1 Introduction

For a general practical introduction to pRoloc, readers are referred to the tutorial, available using vignette("pRoloc-tutorial", package = "pRoloc"). The following document provides a overview of the algorithms available in the package. The respective section describe unsupervised machine learning (USML), supervised machine learning (SML), semi-supervised machine learning (SSML) as implemented in the novelty detection algorithm and transfer learning.

2 Data sets

We provide 62 test data sets in the pRolocdata package that can be readily used with pRoloc. The data set can be listed with pRolocdata and loaded with the data function. Each data set, including its origin, is individually documented.

The data sets are distributed as MSnSet instances. Briefly, these are dedicated containers for quantitation data as well as feature and sample meta-data. More details about MSnSets are available in the pRoloc tutorial and in the MSnbase package, that defined the class.

## MSnSet (storageMode: lockedEnvironment)
## assayData: 888 features, 4 samples 
##   element names: exprs 
## protocolData: none
## phenoData
##   sampleNames: X114 X115 X116 X117
##   varLabels: Fractions
##   varMetadata: labelDescription
## featureData
##   featureNames: P20353 P53501 ... P07909 (888 total)
##   fvarLabels: FBgn Protein.ID ... markers.tl (16 total)
##   fvarMetadata: labelDescription
## experimentData: use 'experimentData(object)'
##   pubMedIds: 19317464 
## Annotation:  
## - - - Processing information - - -
## Added markers from  'mrk' marker vector. Thu Jul 16 22:53:44 2015 
##  MSnbase version: 1.17.12

Other omics data

While our primary biological domain is quantitative proteomics, with special emphasis on spatial proteomics, the underlying class infrastructure on which pRoloc and implemented in the Bioconductor MSnbase package enables the conversion from/to transcriptomics data, in particular microarray data available as ExpressionSet objects using the as coercion methods (see the MSnSet section in the MSnbase-development vignette). As a result, it is straightforward to apply the methods summarised here in detailed in the other pRoloc vignettes to these other data structures.

3 Unsupervised machine learning

Unsupervised machine learning refers to clustering, i.e. finding structure in a quantitative, generally multi-dimensional data set of unlabelled data.

Currently, unsupervised clustering facilities are available through the plot2D function and the MLInterfaces package (Carey et al., n.d.). The former takes an MSnSet instance and represents the data on a scatter plot along the first two principal components. Arbitrary feature meta-data can be represented using different colours and point characters. The reader is referred to the manual page available through ?plot2D for more details and examples.

pRoloc also implements a MLean method for MSnSet instances, allowing to use the relevant infrastructure with the organelle proteomics framework. Although provides a common interface to unsupervised and numerous supervised algorithms, we refer to the pRoloc tutorial for its usage to several clustering algorithms.

Note Current development efforts in terms of clustering are described on the Clustering infrastructure wiki page (https://github.com/lgatto/pRoloc/wiki/Clustering-infrastructure) and will be incorporated in future version of the package.

4 Supervised machine learning

Supervised machine learning refers to a broad family of classification algorithms. The algorithms learns from a modest set of labelled data points called the training data. Each training data example consists of a pair of inputs: the actual data, generally represented as a vector of numbers and a class label, representing the membership to exactly 1 of multiple possible classes. When there are only two possible classes, on refers to binary classification. The training data is used to construct a model that can be used to classifier new, unlabelled examples. The model takes the numeric vectors of the unlabelled data points and return, for each of these inputs, the corresponding mapped class.

4.1 Algorithms used

k-nearest neighbour (KNN) Function knn from package class. For each row of the test set, the \(k\) nearest (in Euclidean distance) training set vectors are found, and the classification is decided by majority vote over the \(k\) classes, with ties broken at random. This is a simple algorithm that is often used as baseline classifier. %% If there are ties for the \(k^{th}\) nearest vector, all candidates are included in the vote.

Partial least square DA (PLS-DA) Function plsda from package . Partial least square discriminant analysis is used to fit a standard PLS model for classification.

Support vector machine (SVM) A support vector machine constructs a hyperplane (or set of hyperplanes for multiple-class problem), which are then used for classification. The best separation is defined as the hyperplane that has the largest distance (the margin) to the nearest data points in any class, which also reduces the classification generalisation error. To assure liner separation of the classes, the data is transformed using a kernel function into a high-dimensional space, permitting liner separation of the classes.

pRoloc makes use of the functions svm from package and ksvm from .

Artificial neural network (ANN) Function nnet from package . Fits a single-hidden-layer neural network, possibly with skip-layer connections.

Naive Bayes (NB) Function naiveBayes from package . Naive Bayes classifier that computes the conditional a-posterior probabilities of a categorical class variable given independent predictor variables using the Bayes rule. Assumes independence of the predictor variables, and Gaussian distribution (given the target class) of metric predictors.

Random Forest (RF) Function randomForest from package .

Chi-square (\(\chi^2\)) Assignment based on squared differences between a labelled marker and a new feature to be classified. Canonical protein correlation profile method (PCP) uses squared differences between a labelled marker and new features. In (Andersen et al. 2003), \(\chi^2\) is defined as , i.e. \(\chi^{2} = \frac{\sum_{i=1}^{n} (x_i - m_i)^{2}}{n}\), whereas (Wiese et al. 2007) divide by the value the squared value by the value of the reference feature in each fraction, i.e. \(\chi^{2} = \sum_{i=1}^{n}\frac{(x_i - m_i)^{2}}{m_i}\), where \(x_i\) is normalised intensity of feature \(x\) in fraction \(i\), \(m_i\) is the normalised intensity of marker \(m\) in fraction \(i\) and \(n\) is the number of fractions available. We will use the former definition.

PerTurbo From (Courty, Burger, and Laurent 2011): PerTurbo, an original, non-parametric and efficient classification method is presented here. In our framework, the manifold of each class is characterised by its Laplace-Beltrami operator, which is evaluated with classical methods involving the graph Laplacian. The classification criterion is established thanks to a measure of the magnitude of the spectrum perturbation of this operator. The first experiments show good performances against classical algorithms of the state-of-the-art. Moreover, from this measure is derived an efficient policy to design sampling queries in a context of active learning. Performances collected over toy examples and real world datasets assess the qualities of this strategy.

The PerTurbo implementation comes from the pRoloc packages.

4.2 Estimating algorithm parameters

It is essential when applying any of the above classification algorithms, to wisely set the algorithm parameters, as these can have an important effect on the classification. Such parameters are for example the width \(sigma\) of the Radial Basis Function (Gaussian kernel) \(exp(-\sigma \| x - x' \|^2 )\) and the \(cost\) (slack) parameter (controlling the tolerance to mis-classification) of our SVM classifier. The number of neighbours \(k\) of the KNN classifier is equally important as will be discussed in this sections.

The next figure illustrates the effect of different choices of \(k\) using organelle proteomics data from (T. P. J. Dunkley et al. 2006) (dunkley2006 from pRolocdata). As highlighted in the squared region, we can see that using a low \(k\) (\(k = 1\) on the left) will result in very specific classification boundaries that precisely follow the contour or our marker set as opposed to a higher number of neighbours (\(k = 8\) on the right). While one could be tempted to believe that optimised classification boundaries are preferable, it is essential to remember that these boundaries are specific to the marker set used to construct them, while there is absolutely no reason to expect these regions to faithfully separate any new data points, in particular proteins that we wish to classify to an organelle. In other words, the highly specific \(k = 1\) classification boundaries are over-fitted for the marker set or, in other words, lack generalisation to new instances. We will demonstrate this using simulated data taken from (James et al. 2013) and show what detrimental effect over-fitting has on new data.