International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

In statistics, the presence of outliers in the data set could wrongly distort the estimation of the mean. In addition, the extreme values increase the variability and consequently, the power of the statistical methods decreases. However, there are disagreements in the literature both about what the nature of outliers is, and about how to deal with them when doing further statistical analyses. A lot of conventional procedures for both detecting and dealing with outliers are discussed. The effect of increase the probability of error of the first order type is demonstrated with two simple simulations. The general conclusion is that an information outside of the data set is necessary for a correct decision. This information could come only from the human expertise of the researchers of the specific domain of in terest. The importance of the topic for outliers is discussed, the need of deeper analyses, accompanied with many simulation studies, is argued.

In this paper we introduce, analyze and apply persistent homology, one of the main algorithms of TDA, on some real data sets from the bio-medical field. Topological data analysis (TDA) is a field which is a synergy between mathematics, data science and computer science. The main goal of TDA is studying the shape of data using topological techniques. TDA proposes new algorithms that deal with these problems based on tools or concepts from algebraic topology and pure mathematics. We analyze the results and give a topological characterization of the dataset and propose to use them in future work.

In this paper we analyze and apply one of the main algorithms of TDA (Topological Data Analysis), Mapper, on some real data sets. We use Mapper for visualization of a data sets, and we tend to get some insights if some key characteristics of the data are captured by the visualization and how they are connected with human perception of the data. Also, we will discuss if the visualization can make progress in further work.