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Title: Log concave densities in symbolic data analysis Authors:  Carlo Drago - University of Rome Niccolo Cusano (Italy) [presenting]
Abstract: Big data require the extraction of relevant information from the data separating them from the noise. In this sense, symbolic data analysis allow us to work efficiently with large data sets by providing relevant approaches which can be used in order to extract the relevant information from data. Symbolic data allows us to represent and considering explicitly the uncertainty present on the data which can be not considered by using some aggregations as the mean. Various proposals already exists as intervals, boxplots, histograms, densities, beanplots, mixtures, and so on. We propose a new approach based on a symbolic data based on log-concave densities. These computations and representations recently attracted many interest. Log-concave densities has interesting properties and they can be considered as symbolic data when it could be clear the effect of some groups of observations or some outliers on the estimated density. Another advantage is that they do not need to choose relevant parameters as the bandwidth. Another relevant point is that there are various approaches to estimate the log-concave density. In this sense, the log-concave density estimation seems to be very useful and appropriated in various fields of application like environmental problems. We will show the features of this approach theoretically, by simulation and on a real application.