INTRODUCTION

Top Abstract Introduction Materials and Methods Results and Discussion References

Rapid and accurate identification of vast numbers of phytoplankton cells is essential in aquatic microbial ecology, since these microalgae collectively fuel the marine food web and have been implicated in climate control and some form nuisance blooms. In the past, research has been hampered by the laborious and time-consuming nature of the analysis (usually in the laboratory a long time after sample collection in the field), leading to inaccurate estimates of abundance because of loss due to fixation and storage and to limitations on the number of cells that can be counted. Analytical flow cytometry (AFC), which measures various diffraction, light scatter, and fluorescence parameters, can provide "fingerprints" for individual phytoplankton cells (12, 14). AFC allows easy discrimination of phytoplankton from nonliving particles in seawater (14), and a small number of categories (less than 10) have been distinguished from bivariate scatter plots (12, 14) or by using artificial neural networks (ANNs) (1, 8, 9, 22). In a preliminary study, attempts were made to discriminate 40 microalgal species from each other by using six AFC parameters (2), but half of them were identified with less than 70% success due to the overlap of character distributions. Clearly, the current analytical capacity falls well short of being able to analyze the full taxonomic spectrum in the world's oceans. For discrimination of large numbers (hundreds) of taxa, different and/or more parameters are required.

Cytometry. Currently available commercial flow cytometers have been designed for use in the laboratory and are able to cope with only a relatively narrow range of particle sizes. For marine use a machine is required that can be used at sea; can cope with a range of cell sizes to include large phytoplankton (>5 µm in diameter), nanoplankton (2 to 5 µm), and picoplankton (<2 µm); is tailored specifically to allow detection of pigments found in phytoplankton; and can sort particles electrostatically or mechanically.

Data analysis problem. AFC yields vast quantities of multivariate data, which present a considerable challenge for data analysis. While multivariate statistical methods have been used (e.g., see references 4 and 6), it can be difficult to find the appropriate technique, and problems may arise if invalid assumptions are made about the data distribution, e.g., assuming normality when data actually have a bi- or multimodal distribution. The use of ANNs is a powerful alternative technique that makes, in general, only minimal assumptions about the nature of the data distribution.

ANNs used for identification generally consist of an interconnected layered structure of simple data-processing elements (nodes): an input layer, which serves merely to distribute input data (one node per identification character); a hidden layer, which models the data distribution; and an output layer, which indicates the identification (one node per taxon) (Fig. 1). When presented with a multivariate data pattern drawn from the probability distribution of one of a number of categories (taxa), ANNs are able to associate the pattern with the category to which it belongs (3, 11). The ANN learns this association in a "training phase," during which the internal structure is adjusted in response to presentation of a representative sample of data patterns for each of the taxa to be identified, together with information as to their correct identification (the "training data"). Once successfully trained, an ANN can recognize patterns which, although never before presented, are sufficiently similar to the training data to allow the correct association to be drawn. The multilayer perceptron network, also known as the backpropagation network, is the ANN paradigm most commonly applied to biological identification problems, including preliminary studies that use flow cytometry data (1, 2, 8, 9, 22). However, this ANN trains very slowly and may perform poorly if the data distribution is complex (19). Radial basis function (RBF) ANNs, on the other hand, are at least as successful in biological identification as other network types (18, 27, 28), train much more rapidly (28), and allow criteria to be applied to reject as being "unknown" patterns from taxa upon which the network has not been trained (19). Rapid training is important, as when additional taxa are encountered ANNs must be retrained. The ability to recognize unknowns is also essential, since when natural samples are analyzed it is likely that several or many species will be encountered which have not been used for training the network.

View larger version (37K): [in this window] [in a new window]   FIG. 1.   Schematic diagram of an RBF neural network classifier. Raw data are distributed from the input layer via a "hidden" layer of processing units or nodes to an "output layer" where the network's decision is formed. The bias node has a constant output value irrespective of input: its use allows output layer nodes to add a constant offset.

RBF neural networks. RBF ANNs model the distributions of the data categories (taxa) to be recognized by superimposing kernels (basis functions) over the data input space. These kernels (implemented by the hidden-layer nodes [HLNs]; Fig. 1) have a defined response to input data that varies depending on the distance of the data point from the center of the kernel. The value of a basis function at any point in the data space is given by a nonlinear function of the scaled distance between that point and the basis function center. A distance scaling parameter for each basis function controls its width or spatial extent.

