Unsupervised Heterogeneous Coupling Learning for Categorical Representation.

Complex categorical data is often hierarchically coupled with heterogeneous relationships between attributes and attribute values and the couplings between objects. Such value-to-object couplings are heterogeneous with complementary and inconsistent interactions and distributions. Limited research exists on unlabeled categorical data representations, ignores the heterogeneous and hierarchical couplings, underestimates data characteristics and complexities, and overuses redundant information, etc. Deep representation learning of unlabeled categorical data is challenging, overseeing such value-to-object couplings, complementarity and inconsistency, and requiring large data, disentanglement, and high computational power. This work introduces a shallow but powerful UNsupervised heTerogeneous couplIng lEarning (UNTIE) approach for representing coupled categorical data by untying the interactions between couplings and revealing heterogeneous distributions embedded in each type of couplings. UNTIE is efficiently optimized w.r.t. a kernel k-means objective function for unsupervised representation learning of heterogeneous and hierarchical value-to-object couplings. Theoretical analysis shows that UNTIE can represent categorical data with maximal separability while effectively represents heterogeneous couplings and disclose their roles in categorical data. The UNTIE-learned representations make significant performance improvement against the state-of-the-art categorical representations and deep representation models on 25 categorical data sets with diversified characteristics

Creativity as Cognitive design \ud The case of mesoscopic variables in Meta-Structures\ud

Creativity is an open problem which has been differently approached by several disciplines since a long time. In this contribution we consider as creative the constructivist design an observer does on the description levels of complex phenomena, such as the self-organized and emergent ones ( e.g., Bènard rollers, Belousov-Zhabotinsky reactions, flocks, swarms, and more radical cognitive and social emergences). We consider this design as related to the Gestaltian creation of a language fit for representing natural processes and the observer in an integrated way. Organised systems, both artificial and most of the natural ones are designed/ modelled according to a logical closed model which masters all the inter-relation between their constitutive elements, and which can be described by an algorithm or a single formal model. We will show there that logical openness and DYSAM (Dynamical Usage of Models) are the proper tools for those phenomena which cannot be described by algorithms or by a single formal model. The strong correlation between emergence and creativity suggests that an open model is the best way to provide a formal definition of creativity. A specific application relates to the possibility to shape the emergence of Collective Behaviours. Different modelling approaches have been introduced, based on symbolic as well as sub-symbolic rules of interaction to simulate collective phenomena by means of computational emergence. Another approach is based on modelling collective phenomena as sequences of Multiple Systems established by percentages of conceptually interchangeable agents taking on the same roles at different times and different roles at the same time. In the Meta-Structures project we propose to use mesoscopic variables as creative design, invention, good continuity and imitation of the description level. In the project we propose to define the coherence of sequences of Multiple Systems by using the values taken on by the dynamic mesoscopic clusters of its constitutive elements, such as the instantaneous number of elements having, in a flock, the same speed, distance from their nearest neighbours, direction and altitude. In Meta-Structures the collective behaviour’s coherence corresponds, for instance, to the scalar values taken by speed, distance, direction and altitude along time, through statistical strategies of interpolation, quasi-periodicity, levels of ergodicity and their reciprocal relationship. In this case the constructivist role of the observer is considered creative as it relates to neither non-linear replication nor transposition of levels of description and models used for artificial systems, like reductionism. Creativity rather lies in inventing new mesoscopic variables able to identify coherent patterns in complex systems. As it is known, mesoscopic variables represent partial macroscopic properties of a system by using some of the microscopic degrees of freedom possessed by composing elements. Such partial usage of microscopic as well as macroscopic properties allows a kind of Gestaltian continuity and imitation between levels of descriptions for mesoscopic modelling. \ud \u