WO1997014958A1

WO1997014958A1 - Cluster analysis

Info

Publication number: WO1997014958A1
Application number: PCT/GB1996/002490
Authority: WO
Inventors: Krishna Chandra Persaud
Original assignee: Aromascan Plc
Priority date: 1995-10-14
Filing date: 1996-10-11
Publication date: 1997-04-24
Also published as: GB9521089D0; AU7223796A

Abstract

There is disclosed a concentration sensitive method for analysis of a plurality of outputs from chemical sensing device comprising the steps of: normalising said plurality of outputs; calculating at least one intensity output, said intensity output being related to the absolute magnitude of at least one of said plurality of outputs; and performing a cluster analysis of the plurality of normalised outputs and the intensity output, or outputs.

Description

CLUSTER ANALYSIS

This invention relates to the use of cluster analysis in chemical sensing, in particular to the use of intensity data in such analyses in order to provide information regarding chemical concentrations.

In recent years there has been a great deal of interest in the field of gas sensing. [For the purposes ofthe present description, it is understood that 'gas sensing' comprises the detection of any chemical in the gas phase, including odours and volatile species]. One approach is to employ, within a single gas sensing device, an array of gas sensors which use semiconducting organic polymers (SOPs) as the active sensing material (see, for example, Persaud K C, Bartlett J G and Pelosi P, in 'Robots and Biological Systems : Towards a new bionics?', Eds. Darios P, Sandini G and Aebisher P, NATO ASI Series F : Computer and Systems Sciences JU22 (1993) 579). Transduction is accomplished by measuring changes in the dc resistance ofthe sensors, these changes being induced by the absoφtion of gaseous species onto the SOPs.

The sensors are selected so as to exhibit differing but overlapping responses to a variety of gases, and therefore the output of an array of sensors is a pattern of response characteristic ofthe gas or gases detected. Since the number of sensors in an array is typically rather large - AromaScan pic manufacture devices having 20 and 32 sensor arrays - it can be said that these patterns are projected into multi-dimensional space of high order. Human vision is very good at recognising structural relationships within two and three dimensional space; however, in multi-dimensional space the perception of such relationships is extremely difficult. Therefore, in order for a human to examine complex multi-dimensional data, it is extremely useful to map such data from the high dimensional pattern space in which they are originally presented onto a low (two or three) dimensional pattern space. There are numerous methods for performing the 'mapping' operation, which may comprise linear or non-linear algorithms. Linear mapping algorithms are used frequently for reasons of simplicity and generality. Such algorithms have been used in gas and odour classification as well as in chemical data classification in order to reduce multi-dimensional pattern space to two or three dimensional space. For gas recognition, Gardner et al (Gardner J W and Bartlett P N, Sensors and Actuators B 18-19 (1994) 221 and references therein) used a principal component analysis (PC A) method - a derivative of the Karhunen-Loeve (K-L) projection and one of the more powerful linear mapping techniques - to classify volatile chemicals by representing similar sets of data in characteristic 'clusters'. Ballantine Jr et al (Ballantine Jr. D S, Rose S L, Grate J W and Wohltjen H, Anal.Chem., 5_£ (1986) 3058) classified vapours using the PCA method and the (K-L) projection. The K-L projection was used in odour classification by Abe et al (Abe H, Kanaya S, Takahashi Y and Sasahi S-I, Analytica Chemica Acta 215 G988) 155) and Nakamoto et al (Nakamoto T, Fukuda A, Morizumi T and Asakura Y, Sensors and Actuators B, 3_ (1991) 221) who investigated the odour of whisky data sets. Kowalski and Bender (Kowalski B R and Bender C F, J Amer.Chem. Soci., 95.3 (1973) 686) employed a similar linear mapping technique, with eigenvector projection, for displaying chemical data.

Non-linear mapping algorithms may be used when linear mapping is unable to preserve complex data structures - which is, in fact, commonly the case with 'real life' data. Non-linear techniques have complicated mathematical formulations compared to linear mapping, and are rarely used for gas classification. However, the responses ofthe array of sensors employed in the aforementioned AromaScan systems represent non-linear, multi-dimensional pattern structures, which (when normalised) contain the concentration independent pattern data sets describing different gases. In this instance non-linear mapping techniques are more applicable than linear techniques. It should be noted that truly concentration independent patterns are generated only when the concentration-response relationship is linear. A particularly useful form of non-linear mapping is the algorithm of Sammon Jr. (Sammon Jr, JW, IEEE Trans, on Computers C-18 (1969) 401 ) and variations thereof, which represent highly effective methods of multivariate data analysis and clearly visualise multi-dimensional patterns onto two and three dimensional patterns. Various modifications to Sammon's algorithms have been proposed (see, for example, Kowalski and Bender, ibid; Nicemann H and Weiss J, IEEE Trans, on computers C-28 (1979) 142; Chang C L and Lee R C T, IEEE Trans, on System, man and cybernetics, (1973) 197; Pykett C E, Electron Lett., 14 (1978) 799; Biswas G, Jain A K and Dubes R C, IEEE Trans, on pattern analysis and machine intelligence, PAMI-3 (1981) 701) which are mainly concerned with reducing memory size and convergence time whilst remaining within the Sammon framework. Such considerations are no longer major problems due to the enormous recent advances in computer technology. Persaud et al (Hatfield J V, Neaves P, Hicks P J, Persaud K and Travers P, Sensors and Actuators B.T8-19 (1994) 221) have used the Sammon technique for vapour sensing applications in order to observe correlations between alcoholic data sets.