Training an RBF ANN occurs in two separate stages: determination of the position and size of the basis functions, followed by calculation of the weight coefficients for the output layer nodes (11, 13, 20, 27). The first stage is subdivided into two steps: selection of the basis function centers, followed by selection of the width of each basis function. The second stage is a simple least-mean-squares optimization procedure, either iterative (13) or utilizing a matrix pseudoinverse method (11, 20, 27). Optionally, these may be followed by a third stage of gradient-descent reduction of error, during which the basis functions and weights are simultaneously adjusted to improve classification performance on the training data (11, 16, 25). The training procedure may be varied by changing the algorithm used to select the basis function centers and by changing the form of the basis function around each center. Several factors related to network configuration affect how well an RBF ANN trains, including the number, positioning, shape (radially or non-radially symmetric), and width of basis functions. Optimal configuration must be determined by experiment.

This study reports on successful discrimination of 34 marine and freshwater phytoplankton taxa by using RBF networks trained on 11-parameter AFC data, obtained by using the EurOPA (European Optical Plankton Analyser) (7, 14). The importance of each parameter to the networks in performing this discrimination is assessed, and the ability of RBF ANNs to reject patterns from novel taxa as unknown is examined.

	MATERIALS AND METHODS

Top Abstract Introduction Materials and Methods Results and Discussion References

Phytoplankton cultures. Eight freshwater species (Table 1) were grown in batch culture in Woods Hole medium (10) for 3 to 4 days at 20°C under a daily 16-h (light)-8-h (dark) regimen (100 microeinsteins m² s²). Five species of cyanobacteria were grown in O-2 medium (24) under the same conditions. Twenty-one marine species (obtained from the Plymouth Culture Collection, Marine Biological Association, United Kingdom) were grown in F/2 enriched seawater medium (10) under continuous illumination at 300 microeinsteins m² s¹ at 17°C.

EurOPA flow cytometer and data. The EurOPA is a compact and easily transportable flow cytometer designed specifically for the analysis of phytoplankton at sea; it was developed during the course of a European Union project in the Marine Science and Technology (MAST-II) programme (7, 14). It allows the simultaneous collection of flow cytometric parameters for particles of up to 500 µm in width and several millimeters in length and uses argon (488-nm) and helium-neon (633-nm) lasers selected to have wavelengths optimal for the excitation of the photosynthetic pigments found in plankton, as well as data acquisition electronics able to cope with a total signal magnitude range of over six decades between the smallest and largest particles encountered during analysis of mixed field samples (14). It also incorporates novel cytometric techniques to improve the capacity for discrimination between species, including a diffraction module (a 5-by-5 square array of photodiode light detectors) which captures particle shape information through polar and azimuthal resolution of the light diffracted at small angles to the beam by particles in flow (5). Pulse-shape analysis of the fluorescence and light scatter signals reveals morphological information about the longitudinal profile of the particles, and a video imaging module allows electronic image capture of particles in flow (26).

Computer hardware and software. All RBF networks were implemented by software written in C by one of the authors (M.F.W.) on a PC.

Optimizing the number of basis functions. The number of basis functions was varied between one and four for each of the 34 classes. The upper limit of 136 basis functions (i.e., four per taxon) was determined primarily by memory limitations of the computer hardware that restricted the number of HLNs and associated weight values that could be stored (although this is no longer a problem with the increasingly powerful machines now becoming available).

Selecting between nonradially symmetric and radially symmetric basis functions. The use of the Euclidean distance metric yields hyperspherical (i.e., radially symmetric) basis functions, whereas the Mahalanobis-generalized distance allows networks with hyperelliptical (i.e., non-radially symmetric) basis functions, which can give better modelling of elongated data clusters. All the basis functions used were Gaussian. Radially symmetric basis functions had the following form:
where x is the presented pattern and m_k is the center of basis function k, _k is the root-mean-square average Euclidean distance between m_k and the cluster of training data patterns associated with it (i.e., those training patterns which are closer to m_k than to any of the other basis function centers), and  is the distance scaling parameter controlling the basis function width. Non-radially symmetric basis functions had the following analogous form:
where _k is the variance-covariance matrix for the cluster of training patterns around m_k and N is the number of dimensions of the input data.

