QUBIC {QUBIC} | R Documentation

## QUBIC: A Qualitative Biclustering Algorithm for Analyses of Gene Expression Data

### Description

`QUBIC` is a biclustering package, with source code upgrading from C code to C++ code. The updated source code can avoid memory allocation error and is much efficient than the original one. Based on our preliminary analysis, it can save 40% running time on a plant microarray data. Whenever using this package, please cite as Yu Zhang, Juan Xie, Jinyu Yang, Anne Fennell, Chi Zhang, Qin Ma; QUBIC: a bioconductor package for qualitative biclustering analysis of gene co-expression data. Bioinformatics, 2017; 33 (3): 450-452. doi: 10.1093/bioinformatics/btw635

`BCQUD` performs a QUalitative BIClustering for a discret matrix.

### Usage

    ## S4 method for signature 'matrix,BCQU'
    biclust(x, method = BCQU(),
            r = 1, q = 0.06,
            c = 0.95, o = 100, f = 1,
            k = max(ncol(x) %/% 20, 2),
            type = 'default', P = FALSE, C = FALSE, verbose = TRUE,
            weight = NULL, seedbicluster = NULL)

    ## S4 method for signature 'matrix,BCQUD'
    biclust(x, method = BCQUD(),
            c = 0.95, o = 100, f = 1,
            k = max(ncol(x) %/% 20, 2),
            type = 'default', P = FALSE, C = FALSE, verbose = TRUE,
            weight = NULL, seedbicluster = NULL)

    qubiclust_d(x, c = 0.95, o = 100, f = 1,
            k = max(ncol(x) %/% 20, 2),
            type = 'default', P = FALSE, C = FALSE, verbose = TRUE,
            weight = NULL, seedbicluster = NULL)

    qubiclust(x, r = 1L, q = 0.06, c = 0.95, o = 100, f = 1,
            k = max(ncol(x) %/% 20, 2),
            type = 'default', P = FALSE, C = FALSE, verbose = TRUE,
            weight = NULL, seedbicluster = NULL)

### Arguments

`x` | the input data matrix, which could be the normalized gene expression matrix or its qualitative representation from Qdiscretization or other discretization ways. (for example: a qualitative representation of gene expression data) For `BCQU()`, the data matrix should be real For `BCQUD()`, the data matrix should be discretized as integer. Zeros in the matrix will be treated as non-relevant value.
`r` | Affect the granularity of the biclusters. The range of possible ranks. A user can start with a small value of `r` (the default value is `1` so the corresponding data matrix consists of values '`1`', '`-1`' and '`0`'), evaluate the results, and then use larger values (should not be larger than half of the number of the columns) to look for fine structures within the identified biclusters.
`q` | Affect the granularity of the biclusters. The percentage of the regulating conditions for each gene. The choice of `q`'s value depends on the specific application goals; that is if the goal is to find genes that are responsive to local regulators, we should use a relatively small q-value; otherwise we may want to consider larger q-values. The default value of `q` is `0.06` in QUBIC (this value is selected based on the optimal biclustering results on simulated data).
`c` | The required consistency level of a bicluster. The default value of `c` is `0.95`
`o` | The number of output biclusters. `o`'s default value is `100`.
`f` | Control parameter, to control the level of overlaps between to-be-identified biclusters. The filter cut-off for data post-processing. For overlaps among to-be-identified biclusters. Its default value is set to `1` to ensure that no two reported biclusters overlap more than `f`.
`k` | The minimum column width of the block, minimum `max(ncol(x) %/% 20, 2)` columns.
`type` | The constrain type. If `type` is omitted or `type='default'`, the original objective function in QUBIC will be used, which is to maximize the minimal value of numbers of rows and columns. If `type='area'`, the program tries to identify the bicluster with the maximal value of number of rows multiplied by number of columns. Other types are reserved for future use.
`P` | The flag to enlarge current bicluster using a p-value contrain, which is defined based on its significance of expression consistency comparing to some simulated submatrix. Default: `FALSE`.
`C` | The flag to set the lower bound of the condition number in a bicluster as 5% of the total condition number in the input data. Only suggested to use when the input data has a few conditions (e.g. less than `20`). Default: `FALSE`.
`verbose` | If '`TRUE`', prints extra information on progress.
`weight` | Alternative weight matrix provided by user, will append to default weight. `o`, `f`, `k`, `P`, `type`, `C` will be ignored if using this parameter.
`seedbicluster` | Seed provided by user, normally should be a result of function `biclust`.
`method` | `BCQU()` or `BCQUD()`, to perform QUBIC algorithm

### Details

For a given representing matrix of a microarray data set, we construct a weighted graph G with genes represented as vertices, edges connecting every pair of genes, and the weight of each edge being the similarity level between the two corresponding (entire) rows. Clearly, the higher a weight, the more similar two corresponding rows are. Intuitively, genes in a bicluster should induce a heavier subgraph of G because under a subset of the conditions, these genes have highly similar expression patterns that should make the weight of each involved edge heavier, comparing to the edges in the background. But it should be noted that some heavy subgraph may not necessarily correspond to a bicluster, i.e. genes from a heavy subgraph may not necessarily have similar expression patterns because different edges in a subgraph may have heavier weights under completely different subsets of conditions. It should also be noted that recognizing all heavy subgraphs in a weighted graph itself is computationally intractable because identification of maximum cliques in a graph is a special case of this, and the maximum clique problem is a well known intractable problem (NP-hard). So in our solution, we do not directly solve the problem of finding heavy subgraphs in a graph. Instead, we built our biclustering algorithm based on this graph representation of a microarray gene expression data, and tackle the biclustering problem as follows. We find all feasible biclusters (I,J) in the given data set such that min{|I|, |J|} is as large as possible, where I and J are subsets of genes and conditions, respectively.