Since the mapping techniques described above result in 'clustering' of similar pattern types around characteristic two or three dimensional coordinates, the application of such techniques and the like will hereinafter be described as cluster analysis.

In the context of chemical sensing, prior art cluster analyses are essentially devoid of information regarding chemical concentration. This is because the cluster analysis is performed on patterns: raw sensor data - the intensity of which is related to chemical concentration - is scaled in an appropriate manner before cluster analysis. In instances where the concentration-sensor response relationship is non-linear, a pattern cluster will be skewed. In this sense the cluster analysis contains concentration information, but no direct use is made of absolute intensity data, and the effect is rather difficult to observe except at high concentrations/non-linearities. The present invention overcomes the aforementioned difficulties by employing intensity information in cluster analyses in order to extract information on chemical concentration. Such fundamental information is frequently desirable, for instance, in the recognition of dangerously high levels of a toxic substance. It should be noted that whilst the invention is primarily directed towards the sensing of gaseous species, the approach is applicable to any area of chemical sensing where the sensing device produces a plurality of outputs which require some form of cluster analysis.

According to the invention there is provided a concentration sensitive method for analysis of a plurality of outputs from a chemical sensing device comprising the steps of : normalising said plurality of outputs; calculating at least one intensity output, each intensity output being related to the absolute magnitude of at least one of said plurality of outputs; and performing a cluster analysis ofthe plurality of normalised outputs and the intensity output or outputs.

The intensity output, or outputs, may be weighted by a scaling factor.

The cluster analysis may comprise a non-linear mapping technique, and this technique may be the Sammon algorithm or a variant thereof.

A mathematical model of the results of the cluster analysis may be employed in order to derive quantitative concentration data.

There may be a single intensity output which is the mean of the moduli of the plurality of outputs. There may be a plurality of intensity outputs wherein each of said intensity outputs comprises the absolute magnitude of an individual output.

The chemical sensing device may be a gas sensing device comprising at least one semiconducting organic polymer (SOP) based sensor, and the gas sensing device may further comprise an array of SOP based sensors wherein the outputs ofthe device correspond to changes in the dc resistance of said sensors.

Embodiments of concentration sensitive methods of analysis according to the invention will now be described with reference to the accompanying drawings, in which :

Figure 1 is a two dimensional cluster map; and

Figure 2 is a graph of sensor response across an array often sensors.

The present invention is a concentration sensitive method of analysis of a plurality of outputs from a chemical sensing device comprising the steps of : normalising said plurality of outputs; calculating at least one intensity output, each intensity output being related to the absolute magnitudes of at least one of said plurality of outputs; and performing a cluster analysis ofthe plurality of normalised outputs and the intensity output, or outputs.

Cluster analyses make no prior assumptions ofthe classes in which pattems belong, and apparent clustering of points is a matter for human judgement. In the field of chemical sensing, pattems generated by repeated exposure of a sensing device to a single compound of differing concentrations are identical if the concentration-output response relationship is linear. When a conventional cluster analysis is employed the points coalesce into a single point or a closely grouped set of points, with the distances between the points representing experimental error. A cluster 10 of the latter type is shown in Figure 1.

However, it is often useful for the cluster analysis to reveal information on chemical concentration, e.g. two samples may be identical in composition but at different concentrations. A non-limiting example is provided by gas sensing devices of the type manufactured by AromaScan pic, which comprise an array of SOP sensors. Transduction is accomplished by measuring the changes in sensor dc resistances produced by exposure ofthe sensors to a gas or a mixture of gases. Figure 2 depicts a generalised response of an array often such sensors to a gas, the response comprising a plurality of outputs 20-38. The outputs 20-38 are recorded as ΔR/R, the fractional change in resistance, where R is the base resistance of a sensor is clean air and ΔR is the change in resistance. It should be noted that an output may be negative. The absolute magnitude of a ΔR/R response (i.e. the modulus |ΔR/R|) increases with increasing concentrations of the detected gas; one embodiment of the present invention utilises this fact by introducing to the cluster analysis an 'intensity' output which is related to the absolute magnitudes of the plurality of outputs 20-38. It is convenient to calculate the absolute mean intensity ofthe response.

