A sequential pattern mining algorithm using rough set theory

Linear Fuzzy Information-Granule-Based Fuzzy C-Means Algorithm for Clustering Time Series

This article aims to design a trend-oriented-granulation-based fuzzy C -means (FCM) algorithm that can cluster a group of time series at an abstract (granular) level. To achieve a better trend-oriented granulation of a time series, l1 trend filtering is firstly carried out to result in segments which are then optimized by the proposed segment merging algorithm. By constructing a linear fuzzy information granule (LFIG) on each segment, a granular time series which well reflects the linear trend characteristic of the original time series is produced. With the novel designed distance that can well measure the trend similarity of two LFIGs, the distance between two granular time series is calculated by the modified dynamic time warping (DTW) algorithm. Based on this distance, the LFIG-based FCM algorithm is developed for clustering time series. In this algorithm, cluster prototypes are iteratively updated by the specifically designed granule splitting and merging algorithm, which allows the lengths of prototypes to change in the process of iteration. This overcomes the serious drawback of the existing approaches, where the lengths of prototypes cannot be changed. Experimental studies demonstrate the superior performance of the proposed algorithm in clustering time series with different shapes or trends.

Fast Frequent Patterns Mining by Multiple Sampling With Tight Guarantee Under Bayesian Statistics

Sampling from large dataset is commonly used in the frequent patterns (FPs) mining. To tightly and theoretically guarantee the quality of the FPs obtained from samples, current methods theoretically stabilize the supports of all the patterns in random samples, despite only FPs do matter, so they always overestimate the sample size. We propose an algorithm called multiple sampling-based FPs mining (MSFP). The MSFP first generates the set of approximate frequent items ( AFI ), and uses the AFI to form the set of approximate FPs without supports ( AFP^* ), where it does not stabilize the value of any item's or pattern's support, but only stabilizes the relationship ≥ or < between the support and the minimum support, so the MSFP can use small samples to successively obtain the AFI and AFP^* , and can successively prune the patterns not contained by the AFI and not in the AFP^* . Then, the MSFP introduces the Bayesian statistics to only stabilize the values of supports of AFP^* 's patterns. If a pattern's support in the original dataset is unknown, the MSFP regards it as random, and keeps updating its distribution by its approximations obtained from the samples taken in the progressive sampling, so the error probability can be bound better. Furthermore, to reduce the I/O processes in the progressive sampling, the MSFP stores a large enough random sample in memory in advance. The experiments show that the MSFP is reliable and efficient.

Neighborhood Attribute Reduction: A Multicriterion Strategy Based on Sample Selection

In the rough-set field, the objective of attribute reduction is to regulate the variations of measures by reducing redundant data attributes. However, most of the previous concepts of attribute reductions were designed by one and only one measure, which indicates that the obtained reduct may fail to meet the constraints given by other measures. In addition, the widely used heuristic algorithm for computing a reduct requires to scan all samples in data, and then time consumption may be too high to be accepted if the size of the data is too large. To alleviate these problems, a framework of attribute reduction based on multiple criteria with sample selection is proposed in this paper. Firstly, cluster centroids are derived from data, and then samples that are far away from the cluster centroids can be selected. This step completes the process of sample selection for reducing data size. Secondly, multiple criteria-based attribute reduction was designed, and the heuristic algorithm was used over the selected samples for computing reduct in terms of multiple criteria. Finally, the experimental results over 12 UCI datasets show that the reducts obtained by our framework not only satisfy the constraints given by multiple criteria, but also provide better classification performance and less time consumption.