-mer scoring matrices comparatively for worm, fly, cress, fish, and human

<p><b>Copyright information:</b></p><p>Taken from "Accurate splice site prediction using support vector machines"</p><p>http://www.biomedcentral.com/1471-2105/8/S10/S7</p><p>BMC Bioinformatics 2007;8(Suppl 10):S7-S7.</p><p>Published online 21 Dec 2007</p><p>PMCID:PMC2230508.</p><p></p> They depict the maximal position-wise contribution of all -mers up to order 8 to the decision of the trained kernel classifiers, transformed into percentile values (cf. the section on interpreting the SVM classifier). Red values are highest contributions, blue lowest. Position 1 denotes the splice site and the start of the consensus dimer

Precision Recall Curve for the three methods MC, WD, WDS estimated on the genome-wide data sets for worm, fly, cress, fish, and human in a nested cross-validation scheme

<p><b>Copyright information:</b></p><p>Taken from "Accurate splice site prediction using support vector machines"</p><p>http://www.biomedcentral.com/1471-2105/8/S10/S7</p><p>BMC Bioinformatics 2007;8(Suppl 10):S7-S7.</p><p>Published online 21 Dec 2007</p><p>PMCID:PMC2230508.</p><p></p> In contrast to the ROC the random guess in this plot corresponds to a horizontal line, that depends on the fraction of positive examples in the test set (e.g. 2% and 3% in the case of the worm acceptor and donor data sets, respectively)

The effect of the width parameter of the Gaussian kernel (<i>σ</i>) for a fixed value of the soft-margin constant.

<p>For large values of <i>σ</i> (A), the decision boundary is nearly linear. As <i>σ</i> decreases, the flexibility of the decision boundary increases (B). Small values of <i>σ</i> lead to overfitting (C). The figure style follows that of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000173#pcbi-1000173-g003" target="_blank">Figure 3</a>.</p

The area under the ROC curve (auROC) of SVMs with the spectrum, mixed spectrum, and weighted degree kernels on the acceptor splice site recognition task for different substring lengths ℓ.

<p>The area under the ROC curve (auROC) of SVMs with the spectrum, mixed spectrum, and weighted degree kernels on the acceptor splice site recognition task for different substring lengths ℓ.</p

Experimental pipeline of the motif extraction process (from left to right).

<p>given a trained SVM, we construct the corresponding POIM before applying the proposed motifPOIM approach to reconstruct underlying motifs (PWMs). Differential POIMs give reasonably initial values for the length and number of motifs.</p

A linear classifier separating two classes of points (squares and circles) in two dimensions.

<p>The decision boundary divides the space into two sets depending on the sign of <i>f</i>(<b>x</b>) = 〈<b>w,x</b>〉+<i>b</i>. The grayscale level represents the value of the discriminant function <i>f</i>(<b>x</b>): dark for low values and a light shade for high values.</p

The effect of the degree of a polynomial kernel.

<p>The polynomial kernel of degree 1 leads to a linear separation (A). Higher-degree polynomial kernels allow a more flexible decision boundary (B,C). The style follows that of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000173#pcbi-1000173-g003" target="_blank">Figure 3</a>.</p

The effect of the soft-margin constant, <i>C</i>, on the decision boundary.

<p>We modified the toy dataset by moving the point shaded in gray to a new position indicated by an arrow, which significantly reduces the margin with which a hard-margin SVM can separate the data. (A) We show the margin and decision boundary for an SVM with a very high value of <i>C</i>, which mimics the behavior of the hard-margin SVM since it implies that the slack variables <i>ξ_i</i> (and hence training mistakes) have very high cost. (B) A smaller value of <i>C</i> allows us to ignore points close to the boundary, and increases the margin. The decision boundary between negative examples and positive examples is shown as a thick line. The thin lines are on the margin (discriminant value equal to −1 or +1).</p

Illustration of the definition of <i>dependent</i> and <i>compatible</i> oligomers (cf. Definition 1).

<p>We say that two positional oligomers are dependent when they overlap each other. If they additionally agree on all shared positions, we say that they are compatible. In this figure, the positional oligomers (<i>TAC</i>, <i>i</i>) and (<i>AAT</i>, <i>i</i>−2) are dependent and compatible since both of them contain the letter <i>T</i> at position <i>i</i>. Whereas the positional 3-mers (<i>TAC</i>, <i>i</i>) and (<i>AAG</i>, <i>i</i>−2) are dependent but not compatible.</p

Memory footprint for POIMs of oligomer length <i>k</i>.

<p>Note that the plot is in semi-logarithmic scale and thus showing an exponential growth for increasing oligomer length rendering a direct approach incomputable for even small <i>k</i> ≥ 12.</p