gappyPairKernel: Gappy Pair Kernel
In kebabs: Kernel-Based Analysis Of Biological Sequences

Description Usage Arguments Details Value Author(s) References See Also Examples

Create a gappy pair kernel object and the kernel matrix

gappyPairKernel(k = 1, m = 1, r = 1, annSpec = FALSE,
  distWeight = numeric(0), normalized = TRUE, exact = TRUE,
  ignoreLower = TRUE, presence = FALSE, revComplement = FALSE,
  mixCoef = numeric(0))

## S4 method for signature 'GappyPairKernel'
getFeatureSpaceDimension(kernel, x)

`k`	length of the substrings (also called kmers) which are considered in pairs by this kernel. This parameter together with parameter m (see below) defines the size of the feature space, i.e. the total number of features considered in this kernel is (\|A\|^(2k))(m+1), with \|A\| as the size of the alphabet (4 for DNA and RNA sequences and 21 for amino acid sequences). Sequences with a total number of characters shorter than 2 * k + m will be accepted but not all possible patterns of the feature space can be taken into account. When multiple kernels with different k and/or m values should be generated, e.g. for model selection an integer vector can be specified instead of a single numeric values. In this case a list of kernel objects with the individual values from the integer vector of parameter k is generated as result. The processing effort for this kernel is highly dependent on the value of k because of the additional factor 2 in the exponent for the feature space size) and only small values of k will allow efficient processing. Default=1
`m`	maximal number of irrelevant positions between a pair of kmers. The value of m must be an integer value larger than 0. For example a value of m=2 means that zero, one or two irrelevant positions between kmer pairs are considered as valid features. (A value of 0 corresponds to the spectrum kernel with a kmer length of 2*k and is not allowed for the gappy pair kernel). When an integer vector is specified a list of kernels is generated as described above for parameter k. If multiple values are specified both for parameter k and parameter m one kernel object is created for each of the combinations of k and m. Default=1
`r`	exponent which must be > 0 (see details section in spectrumKernel). Default=1
`annSpec`	boolean that indicates whether sequence annotation should be taken into account (details see on help page for `annotationMetadata`). Annotation information is only evaluated for the kmer positions of the kmer pair but not for the irrelevant positions in between. For the annotation specific gappy pair kernel the total number of features increases to (\|A\|^(2k))(\|a\|^(2k)(m+1) with \|A\| as the size of the sequence alphabet and \|a\| as the size of the annotation alphabet. Default=FALSE
`distWeight`	a numeric distance weight vector or a distance weighting function (details see on help page for `gaussWeight`). Default=NULL
`normalized`	generated data from this kernel will be normalized (details see below). Default=TRUE
`exact`	use exact character set for the evaluation (details see below). Default=TRUE
`ignoreLower`	ignore lower case characters in the sequence. If the parameter is not set lower case characters are treated like uppercase. Default=TRUE
`presence`	if this parameter is set only the presence of a kmers will be considered, otherwise the number of occurances of the kmer is used. Default=FALSE
`revComplement`	if this parameter is set a kmer pair and its reverse complement are treated as the same feature. Default=FALSE
`mixCoef`	mixing coefficients for the mixture variant of the gappy pair kernel. A numeric vector of length k is expected for this parameter with the unused components in the mixture set to 0. Default=numeric(0)
`kernel`	a sequence kernel object
`x`	one or multiple biological sequences in the form of a `DNAStringSet`, `RNAStringSet`, `AAStringSet` (or as `BioVector`)

Creation of kernel object

The function 'gappyPairKernel' creates a kernel object for the gappy pair kernel. This kernel object can then be used with a set of DNA-, RNA- or AA-sequences to generate a kernel matrix or an explicit representation for this kernel. The gappy pair kernel uses pairs of neighboring subsequences of length k (kmers) with up to m irrelevant positions between the kmers. For sequences shorter than 2*k the self similarity (i.e. the value on the main diagonal in the square kernel matrix) is 0. The explicit representation contains only zeros for such a sample. Dependent on the learning task it might make sense to remove such sequences from the data set as they do not contribute to the model but still influence performance values.

