2 research outputs found
Augmentation of the Reconstruction Performance of Fuzzy C-Means with an Optimized Fuzzification Factor Vector
Information granules have been considered to be the fundamental constructs of
Granular Computing (GrC). As a useful unsupervised learning technique, Fuzzy
C-Means (FCM) is one of the most frequently used methods to construct
information granules. The FCM-based granulation-degranulation mechanism plays a
pivotal role in GrC. In this paper, to enhance the quality of the degranulation
(reconstruction) process, we augment the FCM-based degranulation mechanism by
introducing a vector of fuzzification factors (fuzzification factor vector) and
setting up an adjustment mechanism to modify the prototypes and the partition
matrix. The design is regarded as an optimization problem, which is guided by a
reconstruction criterion. In the proposed scheme, the initial partition matrix
and prototypes are generated by the FCM. Then a fuzzification factor vector is
introduced to form an appropriate fuzzification factor for each cluster to
build up an adjustment scheme of modifying the prototypes and the partition
matrix. With the supervised learning mode of the granulation-degranulation
process, we construct a composite objective function of the fuzzification
factor vector, the prototypes and the partition matrix. Subsequently, the
particle swarm optimization (PSO) is employed to optimize the fuzzification
factor vector to refine the prototypes and develop the optimal partition
matrix. Finally, the reconstruction performance of the FCM algorithm is
enhanced. We offer a thorough analysis of the developed scheme. In particular,
we show that the classical FCM algorithm forms a special case of the proposed
scheme. Experiments completed for both synthetic and publicly available
datasets show that the proposed approach outperforms the generic data
reconstruction approach
Granular Computing: An Augmented Scheme of Degranulation Through a Modified Partition Matrix
As an important technology in artificial intelligence Granular Computing
(GrC) has emerged as a new multi-disciplinary paradigm and received much
attention in recent years. Information granules forming an abstract and
efficient characterization of large volumes of numeric data have been
considered as the fundamental constructs of GrC. By generating prototypes and
partition matrix, fuzzy clustering is a commonly encountered way of information
granulation. Degranulation involves data reconstruction completed on a basis of
the granular representatives. Previous studies have shown that there is a
relationship between the reconstruction error and the performance of the
granulation process. Typically, the lower the degranulation error is, the
better performance of granulation is. However, the existing methods of
degranulation usually cannot restore the original numeric data, which is one of
the important reasons behind the occurrence of the reconstruction error. To
enhance the quality of degranulation, in this study, we develop an augmented
scheme through modifying the partition matrix. By proposing the augmented
scheme, we dwell on a novel collection of granulation-degranulation mechanisms.
In the constructed approach, the prototypes can be expressed as the product of
the dataset matrix and the partition matrix. Then, in the degranulation
process, the reconstructed numeric data can be decomposed into the product of
the partition matrix and the matrix of prototypes. Both the granulation and
degranulation are regarded as generalized rotation between the data subspace
and the prototype subspace with the partition matrix and the fuzzification
factor. By modifying the partition matrix, the new partition matrix is
constructed through a series of matrix operations. We offer a thorough analysis
of the developed scheme. The experimental results are in agreement with the
underlying conceptual framewor