### Value

Returns an Biclust object, which contains bicluster candidates

### Functions

- `BCQU`: Performs a QUalitative BIClustering.

- `BCQUD`: Performs a QUalitative BIClustering for a discret matrix.

- `qubiclust_d`: Performs a QUalitative BIClustering for a discret matrix.

- `qubiclust`: Performs a QUalitative BIClustering.

### References

Yu Zhang, Juan Xie, Jinyu Yang, Anne Fennell, Chi Zhang, Qin Ma; QUBIC: a bioconductor package for qualitative biclustering analysis of gene co-expression data. Bioinformatics, 2017; 33 (3): 450-452.

### See Also

`BCQU-class` `qudiscretize` `qunetwork` `qunet2xml` `biclust`

### Examples

    # Random matrix with one embedded bicluster
    test <- matrix(rnorm(5000), 100, 50)
    test[11:20, 11:20] <- rnorm(100, 3, 0.3)
    res <- biclust::biclust(test, method = BCQU())
    summary(res)
    show(res)
    names(attributes(res))

    ## Not run:
    # Load microarray matrix
    data(BicatYeast)

    # Display number of column and row of BicatYeast
    ncol(BicatYeast)
    nrow(BicatYeast)
    # Bicluster on microarray matrix
    system.time(res <- biclust::biclust(BicatYeast, method = BCQU()))

    # Show bicluster info
    res
    # Show the first bicluster
    biclust::bicluster(BicatYeast, res, 1)
    # Get the 4th bicluster
    bic4 <- biclust::bicluster(BicatYeast, res, 4)[[1]]

    # or
    bic4 <- biclust::bicluster(BicatYeast, res)[[4]]
    # Show rownames of the 4th bicluster
    rownames(bic4)
    # Show colnames of the 4th bicluster
    colnames(bic4)

    ## End(Not run)
    ## Not run:
    # Bicluster on selected of genes
    data(EisenYeast)
    genes <- c("YHR051W", "YKL181W", "YHR124W", "YHL020C", "YGR072W", "YGR145W",
        "YGR218W", "YGL041C", "YOR202W", "YCR005C")
    # same result as res <- biclust::biclust(EisenYeast[1:10,], method=BCQU())
    res <- biclust::biclust(EisenYeast[genes, ], method = BCQU())
    res

    ## End(Not run)
    ## Not run:
    # Get bicluster by row name = 249364_at
    biclust::bicluster(BicatYeast, res, which(res@RowxNumber[which(rownames(BicatYeast) ==
        "249364_at"), ]))

    ## End(Not run)
    ## Not run:
    # Get bicluster by col name = cold_roots_6h
    biclust::bicluster(BicatYeast, res, which(res@NumberxCol[, which(colnames(BicatYeast) ==
        "cold_roots_6h")]))

    ## End(Not run)
    ## Not run:
    # Draw a single bicluster using drawHeatmap {bicust}
    data(BicatYeast)
    res <- biclust::biclust(BicatYeast, BCQU(), verbose = FALSE)
    # Draw heatmap of the first cluster
    biclust::drawHeatmap(BicatYeast, res, 1)

    ## End(Not run)
    ## Not run:
    # Draw a single bicluster using heatmap {stats}
    data(BicatYeast)
    res <- biclust::biclust(BicatYeast, BCQU(), verbose = FALSE)
    bic10 <- biclust::bicluster(BicatYeast, res, 10)[[1]]

    # Draw heatmap of the 10th cluster using heatmap {stats}
    heatmap(as.matrix(t(bic10)), Rowv = NA, Colv = NA, scale = 'none')

    # Draw heatmap of the 10th cluster using plot_heatmap {phyloseq}
    if (requireNamespace('phyloseq'))
        phyloseq::plot_heatmap(otu_table(bic10, taxa_are_rows = TRUE))

    ## End(Not run)
    ## Not run:
    # Draw a single bicluster with original data background and color options
    data(BicatYeast)
    res <- biclust::biclust(BicatYeast, BCQU(), verbose = FALSE)
    palette <- colorRampPalette(c('red', 'yellow', 'green'))(n = 100)
    # Draw heatmap of the first cluster with color
    biclust::drawHeatmap(BicatYeast, res, 1, FALSE, beamercolor = TRUE, paleta = palette)

    ## End(Not run)
    ## Not run:
    # Draw some overlapped biclusters
    data(BicatYeast)
    res <- biclust::biclust(BicatYeast, BCQU(), verbose = FALSE)
    biclusternumber(res, 1)
    biclusternumber(res, 3)
    # Draw overlapping heatmap
    biclust::heatmapBC(x = BicatYeast, bicResult = res, number = c(1, 3), local = TRUE)

    ## End(Not run)
    ## Not run:
    # Draw all the biclusters
    data(BicatYeast)
    res <- biclust::biclust(BicatYeast, BCQU(), verbose = FALSE)
    # Draw the first bicluster on heatmap
    biclust::heatmapBC(x = BicatYeast, bicResult = res, number = 1)
    # Draw all the biclusters, not working well.
    # Overlap plotting only works for two neighbor bicluster defined by the order in the number slot.
    biclust::heatmapBC(x = BicatYeast, bicResult = res, number = 0)

    ## End(Not run)
    # Biclustering of discretized yeast microarray data
    data(BicatYeast)
    disc<-qudiscretize(BicatYeast[1:10,1:10])
    biclust::biclust(disc, method=BCQUD())

[Package QUBIC version 1.6.4 Index]