For values different from 1 (=default value) parameter r leads to a transfomation of similarities by taking each element of the similarity matrix to the power of r. If normalized=TRUE, the feature vectors are scaled to the unit sphere before computing the similarity value for the kernel matrix. For two samples with the feature vectors x and y the similarity is computed as:

s=(x^T y)/(|x| |y|)

For an explicit representation generated with the feature map of a normalized kernel the rows are normalized by dividing them through their Euclidean norm. For parameter exact=TRUE the sequence characters are interpreted according to an exact character set. If the flag is not set ambigous characters from the IUPAC characterset are also evaluated.

The annotation specific variant (for details see annotationMetadata) and the position dependent variants (for details see positionMetadata) either in the form of a position specific or a distance weighted kernel are supported for the gappy pair kernel. The generation of an explicit representation is not possible for the position dependent variants of this kernel.

Creation of kernel matrix

The kernel matrix is created with the function getKernelMatrix or via a direct call with the kernel object as shown in the examples below.

gappyPairKernel: upon successful completion, the function returns a kernel object of class GappyPairKernel.

of getDimFeatureSpace: dimension of the feature space as numeric value

Johannes Palme <kebabs@bioinf.jku.at>

http://www.bioinf.jku.at/software/kebabs

(Mahrenholz, 2011) – C.C. Mahrenholz, I.G. Abfalter, U. Bodenhofer, R. Volkmer and S. Hochreiter. Complex networks govern coiled-coil oligomerizations - predicting and profiling by means of a machine learning approach.
(Bodenhofer, 2009) – U. Bodenhofer, K. Schwarzbauer, M. Ionescu and S. Hochreiter. Modelling position specificity in sequence kernels by fuzzy equivalence relations.

(Kuksa, 2008) – P. Kuksa, P.-H. Huang and V. Pavlovic. Fast Protein Homology and Fold Detection with Sparse Spatial Sample Kernels

J. Palme, S. Hochreiter, and U. Bodenhofer (2015) KeBABS: an R package for kernel-based analysis of biological sequences. Bioinformatics, 31(15):2574-2576, 2015. DOI: 10.1093/bioinformatics/btv176.

getKernelMatrix, getExRep, kernelParameters-method, spectrumKernel, mismatchKernel, motifKernel, GappyPairKernel

## instead of user provided sequences in XStringSet format
## for this example a set of DNA sequences is created
## RNA- or AA-sequences can be used as well with the gappy pair kernel
dnaseqs <- DNAStringSet(c("AGACTTAAGGGACCTGGTCACCACGCTCGGTGAGGGGGACGGGGTGT",
                          "ATAAAGGTTGCAGACATCATGTCCTTTTTGTCCCTAATTATTTCAGC",
                          "CAGGAATCAGCACAGGCAGGGGCACGGCATCCCAAGACATCTGGGCC",
                          "GGACATATACCCACCGTTACGTGTCATACAGGATAGTTCCACTGCCC",
                          "ATAAAGGTTGCAGACATCATGTCCTTTTTGTCCCTAATTATTTCAGC"))
names(dnaseqs) <- paste("S", 1:length(dnaseqs), sep="")

## create the kernel object for dimer pairs with up to ten irrelevant
## position between the kmers of the pair without normalization
gappy <- gappyPairKernel(k=2, m=10, normalized=FALSE)
## show details of kernel object
gappy

## generate the kernel matrix with the kernel object
km <- gappy(dnaseqs)
dim(km)
km[1:5,1:5]

## alternative way to generate the kernel matrix
km <- getKernelMatrix(gappy, dnaseqs)
km[1:5,1:5]

## Not run: 
## plot heatmap of the kernel matrix
heatmap(km, symm=TRUE)

## End(Not run)

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    type

gappy pair kernel: k=2, m=10, normalized=FALSE
[1] 5 5
An object of class "KernelMatrix"
    S1  S2  S3  S4  S5
S1 549  32 112  47  32
S2  32 497  67  65 497
S3 112  67 581  54  67
S4  47  65  54 477  65
S5  32 497  67  65 497
An object of class "KernelMatrix"
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S1 549  32 112  47  32
S2  32 497  67  65 497
S3 112  67 581  54  67
S4  47  65  54 477  65
S5  32 497  67  65 497