Building a clustering tree

A common task in many fields is to group objects or samples based on their characteristics such that objects in one group are more similar to each other than to objects in other groups. This unsupervised process is known as clustering. Many clustering algorithms exist but all of them require some sort of user input to decide how many groups to produce. For example k-means clustering requires a value for k, the number of clusters, and graph-based clustering methods can include a resolution parameter. How do we know what the correct number of clusters is and what are the relationships between clusters at different resolutions? I will show how to construct a clustering tree to help answer these questions. While I will use a single-cell RNA sequencing dataset as an example this approach could be used for any discipline or clustering method. A clustering tree combines information from multiple clusterings with different resolutions and shows the relationships between them. This visualisation can be used to see which clusters are distinct, where new clusters come from and how many samples change clusters as the number of clusters increases. Building a clustering tree provides an alternative way of looking at clusterings, giving extra insight into the clustering process and helping to determine the correct number of clusters to use in further analysis.

Transcript

1. Building a
   clustering tree
   Luke Zappia
   @_lazappi_
   

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2. My data
   OpenStax College, CC BY 3.0 via Wikimedia Commons
   Single-cell RNA-sequencing
   Gene activity in thousands of cells
   ~20000 rows x ~7000 columns
   Look for different cell types
   

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3. How many
   clusters?
   

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6. Can we build a tree of
   clusters?
   

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7. Nodes
   Resolution (k)
   Cluster
   Size
   

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8. Edges
   Cluster from
   (lower resolution)
   Cluster to
   (higher resolution)
   

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9. Edges
   Cluster from
   (lower resolution)
   Cluster to
   (higher resolution)
   Number
   Proportion
   

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10. Proportions
    size = 100
    60
    40
    k = 1 k = 2
    n = 60
    n = 40
    

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11. Proportions
    100
    60
    40
    k = 1 k = 2
    p
    from
    = n / size
    low
    n = 60
    n = 40
    p
    to
    = n / size
    high
    

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12. Proportions
    100
    60
    40
    k = 1 k = 2
    p
    from
    = 0.6
    n = 60
    n = 40
    p
    to
    = 1.0
    p
    from
    = 0.4
    p
    to
    = 1.0
    

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13. Proportions
    100
    60
    40
    k = 1 k = 2 p
    from
    = 0.67
    60
    40
    p
    to
    = 1.0
    40
    30
    40
    20
    30
    10
    30
    k = 3
    p
    from
    = 0.33
    p
    to
    = 0.67
    p
    from
    = 0.25
    p
    to
    = 0.33
    p
    from
    = 0.75
    p
    to
    = 1.0
    

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14. Algorithm
    For each resolution r = 1, ..., R - 1
    For each unique cluster C
    low
    in r
    For each unique cluster C
    high
    in r + 1
    Count C
    low
    , C
    high
    pairs
    Res1 Res2 Res3
    S1 1 1 1
    S2 2 1 2
    S3 1 2 2
    S4 1 3 3
    S5 2 1 4
    

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15. Algorithm
    For each resolution r = 1, ..., R - 1
    Res1, Res2
    For each unique cluster C
    low
    in r
    For each unique cluster C
    high
    in r + 1
    Count C
    low
    , C
    high
    pairs
    Res1 Res2 Res3
    S1 1 1 1
    S2 2 1 2
    S3 1 2 2
    S4 1 3 3
    S5 2 1 4
    

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16. Algorithm
    For each resolution r = 1, ..., R - 1
    For each unique cluster C
    low
    in r
    1, 2
    For each unique cluster C
    high
    in r + 1
    Count C
    low
    , C
    high
    pairs
    Res1 Res2 Res3
    S1 1 1 1
    S2 2 1 2
    S3 1 2 2
    S4 1 3 3
    S5 2 1 4
    

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17. Algorithm
    For each resolution r = 1, ..., R - 1
    For each unique cluster C
    low
    in r
    For each unique cluster C
    high
    in r + 1
    1, 2, 3
    Count C
    low
    , C
    high
    pairs
    Res1 Res2 Res3
    S1 1 1 1
    S2 2 1 2
    S3 1 2 2
    S4 1 3 3
    S5 2 1 4
    

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18. Algorithm
    For each resolution r = 1, ..., R - 1
    For each unique cluster C
    low
    in r
    For each unique cluster C
    high
    in r + 1
    Count C
    low
    , C
    high
    pairs
    1
    Res1 Res2 Res3
    S1 1 1 1
    S2 2 1 2
    S3 1 2 2
    S4 1 3 3
    S5 2 1 4
    

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19. Edge table
    Res1 Res2 Res3
    S1 1 1 1
    S2 2 1 2
    S3 1 2 2
    S4 1 3 3
    S5 2 1 4
    ResFrom ClusterFrom ResTo ClusterTo Number
    Res1 1 Res2 1 1
    Res1 1 Res2 2 1
    Res1 1 Res2 3 1
    Res1 2 Res2 1 2
    Res1 2 Res2 2 0
    Res1 2 Res2 3 0
    

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20. Tree
    Resolution
    0.01
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1.0
    

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21. Resolution
    0.01
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1.0
    

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22. Resolution
    0.01
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1.0
    

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28. Summary
    Choosing the number of clusters is hard but important
    A clustering tree can help by showing:
    - Relationships between clusters
    - Which clusters are distinct
    - Where samples are changing
    

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29. Acknowledgements
    Everyone that makes tools and data available
    Supervisors
    Alicia Oshlack
    Melissa Little
    MCRI Bioinformatics
    Belinda Phipson
    MCRI KDDR
    Alex Combes
    @_lazappi_
    oshlacklab.com
    R Tutorial
    lazappi.id.au/building-a-clustering-tree/
    Slides
    speakerdeck.com/lazappi/building-a-clustering-tree
    

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