Exact system identification with missing data

Markovsky, Ivan

doi:10.1109/cdc.2013.6759874

Cited by 12 publications

(17 citation statements)

References 12 publications

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“…The proposed technique will impact other areas of applied matrix completion, viz. collaborative filtering [29], system identification [30], direction of arrival estimation [31] etc.…”

Section: Contributionmentioning

confidence: 99%

deepMc: deep Matrix Completion for imputation of single cell RNA-seq data

Mongia

Sengupta

Majumdar

2018

Preprint

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Single cell RNA-seq has fueled discovery and innovation in medicine over the past few years and is useful for studying cellular responses at individual cell resolution. But, due to paucity of starting RNA, the data acquired is highly sparse. To address this, We propose a deep matrix factorization based method, deepMc, to impute missing values in gene-expression data. For the deep architecture of our approach, We draw our motivation from great success of deep learning in solving various Machine learning problems. In this work, We support our method with positive results on several evaluation metrics like clustering of cell populations, differential expression analysis and cell type separability.

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“…The proposed technique will impact other areas of applied matrix completion, viz. collaborative filtering [29], system identification [30], direction of arrival estimation [31] etc.…”

Section: Contributionmentioning

confidence: 99%

deepMc: deep Matrix Completion for imputation of single cell RNA-seq data

Mongia

Sengupta

Majumdar

2018

Preprint

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“…In this paper, we consider the exact (deterministic) identification problem in the case of data with missing values. Apart from the preliminary results [13] by the author, currently there are no subspace methods that address this problem. We do not make assumptions about the nature or pattern of the missing values apart from the basic one that they are a part of a valid trajectory of a linear time-invariant system with a given number of inputs and bounded lag.…”

Section: Context and Aim Of The Papermentioning

confidence: 99%

The most powerful unfalsified model for data with missing values

Markovsky

2016

Systems & Control Letters

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The notion of the most powerful unfalsified model plays a key role in system identification. Since its introduction in the mid 80's, many methods have been developed for its numerical computation. All currently existing methods, however, assume that the given data is a complete trajectory of the system. Motivated by the practical issues of data corruption due to failing sensors, transmission lines, or storage devices, we study the problem of computing the most powerful unfalsified model from data with missing values. We do not make assumptions about the nature or pattern of the missing values apart from the basic one that they are a part of a trajectory of a linear time-invariant system. The identification problem with missing data is equivalent to a Hankel structured low-rank matrix completion problem. The method proposed constructs rank deficient complete submatrices of the incomplete Hankel matrix. Under specified conditions the kernels of the submatrices form a nonminimal kernel representation of the data generating system. The final step of the algorithm is reduction of the nonminimal kernel representation to a minimal one. Apart from its practical relevance in identification, missing data is a useful concept in systems and control. Classic problems, such as simulation, filtering, and tracking control can be viewed as missing data estimation problems for a given system. The corresponding identification problems with missing data are "data-driven" equivalents of the classical simulation, filtering, and tracking control problems.

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“…Subspace identification methods, however, are unable to directly handle the problem of missing data since SVD requires matrices to be full rank. A method introduced by 18 utilizes sub‐matrices that contain full rank data by rearranging the data. However, this is not appropriate for handling process data since subspace identification relies on the time‐dependent relationships in the data to identify a state trajectory.…”

Section: Introductionmentioning

confidence: 99%

Subspace based model identification for missing data

2020

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This article addresses the problem of missing process data in data‐driven dynamic modeling approaches. The key motivation is to avoid using imputation methods or deletion of key process information when identifying the model, and utilizing the rest of the information appropriately at the model building stage. To this end, a novel approach is developed that adapts nonlinear iterative partial least squares (NIPALS) algorithms from both partial least squares (PLS) and principle component analysis (PCA) for use in subspace identification. Note that the existing subspace identification approaches often utilize singular value decomposition (SVD) as part of the identification algorithm which is generally not robust to missing data. In contrast, the NIPALS algorithms used in this work leverage the inherent correlation structure of the identification matrices to minimize the impact of missing data values while generating an accurate system model. Furthermore, in computing the system matrices, the calculated scores from the latent variable methods are utilized as the states of the system. The efficacy of the proposed approach is shown via simulation of a nonlinear batch process example.

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Exact system identification with missing data

Cited by 12 publications

References 12 publications

deepMc: deep Matrix Completion for imputation of single cell RNA-seq data

deepMc: deep Matrix Completion for imputation of single cell RNA-seq data

The most powerful unfalsified model for data with missing values

Subspace based model identification for missing data

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