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1. The latent cognitive structures of social networks

   https://doi.org/10.1017/nws.2024.7  

   Aguiar, Izabel; Ugander, Johan (April 2024, Network Science)

   Abstract When people are asked to recall their social networks, theoretical and empirical work tells us that they rely on shortcuts, or heuristics. Cognitive social structures (CSSs) are multilayer social networks where each layer corresponds to an individual’s perception of the network. With multiple perceptions of the same network, CSSs contain rich information about how these heuristics manifest, motivating the question,Can we identify people who share the same heuristics?In this work, we propose a method for identifyingcognitive structureacross multiple network perceptions, analogous to how community detection aims to identifysocial structurein a network. To simultaneously model the joint latent social and cognitive structure, we study CSSs as three-dimensional tensors, employing low-rank nonnegative Tucker decompositions (NNTuck) to approximate the CSS—a procedure closely related to estimating a multilayer stochastic block model (SBM) from such data. We propose the resulting latent cognitive space as an operationalization of the sociological theory ofsocial cognitionby identifying individuals who sharerelational schema. In addition to modeling cognitivelyindependent,dependent, andredundantnetworks, we propose a specific model instance and related statistical test for testing when there issocial-cognitive agreementin a network: when the social and cognitive structures are equivalent. We use our approach to analyze four different CSSs and give insights into the latent cognitive structures of those networks. 

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2. Discovering functionality of urban regions by learning low-dimensional representations of a spatial multiplex network

   Hajiseyedjavadi, Seyedsaeed; Lin, Yu-Ru; Pelechrinis, Konstantinos (August 2018, Proceedings of the Third Mining Urban Data Workshop (MUD 2018))

   The complex relationships in an urban environment can be captured through multiple interrelated sources of data. These relationships form multilayer networks, that are also spatially embedded in an area, could be used to identify latent patterns. In this work, we propose a low-dimensional representation learning approach that considers multiple layers of a multiplex network simultaneously and is able to encode similarities between nodes across different layers. In particular, we introduce a novel neural network architecture to jointly learn low-dimensional representations of each network node from multiple layers of a network. This process simultaneously fuses knowledge of various data sources to better capture the characteristics of the nodes. To showcase the proposed method we focus on the problem of identifying the functionality of an urban region. Using a variety of public data sources for New York City, we design a multilayer network and evaluate our approach. Our results indicate that our proposed approach can improve the accuracy of traditional approaches in an unsupervised task. 

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3. On the Universality of the Logistic Loss Function

   https://doi.org/10.1109/ISIT.2018.8437786  

   Painsky, Amichai; Wornell, Gregory (June 2018, Proceedings of International Symposium on Information Theory)

   A loss function measures the discrepancy between the true values (observations) and their estimated fits, for a given instance of data. A loss function is said to be proper (unbiased, Fisher consistent) if the fits are defined over a unit simplex, and the minimizer of the expected loss is the true underlying probability of the data. Typical examples are the zero-one loss, the quadratic loss and the Bernoulli log-likelihood loss (log-loss). In this work we show that for binary classification problems, the divergence associated with smooth, proper and convex loss functions is bounded from above by the Kullback-Leibler (KL) divergence, up to a multiplicative normalization constant. It implies that by minimizing the log-loss (associated with the KL divergence), we minimize an upper bound to any choice of loss functions from this set. This property justifies the broad use of log-loss in regression, decision trees, deep neural networks and many other applications. In addition, we show that the KL divergence bounds from above any separable Bregman divergence that is convex in its second argument (up to a multiplicative normalization constant). This result introduces a new set of divergence inequalities, similar to the well-known Pinsker inequality. 

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4. Options for multimodal classification based on L1-Tucker decomposition

   https://doi.org/10.1117/12.2520140  

   Chachlakis, Dimitrios; Dhanaraj, Mayur; Prater-Bennette, Ashley; Markopoulos, Panos P.; Ahmad, Fauzia (May 2019, SPIE DCS 2019, vol. 10989)

   Most commonly used classification algorithms process data in the form of vectors. At the same time, modern datasets often comprise multimodal measurements that are naturally modeled as multi-way arrays, also known as tensors. Processing multi-way data in their tensor form can enable enhanced inference and classification accuracy. Tucker decomposition is a standard method for tensor data processing, which however has demonstrated severe sensitivity to corrupted measurements due to its L2-norm formulation. In this work, we present a selection of classification methods that employ an L1-norm-based, corruption-resistant reformulation of Tucker (L1-Tucker). Our experimental studies on multiple real datasets corroborate the corruption-resistance and classification accuracy afforded by L1-Tucker. 

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5. Topological clustering of multilayer networks

   https://doi.org/10.1073/pnas.2019994118  

   Yuvaraj, Monisha; Dey, Asim K.; Lyubchich, Vyacheslav; Gel, Yulia R.; Poor, H. Vincent (May 2021, Proceedings of the National Academy of Sciences)

   Multilayer networks continue to gain significant attention in many areas of study, particularly due to their high utility in modeling interdependent systems such as critical infrastructures, human brain connectome, and socioenvironmental ecosystems. However, clustering of multilayer networks, especially using the information on higher-order interactions of the system entities, still remains in its infancy. In turn, higher-order connectivity is often the key in such multilayer network applications as developing optimal partitioning of critical infrastructures in order to isolate unhealthy system components under cyber-physical threats and simultaneous identification of multiple brain regions affected by trauma or mental illness. In this paper, we introduce the concepts of topological data analysis to studies of complex multilayer networks and propose a topological approach for network clustering. The key rationale is to group nodes based not on pairwise connectivity patterns or relationships between observations recorded at two individual nodes but based on how similar in shape their local neighborhoods are at various resolution scales. Since shapes of local node neighborhoods are quantified using a topological summary in terms of persistence diagrams, we refer to the approach as clustering using persistence diagrams (CPD). CPD systematically accounts for the important heterogeneous higher-order properties of node interactions within and in-between network layers and integrates information from the node neighbors. We illustrate the utility of CPD by applying it to an emerging problem of societal importance: vulnerability zoning of residential properties to weather- and climate-induced risks in the context of house insurance claim dynamics. 

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