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Predicting multiple observations in complex systems through low-dimensional embeddings.

ABSTRACT: Forecasting all components in complex systems is an open and challenging task, possibly due to high dimensionality and undesirable predictors. We bridge this gap by proposing a data-driven and model-free framework, namely, feature-and-reconstructed manifold mapping (FRMM), which is a combination of feature embedding and delay embedding. For a high-dimensional dynamical system, FRMM finds its topologically equivalent manifolds with low dimensions from feature embedding and delay embedding and then sets the low-dimensional feature manifold as a generalized predictor to achieve predictions of all components. The substantial potential of FRMM is shown for both representative models and real-world data involving Indian monsoon, electroencephalogram (EEG) signals, foreign exchange market, and traffic speed in Los Angeles Country. FRMM overcomes the curse of dimensionality and finds a generalized predictor, and thus has potential for applications in many other real-world systems.

SUBMITTER: Wu T

PROVIDER: S-EPMC10933326 | biostudies-literature | 2024 Mar

REPOSITORIES: biostudies-literature

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Predicting multiple observations in complex systems through low-dimensional embeddings.

Wu Tao T Gao Xiangyun X An Feng F Sun Xiaotian X An Haizhong H Su Zhen Z Gupta Shraddha S Gao Jianxi J Kurths Jürgen J

Nature communications 20240312 1

Forecasting all components in complex systems is an open and challenging task, possibly due to high dimensionality and undesirable predictors. We bridge this gap by proposing a data-driven and model-free framework, namely, feature-and-reconstructed manifold mapping (FRMM), which is a combination of feature embedding and delay embedding. For a high-dimensional dynamical system, FRMM finds its topologically equivalent manifolds with low dimensions from feature embedding and delay embedding and the ...[more]

PMID: 38472208

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Project description:Early prediction of the potential for neurological recovery after resuscitation from cardiac arrest is difficult but important. Currently, no clinical finding or combination of findings are sufficient to accurately predict or preclude favorable recovery of comatose patients in the first 24 to 48 hours after resuscitation. Thus, life-sustaining therapy is often continued for several days in patients whose irrecoverable injury is not yet recognized. Conversely, early withdrawal of life-sustaining therapy increases mortality among patients who otherwise might have gone on to recover. In this work, we present Canonical Autocorrelation Analysis (CAA) and Canonical Autocorrelation Embeddings (CAE), novel methods suitable for identifying complex patterns in high-resolution multivariate data often collected in highly monitored clinical environments such as intensive care units. CAE embeds sets of datapoints onto a space that characterizes their latent correlation structures and allows direct comparison of these structures through the use of a distance metric. The methodology may be particularly suitable when the unit of analysis is not just an individual datapoint but a dataset, as for instance in patients for whom physiological measures are recorded over time, and where changes of correlation patterns in these datasets are informative for the task at hand. We present a proof of concept to illustrate the potential utility of CAE by applying it to characterize electroencephalographic recordings from 80 comatose survivors of cardiac arrest, aiming to identify patients who will survive to hospital discharge with favorable functional recovery. Our results show that with very low probability of making a Type 1 error, we are able to identify 32.5% of patients who are likely to have a good neurological outcome, some of whom have otherwise unfavorable clinical characteristics. Importantly, some of these had 5% predicted chance of favorable recovery based on initial illness severity measures alone. Providing this information to support clinical decision-making could motivate the continuation of life-sustaining therapies for these patients.

Dataset Information

Predicting multiple observations in complex systems through low-dimensional embeddings.

Publications

Predicting multiple observations in complex systems through low-dimensional embeddings.

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