Tabular data in relational databases represents a significant portion of industrial data. Hence, analyzing and interpreting tabular data is of utmost importance. Application tasks on tabular data are manifold and are often not specified when setting up an industrial database. To address this, we present a novel framework for generating universal, i.e., task-independent embeddings of tabular data for performing downstream tasks without predefined targets. Our method transforms tabular data into a graph structure, leverages Graph Auto-Encoders to create entity embeddings, which are subsequently aggregated to obtain embeddings for each table row, i.e., each data sample. This two-step approach has the advantage that unseen samples, consisting of similar entities, can be embedded without additional training. Downstream tasks such as regression, classification or outlier detection, can then be performed by applying a distance-based similarity measure in the embedding space. Experiments on real-world datasets demonstrate that our method achieves superior performance compared to existing universal tabular data embedding techniques.

This paper considers the problem of modeling and estimating community memberships of nodes in a directed network where every row (column) node is associated with a vector determining its membership in each row (column) community. To model such directed network, we propose directed degree corrected mixed membership (DiDCMM) model by considering degree heterogeneity. DiDCMM is identifiable under popular conditions for mixed membership network when considering degree heterogeneity. Based on the cone structure inherent in the normalized version of the left singular vectors and the simplex structure inherent in the right singular vectors of the population adjacency matrix, we build an efficient algorithm called DiMSC to infer the community membership vectors for both row nodes and column nodes. By taking the advantage of DiMSC's equivalence algorithm which returns same estimations as DiMSC and the recent development on row-wise singular vector deviation, we show that the proposed algorithm is asymptotically consistent under mild conditions by providing error bounds for the inferred membership vectors of each row node and each column node under DiDCMM. The theory is supplemented by a simulation study.

Mixed membership problem for undirected network has been well studied in network analysis recent years. However, the more general case of mixed membership for directed network remains a challenge. Here, we propose an interpretable model: bipartite mixed membership stochastic blockmodel (BiMMSB for short) for directed mixed membership networks. BiMMSB allows that row nodes and column nodes of the adjacency matrix can be different and these nodes may have distinct community structure in a directed network. We also develop an efficient spectral algorithm called BiMPCA to estimate the mixed memberships for both row nodes and column nodes in a directed network. We show that the approach is asymptotically consistent under BiMMSB. We demonstrate the advantages of BiMMSB with applications to a small-scale simulation study, the directed Political blogs network and the Papers Citations network.