Optimizing basis function width. The shape of the Gaussian basis functions can be adjusted by changing the width parameter . As  is decreased, the width of each basis function (the size of the receptive field) decreases, and the functions become more sharply peaked around the center. Broader functions can allow smoother interpolation between basis functions.  was varied between 1 and 14.

Basis function center selection strategy. Three methods of center selection were compared: random selection of patterns from the training data set, random selection followed by the K-means algorithm (13, 23), and random selection followed by the Kohonen LVQ algorithm (15, 16).

Use of gradient-descent algorithm. The gradient descent algorithm was applied after the networks had been trained. The procedure allows simultaneous iterative adjustment of all network parameters (the basis function center positions, the basis function size and shape, and the values of the weighted connections between the hidden and output layers) in order to minimize the identification error on the training data (11, 17, 25).

Construction of optimal RBF network to discriminate 34 species. After the experiments to determine effects of network configuration on training, an RBF network was trained to discriminate between all 34 species simultaneously. Two non-radially symmetric Gaussian basis functions were used per output class (i.e., 68 HLNs) with a width parameter  of 1.25, the centers of which were selected through use of the Kohonen LVQ algorithm. This particular architecture was found (see below) to be a good compromise, producing networks which were computationally efficient (necessary for pattern identification at rates comparable with data acquisition rates), yet with near-optimal classification performances (typically within 1% of the optimal performance).

Effect of exclusion of individual parameters. To investigate whether any of the 11 parameters were redundant in making the identifications, each was removed in turn from the training data patterns, and an RBF network using the above architecture trained on the resulting reduced-dimensionality data. Additionally, networks with the above architecture were trained utilizing the seven fluorescence light scatter-size measurements alone (parameters 1 to 7) and the four diffraction-pattern parameters alone (parameters 8 to 11). After training, the abilities of the networks to identify the test data patterns correctly were compared to the results for a network that used all 11 parameters.

Rejection of data patterns from novel taxa. An RBF network with the above architecture was constructed and trained to discriminate between 20 species by using all 11 parameters. These 20 species were a randomly selected subset of the 34 species present in the original training data. The network was then used to test two possible criteria for the rejection of data patterns from "novel" taxa, i.e., the 14 species not used for training: (i) rejection if the summed value of all the basis functions (i.e., the sum of the outputs of all the HLNs of the network excluding the bias node) was less than a threshold value  and (ii) rejection if the output of the closest basis function (i.e., the HLN with the largest output) was less than . Two indicators of performance were measured for each criterion: the proportion of the test data patterns for the 20 "known" species that were rejected (incorrectly) and the proportion of test data patterns for the 14 "novel" species that were rejected (correctly). For each criterion, investigation was made of the effect of varying the threshold value  from 0.0 (i.e., no rejection) upwards on the proportion of test data patterns from the 20 known and 14 unknown species that were rejected.

	RESULTS AND DISCUSSION

Top Abstract Introduction Materials and Methods Results and Discussion References

Optimization of RBF networks. Increasing the number of basis functions (up to the limits imposed by the computer hardware) always improved performance on test data for networks employing radially symmetric (i.e., Euclidean-distance) basis functions (Fig. 2a). Increasing the basis function width parameter improved performance up to a point for such networks, although the value for which the performance approached its maximum was different for the different basis function selection procedures (Fig. 2b). While use of the LVQ-supervised clustering algorithm to adjust the center selection produced networks with much better performance where basis functions were comparatively "narrow," increasing the width of the basis functions removed this discrepancy, and for wider basis functions the performance of networks employing LVQ to select centers was no better than that of networks employing random centre selection. Use of the K-means algorithm to adjust the center selection was always least successful.

