Applying non-negative tensor factorization to centered data

P. Fogel, C. Geissler, H. J. Von Mettenheim, and G. Luta. BMI, Vol. 174, n°3 (2023).

Abstract: We present here an original application of the non-negative matrix factorization (NMF) method, applied to the case of extra-financial data. NMF allows to reduce the useful dimension of a dataset by simultaneously creating new meta-features linked to the original variables through non-negative loadings, and nonnegative scores linking the observations to the meta-features. Thanks to the non-negativity constraints, meta-features can be easily interpreted by looking at the features with the highest loadings in the NMF representation. However, the lowest loadings are generally ignored. We show that this asymmetrical treatment can be problematic in some instances of data sets. The innovation introduced in this paper is to apply a tensorized version of NMF to centered data, which we call Semi Non-Negative Tensor Factorization (semi-NTF). The method is illustrated on a set of ESG scores of European equity issuers, resulting in a fully interpretable reduced set of meta-features. In particular, we show that the scores associated with these meta-features are significantly less correlated with each other than the ready-to-use ESG scores, leading to improved discriminatory power of the meta-features.

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