2,979 publications from this institution
The key issue of determining a suitable (feasible) number of clusters still remains open. This paper proposes a graph-theoretic clustering iterative algorithm that employs a novel idea of using noise and information associated with it to determine clusters. The proposed method does not require any parameters whose values have to be supplied by the user. A series of experiments reported in the study show that the proposed algorithm can extract significant cluster information even in case of complicated geometry of data sets.
Recently, granular models have been highlighted in system modeling and applied to many fields since their outcomes are information granules supporting human-centric comprehension and reasoning. In this study, a design method of granular model driven by hyper-box iteration granulation is proposed. The method is composed mainly of partition of input space, formation of input hyper-box information granules with confidence levels, and granulation of output data corresponding to input hyper-box information granules. Among them, the formation of input hyper-box information granules is realized through performing the hyper-box iteration granulation algorithm governed by information granularity on input space, and the granulation of out data corresponding to input hyper-box information granules is completed by the improved principle of justifiable granularity to produce triangular fuzzy information granules. Compared with the existing granular models, the resulting one can yield the more accurate numeric and preferable granular outcomes simultaneously. Experiments completed on the synthetic and publicly available datasets demonstrate the superiority of the granular model designed by the proposed method at granular and numeric levels. Also, the impact of parameters involved in the proposed design method on the performance of ensuing granular model is explored.
As an augmentation of classic fuzzy models, granular fuzzy models (GFMs) have been applied to many fields being in rapport with experimental data, models, and users. However, most of the existing methods used to construct GFMs are based on the principle of optimal allocation of information granularity, which requires that a numeric model be provided in advance. In this paper, a straightforward and convincing modeling method is proposed to directly construct GFM on a basis of experimental data. The method first granulates the output space to form some interval information granules with distinct semantics and then uses them to partition the entire input space into a series of input subspaces. Subsequently, an initial GFM is emerged by using "If-Then" rules to relate with those interval information granules positioned in the output space and structures expressed in prototypes that are produced by clustering individual input subspaces. Further, the initial GFM is also refined by continuously migrating prototypes in individual input subspaces. The experimental studies using the synthetic dataset and several real-world datasets are reported. They offer a useful insight into the feasibility and effectiveness of the proposed modeling method and reveal the impact of parameters on the performance of the ensuing GFMs. An application example is also presented to exhibit the advantages of the resulting GFM.
The article concentrates on selected aspects of knowledge representation. It is considered how fuzzy sets viewed as linguistic labels (information granules) determine a representation frame. the representation scheme is discussed with respect to its perception level and a scope of individual labels. Both the features can be handled by fuzzy sets and easily modeled by changing associated parameters of corresponding membership functions. Problems of prototype determination in the original space (in which the objects are characterized) as well as in the space of linguistic labels are studied. It is argued that the space of grades of membership functions is more suitable to capture a notion of the prototype. Different aspects of matching are also brought into account.
Abstract It is an interesting topic to interpret artificial neural networks (ANNs) by considering some change various approaches. This paper explores the relationship between the input and output units of the simplest ANN, a single layer perceptron for the binary classification problem, from the probability point of view. If the feature variables of datasets follow independent normal distribution and outputs are activated by sigmoid function or smooth Relu function, we advocate that the probability density function (pdf) of the output variable is an exponential family distribution. Furthermore, by introducing an intermediate variable, the pdf of the output variable can be written as a linear combination of three normal distributions with same spread but different centers. Based on these results, the probability of the predicted class label can be written as a standard normal cumulative distribution function (cdf). The originality of this paper comes with interesting theoretical results to provide ANNs with a new description of the relationship between input variables to output variables, which can enable ANNs to be understood from a new perspective. Extensive experiments based on one artificial synthesized dataset and ten real‐world benchmark datasets validate the reasonability of those results.
