Hyper Surface Classification Research Articles

Parallel sampling from big data with uncertainty distribution

Data are inherently uncertain in most applications. Uncertainty is encountered when an experiment such as sampling is to proceed, the result of which is not known to us while leading to variety of potential outcomes. With the rapid developments of data collection and distribution storage technologies, big data have become a bigger-than-ever problem. And dealing with big data with uncertainty distribution is one of the most important issues of big data research. In this paper, we propose a Parallel Sampling method based on Hyper Surface for big data with uncertainty distribution, namely PSHS, which adopts a universal concept of Minimal Consistent Subset (MCS) of Hyper Surface Classification (HSC). Our inspiration for handling uncertainties in sampling from big data depends on (1) the inherent structure of the original sample set is uncertain for us, (2) boundary set formed of all the possible separating hyper surfaces is a fuzzy set and (3) the uncertainty of elements in MCS. PSHS is implemented based on MapReduce framework, which is a current and powerful parallel programming technique used in many fields. Experiments have been carried out on several data sets including real world data from UCI repository and synthetic data. The results show that our algorithm shrinks data sets while maintaining identical distribution, which is useful for obtaining the inherent structure of the data sets. Furthermore, the evaluation criterions of speedup, scaleup and sizeup validate its efficiency.

Study on Complexity in Hyper Surface Classification

Hyper Surface Classification (HSC) is a simple covering based classification algorithm.Experiments show that HSC can efficiently and accurately classify large-sized data in two-dimensional space and three-dimensional space.However,little research has been done on theoretical problems in HSC.This paper studies several theoretical problems in HSC.First,the paper shows that given the biggest dividing level l,the VC dimension of the hypothesis space is d2l.Under the PAC theory,it arrives at the conclusion on sample complexity,the algorithm probably learn a hypothesis that is approximately correct.Then,the time complexity and space complexity are analyzed.Finally,sample set without contradiction is defined,and show that if the inputting sample set is a finite sample set without contradiction,the algorithm must be convergent.

MINIMAL CONSISTENT SUBSET FOR HYPER SURFACE CLASSIFICATION METHOD

Hyper Surface Classification (HSC), which is based on Jordan Curve Theorem in Topology, has proven to be a simple and effective method for classifying a larger database in our previous work. To select a representative subset from the original sample set, the Minimal Consistent Subset (MCS) of HSC is studied in this paper. For HSC method, one of the most important features of MCS is that it has the same classification model as the entire sample dataset, and can totally reflect its classification ability. From this point of view, MCS is the best way of sampling from the original dataset for HSC. Furthermore, because of the minimum property of MCS, every single deletion or multiple deletions from it will lead to a reduction in generalization ability, which can be exactly predicted by the proposed formula in this paper.

Classification based on dimension transposition for high dimension data

Based on Jordan Curve Theorem, a universal classification method called hyper surface classification (HSC) has recently been proposed. Experimental results are exciting, which show that in three-dimensional space, this method works fairly well in both accuracy and efficiency even for large size data up to 107. However, designing a number of new classifiers is needed with the growing of feature dimension. To solve the problem, a kind of efficient dimension transposition method that is suitable for HSC and without losing any essential information is put forward in this paper. The dimension transposition method rearrange all of the numerals in the higher dimensional data to lower dimensional data without changing each numeral, but only change their position according to some orders. The experiment shows that the method can classify high dimension data with high accuracy.