Tensor-Decomposition-based Unsupervised Feature Extraction in Single-cell Multiomics Data Analysis

Presentation at ICBBS2021
http://www.icbbs.org/
at 31th Oct. 2021
(On line presentation)

Published paper is
Taguchi, Y.-h.; Turki, T. Tensor-Decomposition-Based Unsupervised Feature Extraction in Single-Cell Multiomics Data Analysis. Genes 2021, 12, 1442. https://doi.org/10.3390/genes12091442

Transcript

1. Tensor-Decomposition-based Unsupervised Feature Extraction
   in Single-cell Multiomics Data Analysis
   Y-h. Taguchi
   Chuo University, Tokyo, Japan.
   and
   Turki Turki
   King Abdulaziz University, Jeddah, Saudi Arabia
   Taguchi, Y.-h.; Turki, T. Tensor-Decomposition-Based
   Unsupervised Feature Extraction in Single-Cell Multiomics Data
   Analysis. Genes 2021, 12, 1442.
   https://doi.org/10.3390/genes12091442
   

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2. Introduction
   It is difficult to integrate multiomics single cell data set because
   1) The number of features is huge (~108 for site-wise measurements)
   2) Full of missing data (only a few percentages of non-missing values
   for site-wise measurements).
   3) Difficult to integrate distinct number of features, mRNA ~ 104.
   

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3. Conventional approaches:
   Conventional approaches:
   Give up integrating multiomics data.
   (Analyze individual omics data separately).
   Screening filled features (i.e. excluding features with missing values)
   Filling missing values artificially (e.g., using Bayes predictors)
   The proposed approach:
   The proposed approach:
   Integrate multiomics data sets full of missing values as well as
   associated with distinct number of features without any pre-process
   (as it is) using tensor decomposition (TD).
   

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4. GSE154762: Dataset 1
   GSE154762: Dataset 1
   Number of cells: 899
   Gene expression+DNA mathylation+DNA accessibility
   GSE121708: Dataset 2
   Number of cells: 852 (758 for gene expression)
   Gene expression+DNA mathylation+DNA accessibility
   

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5. PreProcess
   Gene expression: nothing
   DNA methylation: -1:unmethylated, 0:missing values, 1:metylated
   DNA accessibility: average over every 200 nucleotide regions.
   (It is four histone proteins + a linker protein)
   Standardized:
   Gene expression: zero mean, variance of 1
   DNA methylation and accessibility for data set 1:
   Mean absolute values is one
   Those for data set 2: nothing (because of heterogeneity)
   

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6. For data set 1 or 2:
   x
   ijk
   ∈ℝN
   k
   ×M ×3
   N
   k
   : Number of features of kth omics data:
   k=1: gene expression, k=2: DNA methylation, k=3: DNA accessibility
   M:number of cells.
   Since N
   k
   s are not common we need to adjust N
   k
   s into one value.
   

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7. Full of missing values
   Full of missing values
   

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8. x
   ijk
   =∑
   l=1
   L
   λl
   u
   lik
   u
   l jk
   x
   ljk
   =∑
   i=1
   N
   k x
   ijk
   u
   lik
   ∈ℝL× M×K
   Apply TD to x
   ljk
   to get
   where we emply L=10
   x
   ljk
   =∑
   l
   1
   =1
   L
   ∑
   l
   2
   =1
   M
   ∑
   l
   3
   =1
   3
   G(l
   1
   l
   2
   l
   3
   )u
   l
   1 l
   u
   l
   2
   j
   u
   l
   3
   k
   

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9. What is tensor decomposition(TD)?
   Expand tensor as a series of product of vectors,
   x
   ijk
   l:reduced
   dimension
   j:cells
   k:multiomics
   G
   k
   j
   l
   l
   1
   l
   2
   l
   3
   =
   u
   l
   1
   l
   u
   l
   2
   j
   u
   l
   3
   k
   u
   l
   1
   i
   u
   l
   2
   j
   u
   l
   3
   k
   x
   ljk
   ≃∑
   l
   1
   =1
   L
   1 ∑
   l
   2
   =2
   L
   2 ∑
   l
   3
   =1
   L
   3 G (l
   1
   l
   2
   l
   3
   )u
   l
   1
   l
   u
   l
   2
   j
   u
   l
   3
   k
   

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10. Select u
    l2j
    associated with classification, s.
    Data set 1:human oocyte maturation
    Classification: Cell types
    Data set 2:four time points of the mouse embryo
    Classification: time points
    a
    l2s
    ,b
    l2
    : regression coefficients
    δ
    js
    =1 when j ∈ s, otherwise =0
    Check which u
    l2j
    is coincident with classes, s.
    u
    l
    2
    j
    =a
    l
    2
    s
    δjs
    +b
    l
    2
    

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11. 18 (for data set 1) and 12 (for data set 2) u
    l2j
    are significantly
    correlated with classifications.
    UMAP was applied to top 30 u
    l2j
    and we got two dimensional
    embedding as can be seen in the following slides.
    

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12. data set 1
    

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13. data set 2
    

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14. We also performed gene selections and biological validation of
    them using enrichment analysis. But no time to present them.
    Conclusions:
    Conclusions:
    We have applied TD to integration of single cell multiomics data
    sets.
    Without specific preprocessing, TD successfully obtained low
    dimensional embedding with which UMAP can generate
    embedding coincident with classification.
    

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