In different application fields, heterogeneous data sets are structured into either matrices or higher-order tensors. In some cases, these structures present the property of having common underlying factors, which is used to improve the efficiency of factor-matrices estimation in the process of the so-called coupled matrix-tensor factorization (CMTF). Many methods target the CMTF problem relying on alternating algorithms or gradient approaches. However, computational complexity remains a challenge when the data sets are tensors of high-order, which is linked to the well-known "curse of dimensionality". In this paper, we present a methodological approach, using the Joint dImensionality Reduction And Factors rEtrieval (JIRAFE) algorithm for joint factorization of high-order tensor and matrix. This approach reduces the high-order CMTF problem into a set of 3-order CMTF and canonical polyadic decomposition (CPD) problems. The proposed algorithm is evaluated on simulation and compared with a gradient-based method.

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