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Recent advances in high-throughput sequencing technologies have enabled the extraction of multiple features that depict patient samples at diverse and complementary molecular levels. The generation of such data has led to new challenges in computational biology regarding the integration of high-dimensional and heterogeneous datasets that capture the interrelationships between multiple genes and their functions. Thanks to their versatility and ability to learn synthetic latent representations of complex data, deep learning methods offer promising perspectives for integrating multi-omics data. These methods have led to the conception of many original architectures that are primarily based on autoencoder models. However, due to the difficulty of the task, the integration strategy is fundamental to take full advantage of the sources' particularities without losing the global trends. This paper presents a novel strategy to build a customizable autoencoder model that adapts to the dataset used in the case of high-dimensional multi-source integration. We will assess the impact of integration strategies on the latent representation and combine the best strategies to propose a new method, CustOmics (https://github.com/HakimBenkirane/CustOmics). We focus here on the integration of data from multiple omics sources and demonstrate the performance of the proposed method on test cases for several tasks such as classification and survival analysis.