Intrinsic-Dimension analysis for guiding dimensionality reduction and data-fusion in multi-omics data processing

Abstract The advent of high-throughput sequencing technologies has revolutionized the field of multi-omics patient data analysis. While these techniques offer a wealth of information, they often generate datasets with dimensions far surpassing the number of available cases. This discrepancy in size gives rise to the challenging “small-sample-size” problem, significantly compromising the reliability of any subsequent estimate, whether supervised or unsupervised. This calls for effective dimensionality reduction techniques to transform high-dimensional datasets into lower-dimensional spaces, making the data manageable and facilitating subsequent analyses. Unfortunately, the definition of a proper di-mensionality reduction pipeline is not an easy task; besides the problem of identifying the best dimensionality reduction method, the definition of the dimension of the lower-dimensional space into which each dataset should be transformed is a crucial issue that influences all the subsequent analyses and should therefore be carefully considered. Further, the availability of multi-modal data calls for proper data-fusion techniques to produce an integrated patient-view into which redundant information is removed while salient and complementary information across views is leveraged to improve the performance and reliability of both unsupervised and supervised learning techniques. This paper proposes leveraging the intrinsic dimensionality of each view in a multi-modal dataset to define the dimensionality of the lower-dimensional space where the view is transformed by dimensionality reduction algorithms. Further, it presents a thorough experimental study that compares the traditional application of a unique-step of dimensionality reduction with a two-step approach, involving a prior feature selection followed by feature extraction. Through this comparative evaluation, we scrutinize the performance of widely used dimensionality reduction algorithms. Importantly, we also investigate their impact on unsupervised data-fusion techniques, which are pivotal in biomedical research. Our findings shed light on the most effective strategies for handling high-dimensional multi-omics patient data, offering valuable insights for future studies in this domain. Highlights We introduce a flexible pipeline to guide in a principled way feature selection and feature extraction methods to reduce the high dimensions and to contrast the curse of dimensionality that affects multi-omics data. We harness the power of cutting-edge Intrinsic Dimensionality (id) estimation through block-analysis, providing an unbiased estimation of the individual ids for each view within a multi-modal dataset. We use an exhaustive set of diverse multi-omics cancer datasets from the well-known TCGA dataset to show that the automatic analysis of the distribution of the block-ids characterizing each omics-view leverages dimensionality reduction, by (1) evidencing feature noise and redundancy, and (2) providing an unbiased estimate of the id for each view, to be used for setting the dimension of the reduced space. This avoids empirical or heuristic choices and allows tailoring the reduction to each data-view. The crucial information gained by block-analysis allowed proposing a two-step dimensionality-reduction approach combining feature selection and feature extraction. Our comparative evaluation shows the effectiveness of the proposed technique and its synergy with state-of-the-art data-fusion techniques applied in a multi-omics context. We show that the proposed reduction pipeline leverages traditional dimensionality reduction and state-of-the-art data-fusion algorithms. Indeed, it obtains effective performance when predicting overall survival events with simple random forest classifiers, often preferred in the biomedical field due to their robustness, efficiency, and interpretable nature. Competing Interest Statement The authors have declared no competing interest.