View larger version (15K): [in this window] [in a new window]   FIG. 2.   Effect of basis function width, shape, and placement strategy on the proportion of test data patterns for 34 species that were identified correctly. (a) Effect of basis function width, for radially symmetric basis functions. Basis function centers were a randomly selected subset of the training data. Curves for four different network sizes are shown: 34 HLNs (), 68 HLNs (), 102 HLNs (), and 136 HLNs (). (b and c) Effect of basis function center selection strategy for radially symmetric basis functions (b) and non-radially symmetric basis functions (c) (formed by using the Mahalanobis distance). Curves for two network sizes (34 HLNs [open symbols] and 136 HLNs [closed symbols]) are shown for three selection strategies: random selection (squares), random selection followed by K-means unsupervised clustering (inverted triangles), random selection followed by LVQ supervised clustering (triangles).

Performance of optimal network. The optimal network identified 90.3% of the test data patterns correctly after training. Application of the gradient-descent optimization procedure improved this to 91.5% (Table 1), with the largest single improvement occurring through a reduction in the percentage of Oscillatoria misidentified by the network as Aphanizomenon (from 10.2 to 2.0%). Six species were recognized with 98.0% success or better (Alexandrium tamarensis, Chroomonas salina, Cryptomonas baltica, Cryptomonas calceiformis, Porphyridium pupureum and Rhodomonas). All other species were recognised with at least 80% success, with the exceptions of Tetraselmis rubescens (71.0% success, confused primarily with Gymnodinium simplex and Chlorella salina) and the Pseudopedinella species (68.2% success, confused primarily with Halosphaera russellii but also with Phaeocystis globosa). The excellent performance of the network described here for recognition of 34 species is far superior to the performance of any of the neural networks described previously for identifying phytoplankton (1-4, 9, 16, 22), in terms of the simultaneous recognition of a large number of species with a high recognition accuracy.

Effect of exclusion of parameters. It is important to know how well phytoplankton can be discriminated if one (or indeed more than one) parameter is missing. For example, if the flow cytometer is being used at sea, parameters may be lost because of problems with optical alignment or failure of one of the lasers in a multilaser instrument such as the EurOPA. The four fluorescence parameters appeared to be the most important (since their individual exclusion resulted in the largest decrease in the proportion of successfully identified test data patterns), although no single parameter decreased performance by more than 5% when excluded (Table 3). Clearly, good identification was achieved even when one parameter was missing, and the effect of the loss of several parameters could be investigated in a similar way.

Rejection of data patterns from "novel" taxa. For criterion 1 (a constraint on summed output of all HLNs), as the threshold value was increased, the proportion of rejected data patterns from the 14 novel species initially rose sharply to around 20% and thereafter showed an approximately linear dependence on  (Fig. 3a). The proportion of rejected data patterns from the 20 known species was quite low for  values of 0.5 but thereafter increased more rapidly than the proportion of rejected patterns from the novel species. Criterion 2 (a constraint on the value of the maximum HLN output) gave a much better ratio between the proportion of novel species rejected against the proportion of known species rejected (Fig. 3b). For example, use of criterion 1 with a  of 0.7 caused the proportion of correctly identified data patterns for the known species to decrease from 93.8% (no rejection) to 86.8% but successfully rejected 52.8% of the data patterns from the novel species. Use of criterion 2, with a  value of 0.4, caused virtually the same decrease in the proportion of correctly identified data patterns for the known species but increased the proportion of successfully rejected patterns from the novel species to 71.6% (Table 5). In each case four of the novel species were successfully rejected with 100% accuracy.

View larger version (14K): [in this window] [in a new window]   FIG. 3.   Use of a threshold parameter  as a constraint on the summed output of all HLNs (a) and the maximum HLN output value (b) to reject data from "novel" species (not present in the training data). The proportion of test data patterns failing to satisfy the constraint, and therefore rejected as unknown, is shown for the 20 trained species () and the 14 novel species ().

Future developments. The approach clearly has considerable potential, but extending it from using pure cultures in the laboratory to mixed populations in natural aquatic environments poses a number of problems. First, it is essential to be able to obtain "good" training data from the environment of interest, since conditions under which cells grow affect their flow cytometric signatures and networks trained on data from cultures may not perform well in identifying field samples. Second, scaling up to a large number of species is nontrivial, and large numbers may make it impractical to train single large networks. Third, though estimating proportions of different species present in mixed samples is straightforward when there is no uncertainty in identification of individual cells, when the identity is equivocal (due to overlapping flow cytometric parameter distributions), recourse to statistical methods is needed in order to place confidence limits on the accuracy of the estimated proportions. These problems are all being addressed currently.