Abstract. Cluster analysis is one of the most commonly applied unsupervised machine learning techniques. Its aim is to automatically discover an underlying structure of a data set represented by a partition of its elements: mutually disjoint and nonempty subsets are determined in such a way that observations within each group are ``similar'' and entities in distinct clusters ``differ'' as much as possible from each other.
It turns out that two state-of-the-art clustering algorithms -- namely the Genie and HDBSCAN* methods -- can be computed based on the minimum spanning tree (MST) of the pairwise dissimilarity graph. Both of them are not only resistant to outliers and produce high-quality partitions, but also are relatively fast to compute.
The aim of this tutorial is to discuss some key issues of hierarchical clustering and explore their relations with graph and data aggregation theory.
stringiis out. Check out the change-log for more information.
* [GENERAL] #193: `stringi` is now bundled with ICU4C 61.1, which is used on most Windows and OS X builds as well as on *nix systems not equipped with ICU. However, if the C++11 support is disabled, stringi will be built against ICU4C 55.1. The update to ICU brings Unicode 10.0 support, including new emoji characters. * [BUGFIX] #288: stri_match did not return the correct number of columns when input was empty. * [NEW FEATURE] #188: `stri_enc_detect` now returns a list of data frames. * [NEW FEATURE] #289: `stri_flatten` gained `na_empty` `omit_empty` arguments. * [NEW FEATURE] New functions: `stri_remove_empty`, `stri_na2empty` * [NEW FEATURE] #285: Coercion from a non-trivial list (one that consists of atomic vectors, each of length 1) to an atomic vector now issues a warning. * [WARN] Removed `-Wparentheses` warnings in `icu55/common/cstring.h:38:63` and `icu55/i18n/windtfmt.cpp` in the ICU4C 55.1 bundle.
Abstract. The aggregation of several objects into a single one is a common study subject in mathematics. Unfortunately, whereas practitioners often need to deal with the aggregation of many different types of objects (rankings, graphs, strings, etc.), the current theory of aggregation is mostly developed for dealing with the aggregation of values in a poset. In this presentation, we will reflect on the limitations of this poset-based theory of aggregation and “jump through the poset glass”. On the other side, we will not find Wonderland, but, instead, we will find more questions than answers. Indeed, a new theory of aggregation is being born, and we will need to work together on this reboot for years to come.
Abstract. Citations scores and the h-index are basic tools used for measuring the quality of scientific work. Nonetheless, while evaluating academic achievements one rarely takes into consideration for what reason the paper was mentioned by another author - whether in order to highlight the connection between their work or to bring to the reader’s attention any mistakes or flaws. In my talk I will shed some insight into the problem of “negative” citations analyzing data from the Stack Exchange and using the proposed agent-based model. Joint work with Marek Gągolewski and Grzegorz Siudem.
Abstract. We look at different approaches to learning the weights of the weighted arithmetic mean such that the median residual or sum of the smallest half of squared residuals is minimized. The more general problem of multivariate regression has been well studied in statistical literature however in the case of aggregation functions we have the restriction on the weights and the domain is usually restricted so that ‘outliers’ may not be arbitrarily large. A number of algorithms are compared in terms of accuracy and speed. Our results can be extended to other aggregation functions.
Abstract. Hirsch's h-index is perhaps the most popular citation-based measure of scientific excellence. Many of its natural generalizations can be expressed as simple functions of some discrete Sugeno integrals.
In this talk we shall review some less-known results concerning various stochastic properties of the discrete Sugeno integral with respect to a symmetric normalized capacity, i.e., weighted lattice polynomial functions of real-valued random variables -- both in i.i.d. (independent and identically distributed) and non-i.i.d. (with some dependence structure) cases. For instance, we will be interested in investigating their exact and asymptotic distributions. Based on these, we can, among others, show that the h-index is a consistent estimator of some natural probability distribution's location characteristic. Moreover, we can derive a statistical test to verify whether the difference between two h-indices (say, h'=7 vs. h''=10 in cases where both authors published 40 papers) is actually significant.
What is more, we shall discuss some agent-based models that describe the processes generating citation networks based on, e.g., the preferential attachment (``rich gets richer'') rule. Due to such an approach, we are able to simulate a scientist's activity and then estimate the expected values for the h-index and similar functions based on very simple sample statistics, such as the total number of citations and the total number of publications. Such results can help explain what does the h-index really measure.