Concentration independent pattems are produced by normalising the outputs 20-38 of the sensor array. The normalisation is performed by calculating the percentage fractional change in resistance for each sensor over the entire array. This given by equation (1) :

ΔJ.

where n = 10 in the present example. The normalised outputs together with the intensity output are subjected to cluster analysis, the intensity output being scaled so that it is either comparable to the normal range of number present in pattern information or greater, so that the cluster analysis is biased towards intensity rather than pattern information. The scaling or weighting factor may be user determined.

As described earlier, the non-linear Sammon mapping technique, or variations thereof, represent a preferred class of cluster analysis in the case of SOP based sensor arrays for gas detection. However, other forms of cluster analysis (linear or non¬ linear) such as principal component analysis or variants such as factor analysis may also be applied. Indeed, such forms may prove preferable in other chemical sensing applications.

The results of a two dimensional analysis according to the present invention are displayed generally in Figure 1 , which reveals that measurements of an odour at different concentrations thereof appear as a streak 12, the distance between two points being dependent on the difference in sample concentrations during the corresponding measurements.

In the above described embodiment a single intensity output, representing the absolute mean intensity of output response, is employed in the cluster analysis. An altemative approach, which is also within the scope of the invention , is to utilise a number of intensity outputs, each intensity output representing the absolute magnitude of a single selected sensor output. Thus a selected subset ofthe overall response to the sensor array may be employed in the cluster analysis. The intensity outputs may be scaled by suitable weighting factors. It should be noted that generally when SOP based sensors of the type described above are exposed to a single gas, the concentration-response relationship is linear over a wide range of gas concentrations. However, when the array of sensors is exposed to a mixture of chemicals, the concentration response relationship may be non¬ linear, even if the mixture composition remains constant as the concentration varies. This phenomenon is due to competition for adsoφtion between compounds of differing binding affinities, since this competition is dependent on the concentrations of the compounds. At low concentrations compounds with the highest binding affinities are adsorbed onto the SOPs; and therefore the sensors are only responsive to these compounds. (The modulation of sensor resistance is due to - as yet not fully characterised - changes in SOP electronic structure and charge distribution caused by the adsoφtion of gases). As concentrations increase, compounds of lower binding affinity, begin to compete for binding. Therefore, normalised response pattems recorded at different concentrations will differ in appearance. As a result, cluster analysis gives rise to a streak, rather than a tight cluster. In this sense, the cluster analysis contains some information on chemical concentration, but any effect is difficult to observe at low concentrations. The use of intensity data in the cluster analysis results in concentration dependent mapping in which it is easy to visually distinguish one point from another on the basis of concentration.

A further aspect ofthe present invention is the extraction of quantitative concentration data from the results ofthe cluster analysis. Since the distances between points are proportional to concentration, it is possible to apply an appropriate mathematical model (such as a polynomial fit), to the data in order to inteφolate or extrapolate unknown pattems and thereby extract concentrations.

It will be appreciated that it is not intended to limit the invention to the above examples only, many variations, such as might readily occur to one skilled in the art, being possible without departing from the scope thereof. For instance, the plurality of outputs used in the cluster analysis need not emanate from an array of sensors. UK Patent GB 2 203 553 B discloses a SOP based sensor used in conjunction with an ac transduction technique. In this instance, it may be desirable to measure changes in impedance characteristics at a plurality of ac frequencies : in this way, a single sensor may provide the plurality of outputs. The outputs of arrays of chemical sensors used to monitor liquid analytes may also be amenable to the cluster analysis described herein.

Claims

1. A concentration sensitive method for analysis of a plurality of outputs from chemical sensing device comprising the steps of : normalising said plurality of outputs; calculating at least one intensity output, said intensity output being related to the absolute magnitude of at least one of said plurality of outputs; and performing a cluster analysis ofthe plurality of normalised outputs and the intensity output, or outputs.

2. A concentration sensitive method according to claim 1 in which the intensity output, or outputs, is weighted by a scaling factor.

3. A concentration sensitive method according to claim 1 or claim 2 in which the cluster analysis comprises a non-linear mapping technique.

4. A concentration sensitive method according to claim 3 in which the non¬ linear mapping technique is the Sammon algorithm or a variant thereof.

5. A concentration sensitive method according to any ofthe previous claims in which a mathematical model ofthe results ofthe cluster analysis is employed to derive quantitative concentration data.

6. A concentration sensitive method according to any ofthe previous claims in which a single intensity output is calculated, said intensity output being the mean of the moduli ofthe plurality of outputs.

7. A concentration sensitive method according to any of claims 1 - 5 in which a plurality of intensity outputs are calculated, each of said intensity outputs comprising the absolute magnitude of an individual output.

8. A concentration sensitive method according to any ofthe previous claims in which the chemical sensing device is a gas sensing device comprising at least one semiconducting organic polymer based sensor.

9. A concentration sensitive method according to claim 8 in which the gas sensing device comprises an array of sensors and the outputs ofthe device correspond to changes in the dc resistance of said sensors.