Recognition of Electroencephalography-Related Features of Neuronal Network Organization in Patients With Schizophrenia Using the Generalized Choquet Integrals

In this study, we focused on the verification of suitable aggregation operators enabling accurate differentiation of selected neurophysiological features extracted from resting-state electroencephalographic recordings of patients who were diagnosed with schizophrenia (SZ) or healthy controls (HC). We built the Choquet integral-based operators using traditional classification results as an input to the procedure of establishing the fuzzy measure densities. The dataset applied in the study was a collection of variables characterizing the organization of the neural networks computed using the minimum spanning tree (MST) algorithms obtained from signal-spaced functional connectivity indicators and calculated separately for predefined frequency bands using classical linear Granger causality (GC) measure. In the series of numerical experiments, we reported the results of classification obtained using numerous generalizations of the Choquet integral and other aggregation functions, which were tested to find the most appropriate ones. The obtained results demonstrate that the classification accuracy can be increased by 1.81% using the extended versions of the Choquet integral called in the literature, namely, generalized Choquet integral or pre-aggregation operators.

Empowering Natural Language Interfaces to Databases with Aggregations

A Natural Language Interface to Database (NLIDB) refers to a database interface that translates a question asked in natural language into a structured query. Aggregation questions express aggregation functions, such as count, sum, average, minimum and maximum, and optionally a group by clause and a having clause. NLIDBs deliver good results for standard questions but usually do not deal with aggregation questions. The main contribution of this article is a generic module, called GLAMORISE (GeneraL Aggregation MOdule using a RelatIonal databaSE), that extends NLIDBs to cope with aggregation questions. GLAMORISE covers aggregations with ambiguities, timescale differences, aggregations in multiple attributes, the use of superlative adjectives, basic recognition of measurement units, and aggregations in attributes with compound names.

Aggregation of Weak Fuzzy Norms

Aggregation is a mathematical process consisting in the fusion of a set of values into a unique one and representing them in some sense. Aggregation functions have demonstrated to be very important in many problems related to the fusion of information. This has resulted in the extended use of these functions not only to combine a family of numbers but also a family of certain mathematical structures such as metrics or norms, in the classical context, or indistinguishability operators or fuzzy metrics in the fuzzy context. In this paper, we study and characterize the functions through which we can obtain a single weak fuzzy (quasi-)norm from an arbitrary family of weak fuzzy (quasi-)norms in two different senses: when each weak fuzzy (quasi-)norm is defined on a possibly different vector space or when all of them are defined on the same vector space. We will show that, contrary to the crisp case, weak fuzzy (quasi-)norm aggregation functions are equivalent to fuzzy (quasi-)metric aggregation functions.

Can the crowd judge truthfulness? A longitudinal study on recent misinformation about COVID-19

Recently, the misinformation problem has been addressed with a crowdsourcing-based approach: to assess the truthfulness of a statement, instead of relying on a few experts, a crowd of non-expert is exploited. We study whether crowdsourcing is an effective and reliable method to assess truthfulness during a pandemic, targeting statements related to COVID-19, thus addressing (mis)information that is both related to a sensitive and personal issue and very recent as compared to when the judgment is done. In our experiments, crowd workers are asked to assess the truthfulness of statements, and to provide evidence for the assessments. Besides showing that the crowd is able to accurately judge the truthfulness of the statements, we report results on workers’ behavior, agreement among workers, effect of aggregation functions, of scales transformations, and of workers background and bias. We perform a longitudinal study by re-launching the task multiple times with both novice and experienced workers, deriving important insights on how the behavior and quality change over time. Our results show that workers are able to detect and objectively categorize online (mis)information related to COVID-19; both crowdsourced and expert judgments can be transformed and aggregated to improve quality; worker background and other signals (e.g., source of information, behavior) impact the quality of the data. The longitudinal study demonstrates that the time-span has a major effect on the quality of the judgments, for both novice and experienced workers. Finally, we provide an extensive failure analysis of the statements misjudged by the crowd-workers.

On Self-Aggregations of Min-Subgroups

Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions . However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets.

Learning Aggregation Functions

Learning on sets is increasingly gaining attention in the machine learning community, due to its widespread applicability. Typically, representations over sets are computed by using fixed aggregation functions such as sum or maximum. However, recent results showed that universal function representation by sum- (or max-) decomposition requires either highly discontinuous (and thus poorly learnable) mappings, or a latent dimension equal to the maximum number of elements in the set. To mitigate this problem, we introduce LAF (Learning Aggregation Function), a learnable aggregator for sets of arbitrary cardinality. LAF can approximate several extensively used aggregators (such as average, sum, maximum) as well as more complex functions (e.g. variance and skewness). We report experiments on semi-synthetic and real data showing that LAF outperforms state-of-the-art sum- (max-) decomposition architectures such as DeepSets and library-based architectures like Principal Neighborhood Aggregation, and can be effectively combined with attention-based architectures.