Biomedical Engineering Reference
In-Depth Information
arbitrary clusters A and B are re-drawn for easy comparison with Fig.
3
. It is also
obvious that feed composition 1 appears to result in cultivations with much more
variable outcomes. Such analysis can lead to further investigations as to the causes
of variability where the loadings of process variables used in the model can
indicate possible causes of deviation/variability.
When Multiwat Principal Componetnt Analysis (MPCA) is used within a
MSPC scheme, the issues with cluster boundaries are addressed typically by
constructing confidence limits around the cluster of nominal behaviour and using
Hotteling's T
2
statistics to identify any deviation from such behaviour. For an
example of MSPC application to bioprocess monitoring see e.g. Nucci et al. [
41
],
where PCA was used for monitoring of penicillin G acylase production.
3.3 Neural Networks and Non-Linear Approaches
Neural networks represent an alternative non-linear feature extraction approach
that has been successfully applied in biosciences in the past. Although traditional
types of neural networks, such as feedforward or radial basis function (RBF)
networks (see
Sect. 4.3.1
) can be used to predict correct class membership on the
basis of input data, there are types of neural networks that were specifically
developed for feature extraction. These include probabilistic neural networks
(PNNs) with Bayesian decision strategies used as a basis of classification
boundaries, which were used for example for growth phase classification [
29
],
pharmaceutical applications [
47
] or biosystem reverse engineering [
30
].
Kramer [
26
] developed autoassociative neural networks as an alternative to PCA,
claiming that the bottleneck layer in this neural network structure (Fig.
5
) extracts
essential non-linear features contained in the data in order to perform an accurate
unity mapping of process data onto the same space. Such networks were shown to
yield important information in fault detection for bioprocess monitoring [
15
,
21
].
The category of non-linear approaches and neural networks utilising competi-
tive training includes learning vector quantisation (LVQ), self-organising maps
(SOM) and support vector machines (SVM). LVQ is based on the principle of a
competitive learning algorithm defining a reduced set of reference vectors that
cover the same space as the original training set patterns and has been shown to be
effective in the interpretation of sensor array data [
48
]. The SOM network uses a
'best matching unit' (BMU, similarly to the reference vectors of LVQ) to map
each new training data point onto one of the nodes in the map [
23
,
63
]. The BMU
(Fig.
6
) is assigned on the basis of appropriate distance metrics, and the network
parameters (weights) are adjusted to match the presented training examples as
closely as possible. In this process, the original regular, usually two-dimensional
grid warps to map the topological characteristics of the training data.
This non-linear mapping of high-dimensional bioprocess data enables the SOM
to be used as a visualisation tool, as reported for example by Nikhil et al. [
39
],
where they were used to detect three distinct metabolic states during biohydrogen
Search WWH ::
Custom Search