A taxonomy framework for unsupervised outlier detection techniques for multi-type data sets

The term "outlier" can generally be defined as an observation that is significantly different from the other values in a data set. The outliers may be instances of error or indicate events. The task of outlier detection aims at identifying such outliers in order to improve the analysis of data and further discover interesting and useful knowledge about unusual events within numerous applications domains. In this paper, we report on contemporary unsupervised outlier detection techniques for multiple types of data sets and provide a comprehensive taxonomy framework and two decision trees to select the most suitable technique based on data set. Furthermore, we highlight the advantages, disadvantages and performance issues of each class of outlier detection techniques under this taxonomy framework

Coresets-Methods and History: A Theoreticians Design Pattern for Approximation and Streaming Algorithms

We present a technical survey on the state of the art approaches in data reduction and the coreset framework. These include geometric decompositions, gradient methods, random sampling, sketching and random projections. We further outline their importance for the design of streaming algorithms and give a brief overview on lower bounding techniques

Random projections for Bayesian regression

This article deals with random projections applied as a data reduction technique for Bayesian regression analysis. We show sufficient conditions under which the entire $d$-dimensional distribution is approximately preserved under random projections by reducing the number of data points from $n$ to $k\in O(\operatorname{poly}(d/\varepsilon))$ in the case $n\gg d$. Under mild assumptions, we prove that evaluating a Gaussian likelihood function based on the projected data instead of the original data yields a $(1+O(\varepsilon))$-approximation in terms of the $\ell_2$ Wasserstein distance. Our main result shows that the posterior distribution of Bayesian linear regression is approximated up to a small error depending on only an $\varepsilon$-fraction of its defining parameters. This holds when using arbitrary Gaussian priors or the degenerate case of uniform distributions over $\mathbb{R}^d$ for $\beta$. Our empirical evaluations involve different simulated settings of Bayesian linear regression. Our experiments underline that the proposed method is able to recover the regression model up to small error while considerably reducing the total running time

A Fuzzy Clustering Algorithm for High Dimensional Streaming Data

In this paper we propose a dimension reduced weighted fuzzy clustering algorithm (sWFCM-HD). The algorithm can be used for high dimensional datasets having streaming behavior. Such datasets can be found in the area of sensor networks, data originated from web click stream and data collected by internet traffic flow etc. These data’s have two special properties which separate them from other datasets: a) They have streaming behavior and b) They have higher dimensions. Optimized fuzzy clustering algorithm has already been proposed for datasets having streaming behavior or higher dimensions. But as per our information, nobody has proposed any optimized fuzzy clustering algorithm for data sets having both the properties, i.e., data sets with higher dimension and also continuously arriving streaming behavior. Experimental analysis shows that our proposed algorithm (sWFCM-HD) improves performance in terms of memory consumption as well as execution time Keywords-K-Means, Fuzzy C-Means, Weighted Fuzzy C-Means, Dimension Reduction, Clustering