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Sparse low-rank separated representation models for learning from data.

ABSTRACT: We consider the problem of learning a multivariate function from a set of scattered observations using a sparse low-rank separated representation (SSR) model. The model structure considered here is promising for high-dimensional learning problems; however, existing training algorithms based on alternating least-squares (ALS) are known to have convergence difficulties, particularly when the rank of the model is greater than 1. In the present work, we supplement the model structure with sparsity constraints to ensure the well posedness of the approximation problem. We propose two fast training algorithms to estimate the model parameters: (i) a cyclic coordinate descent algorithm and (ii) a block coordinate descent (BCD) algorithm. While the first algorithm is not provably convergent owing to the non-convexity of the optimization problem, the BCD algorithm guarantees convergence to a Nash equilibrium point. The computational cost of the proposed algorithms is shown to scale linearly with respect to all of the parameters in contrast to methods based on ALS. Numerical studies on synthetic and real-world regression datasets indicate that the proposed SSR model structure holds significant potential for machine learning problems.

SUBMITTER: Audouze C

PROVIDER: S-EPMC6364613 | biostudies-literature | 2019 Jan

REPOSITORIES: biostudies-literature

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Sparse low-rank separated representation models for learning from data.

Audouze Christophe C Nair Prasanth B PB

Proceedings. Mathematical, physical, and engineering sciences 20190109 2221

We consider the problem of learning a multivariate function from a set of scattered observations using a sparse low-rank separated representation (SSR) model. The model structure considered here is promising for high-dimensional learning problems; however, existing training algorithms based on alternating least-squares (ALS) are known to have convergence difficulties, particularly when the rank of the model is greater than 1. In the present work, we supplement the model structure with sparsity c ...[more]

PMID: 30760956

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Project description:Head motion induced by impacts has been deemed as one of the most important measures in brain injury prediction, given that the vast majority of brain injury metrics use head kinematics as input. Recently, researchers have focused on using fast approaches, such as machine learning, to approximate brain deformation in real time for early brain injury diagnosis. However, training such models requires large number of kinematic measurements, and therefore data augmentation is required given the limited on-field measured data available. In this study we present a principal component analysis-based method that emulates an empirical low-rank substitution for head impact kinematics, while requiring low computational cost. In characterizing our existing data set of 537 head impacts, each consisting of 6 degrees of freedom measurements, we found that only a few modes, e.g., 15 in the case of angular velocity, is sufficient for accurate reconstruction of the entire data set. Furthermore, these modes are predominantly low frequency since over 70% of the angular velocity response can be captured by modes that have frequencies under 40 Hz. We compared our proposed method against existing impact parametrization methods and showed significantly better performance in injury prediction using a range of kinematic-based metrics-such as head injury criterion (HIC), rotational injury criterion (RIC), and brain injury metric (BrIC)-and brain tissue deformation-based metrics-such as brain angle metric (BAM), maximum principal strain (MPS), and axonal fiber strains (FS). In all cases, our approach reproduced injury metrics similar to the ground truth measurements with no significant difference, whereas the existing methods obtained significantly different (p < 0.01) values as well as substantial differences in injury classification sensitivity and specificity. This emulator will enable us to provide the necessary data augmentation to build a head impact kinematic data set of any size. The emulator and corresponding examples are available on our website.

Dataset Information

Sparse low-rank separated representation models for learning from data.

Publications

Sparse low-rank separated representation models for learning from data.

Similar Datasets

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