On the usage of the probability integral transform to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems

We present a new distributed fuzzy partitioning method to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems. The proposed algorithm builds a fixed number of fuzzy sets for all variables and adjusts their shape and position to the real distribution of training data. A two-step process is applied : 1) transformation of the original distribution into a standard uniform distribution by means of the probability integral transform. Since the original distribution is generally unknown, the cumulative distribution function is approximated by computing the q-quantiles of the training set; 2) construction of a Ruspini strong fuzzy partition in the transformed attribute space using a fixed number of equally distributed triangular membership functions. Despite the aforementioned transformation, the definition of every fuzzy set in the original space can be recovered by applying the inverse cumulative distribution function (also known as quantile function). The experimental results reveal that the proposed methodology allows the state-of-the-art multi-way fuzzy decision tree (FMDT) induction algorithm to maintain classification accuracy with up to 6 million fewer leaves.Comment: Appeared in 2018 IEEE International Congress on Big Data (BigData Congress). arXiv admin note: text overlap with arXiv:1902.0935

Matrix formulation of fuzzy rule-based systems

In this paper, a matrix formulation of fuzzy rule based systems is introduced. A gradient descent training algorithm for the determination of the unknown parameters can also be expressed in a matrix form for various adaptive fuzzy networks. When converting a rule-based system to the proposed matrix formulation, only three sets of linear/nonlinear equations are required instead of set of rules and an inference mechanism. There are a number of advantages which the matrix formulation has compared with the linguistic approach. Firstly, it obviates the differences among the various architectures; and secondly, it is much easier to organize data in the implementation or simulation of the fuzzy system. The formulation will be illustrated by a number of examples

Evolving Large-Scale Data Stream Analytics based on Scalable PANFIS

Many distributed machine learning frameworks have recently been built to speed up the large-scale data learning process. However, most distributed machine learning used in these frameworks still uses an offline algorithm model which cannot cope with the data stream problems. In fact, large-scale data are mostly generated by the non-stationary data stream where its pattern evolves over time. To address this problem, we propose a novel Evolving Large-scale Data Stream Analytics framework based on a Scalable Parsimonious Network based on Fuzzy Inference System (Scalable PANFIS), where the PANFIS evolving algorithm is distributed over the worker nodes in the cloud to learn large-scale data stream. Scalable PANFIS framework incorporates the active learning (AL) strategy and two model fusion methods. The AL accelerates the distributed learning process to generate an initial evolving large-scale data stream model (initial model), whereas the two model fusion methods aggregate an initial model to generate the final model. The final model represents the update of current large-scale data knowledge which can be used to infer future data. Extensive experiments on this framework are validated by measuring the accuracy and running time of four combinations of Scalable PANFIS and other Spark-based built in algorithms. The results indicate that Scalable PANFIS with AL improves the training time to be almost two times faster than Scalable PANFIS without AL. The results also show both rule merging and the voting mechanisms yield similar accuracy in general among Scalable PANFIS algorithms and they are generally better than Spark-based algorithms. In terms of running time, the Scalable PANFIS training time outperforms all Spark-based algorithms when classifying numerous benchmark datasets.Comment: 20 pages, 5 figure

Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference