
end for
6: obtain the clustering with k clusters in the dendrogram
Output: the consensus clustering p
Ã
Research on Chinese Short Text Clustering …
627
m
ij ¼
1; F
m
ðd i Þ ¼ F
m
ðd j Þ
0; F
m
ðd i Þ 6 ¼ F
m
ðd j Þ
&
ð11Þ
In the base clusters, each cluster can be treated as a local region, so the reliability of
clusters should be considered, while weighting term x
m
i is incorporated to assign
weights to clusters via the ROC measure. So the ROC-CA matrix not only considers the
reliability of base clusters but also considers the locally diversity.
The final consistency method adopted in this paper is a hierarchical clustering
algorithm combined with ROC-CA matrix. Hierarchical agglomerative clustering is a
typically used clustering method, which always takes a similarity matrix as input and
performs region merging iteratively to achieve a dendrogram, i.e., a hierarchical representation of clusterings. The input is ROC-CA matrix, which can denote as:
Q
ð0Þ
¼ fQ
ð0Þ
ij g NÂN , where Q
ð0Þ
ij ¼ a ij . The N original data are treated as the N regions,
denoted as: R
ð0Þ
¼ fR
ð0Þ
1 ; . . .; R
ð0Þ
N g. According to the given initial region and similarity
matrix, the region merging iteration begins, and two regions with the highest similarity
are selected for merging each time. The region in the tth is denoted as:
R
ðtÞ
¼ fR
ðtÞ
1 ; . . .; R
ðtÞ
R ðtÞ
j j
g, the similarity matrix is denoted as: Q
ðtÞ
¼ fQ
ðtÞ
ij g R ðtÞ
j jÂR ðtÞ
j j ,
where Q
ðtÞ
ij ¼
1
R
ðtÞ
i
j j R
ðtÞ
j
j j
P
d k 2R
ðtÞ
i ;d l 2R
ðtÞ
j
a kl .
Algorithm 4: Locally Weighted Consensus Function
Input: P: Ensemble of base clusterings; k: number of clusters;
Method:
1: C_{i} in P;
2: compute the ROC measure of the clusters in P;
3: formulate the ROC-CA matrix;
4: initialize the set of regions R
ð0Þ and the similarity matrix Q
ð0Þ ;
5: construct the dendrogram iteratively:
for t = 1, 2, …, N−1
merge the two most similar regions in R
ðtÀ1Þ
obtain the new set of regions R
ðtÞ
obtain the new similarity matrix Q
ðtÞ
end for
6: obtain the clustering with k clusters in the dendrogram
Output: the consensus clustering p
Ã
Research on Chinese Short Text Clustering …
627