Statistical Measurement Validation with Application to Electronic Nose

Technology

Mina Mirshahi, Vahid Partovi Nia and Luc Adjengue

Department of Mathematics and Industrial Engineering, Polytechnique Montreal, Montreal, Quebec, Canada

Keywords:

Artiﬁcial Olfaction, Electronic Nose, Gas Sensor, Odor, Outlier, Robust Covariance Estimation.

Abstract:

An artiﬁcial olfaction called electronic nose (e-nose) relies on an array of gas sensors with the capability of

mimicking the human sense of smell. Applying an appropriate pattern recognition on the sensor’s output

returns odor concentration and odor classiﬁcation. Odor concentration plays a key role in analyzing odors.

Assuring the validity of measurements in each stage of sampling is a critical issue in sampling odors. An ac-

curate prediction for odor concentration demands for careful monitoring of the gas sensor array measurements

through time. The existing e-noses capture all odor changes in its environment with possibly varying range of

error. Consequently, some measurements may distort the pattern recognition results. We explore e-nose data

and provide a statistical algorithm to assess the data validity. Our online algorithm is computationally efﬁcient

and treats data as being sampled.

1 INTRODUCTION

The ability to recognize the chemicals in the envi-

ronment is a very basic and essential need for the

living organisms; from a single-cell amoebae to hu-

man beings, all species are provided with a chemi-

cal awareness system. Human beings have three sen-

sory systems to detect odors: sense of taste, sense of

smell, and chemical feel with receptors all over the

body. All species employ their chemical senses to

approach and being attracted to possibly safe condi-

tions, as well as avoiding and being resisted to the

harmful ones. As for human beings, in every breath,

the sense of smell collects a sample from its environ-

ment and forwards it to the brain for further analyses.

Unlike the sense of taste, smell can be captured from

a distance and assist the brain in producing a warn-

ing. Unfortunately, the human sense of smell does

not respond to all harmful air pollutants. Additionally,

sensitivity of humans to many air pollutants varies —

one can be accustomed to a toxic smell. In the last

decade, great attention has been paid to the subject

of air quality because it directly inﬂuences the envi-

ronmental and human health. A crucial element in

assessment of indoor and outdoor air quality is audit-

ing the odorants. There exists various odor measure-

ment techniques such as dilution-to-threshold, olfac-

tometers, and referencing techniques (McGinley and

Inc, 2002). The performance of these approaches de-

pend on human evaluation. Due to the high variabil-

ity of individual’s sensitivity, the common methods

mostly lack accuracy. In 1982, the ﬁrst gas multi-

sensor array was invented as primary artiﬁcial olfac-

tion (Persaud and Dodd, 1982). The term electronic

nose (e-nose) was introduced by Gardner and Bartlett

(1994). E-nose is an artiﬁcial olfactory system which

consists of an array of gas sensors. The e-nose is

designed for recognizing complex odors in its sur-

rounding environment. The gas sensor array receives

chemical information about gaseous mixtures as in-

put and converts it to measurable signals. Sensors

act independently and simultaneously in this device.

Cross-sensitivity of gas sensors is inevitable in sen-

sor array structure. The cross-sensitivity is the inter-

action among chemicals that leads to a different sig-

nal from the component in a mixture compared to the

single component. Gas sensor’s performance is af-

fected by different elements which make it unstable

and less sensitive to odors. One of the most serious

deterioration in sensors is owing to a phenomenon

called drift. Drift is a temporal change in sensor’s

response while all other external conditions are kept

constant. The majority of manufactured sensor ar-

rays are subject to drift, and several methods have

been introduced to overcome this problem (Carlo and

Falasconi, 2012; Artursson et al., 2000; Padilla et al.,

2010; Zuppa et al., 2007). The behavior of a sensor is

directly inﬂuenced by the surrounding chemical and

Mirshahi, M., Nia, V. and Adjengue, L.

Statistical Measurement Validation with Application to Electronic Nose Technology.

DOI: 10.5220/0005628204070414

In Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2016), pages 407-414

ISBN: 978-989-758-173-1

407

physical conditions. For instance, the sensor response

may depend on the temperature of the gas under ex-

amination. Therefore, thermal conditions around the

sensing elements need to be supervised. The multi-

variate response of gas sensor arrays undergoes dif-

ferent pre-processing procedures before the predic-

tion is performed using statistical tools such as regres-

sion, classiﬁcation, or clustering. Numerous methods

have been developed for analyzing the gas sensor ar-

ray data, including Gutierrez-Osuna (2002); Kermiti

and Tomic (2003); Bermak et al. (2006).

2 PROBLEM STATEMENT

The e-nose has partially addressed the human sense of

smell in diverse industrial sites. Unwanted variabil-

ity may occur in sensor’s output data. This happens

due to environmental factors or physical impairment

of the system, since e-noses are installed in outdoor

ﬁelds where the conditions can dramatically ﬂuctu-

ate. This demands for monitoring the critical factors

through adding extra sensors and temperature com-

pensation in sensor pre-processing. The sensor’s out-

put is used to quantify odor concentration. Transfer-

ring the data to olfactometry is both time consuming

and costly. Only small portions of data are appointed

for further analyses of its concentration in olfactom-

etry. Pattern recognition methods are employed in

order to predict the odor concentration for each set

of sensor values. To assess the accuracy of predic-

tions, the validity of sensor values must be ensured.

Sensors in the e-nose structure may report incorrect

values or some stop functioning for a short period of

time. These anomalies are ought to be diagnosed and

reported in real time using a computationally efﬁcient

algorithm.

3 DATA DESCRIPTION

The data under the study include 11 distinct attributes,

each representing sensor values of the e-nose. Sen-

sors react to almost all gases in the air, but they are

designed so that each sensor is more sensitive to a

speciﬁc type of gas. Some of the sensors are highly

positively correlated with each other, see Figure 1 and

Figure 2 (left panel).

Suppose that x

p×1

is a random vector of p = 11 at-

tributes, in which a

illustrates the transpose of vector

a, and its n independent realization are stored in the

rows of data matrix X

n×p

. The covariance matrix of

Time

Sensor’s Output × 10

Jan−28 Jan−29 Jan−30

5.1 5.2

Figure 1: Senor’s output during three days of sampling for

4 randomly selected sensors.

p×1

, say Σ = [σ

i j

]

i, j=1,2,..., p

, is deﬁned as

p×p

= Cov(x) = E{(x − µ)(x − µ)

where µ represents the mean of x, E is the expecta-

tion operator. The covariance, σ

i j

, measures the de-

gree to which two attributes are linearly associated. It

is well-known that the inverse of covariance matrix,

commonly known as precision matrix, yields the par-

tial correlation between the attributes. The partial cor-

relation is the correlation between two attributes con-

ditioning on the effect of other attributes. Non-zero

elements of Σ

−1

implies the conditional dependence.

Therefore, the sparse estimation of Σ

−1

pinpoints the

block dependent structure of attributes. The sparse es-

timation of Σ

−1

set some of the Σ

−1

entries exactly

to zero. Investigation of the inherent dependence be-

tween the sensor values is then performed by means

of the partial correlation. In order to obtain a clear

image of sensors which are potentially grouped to-

gether, the graphical lasso (Friedman et al., 2008) is

used. Friedman et al. (2008) considered estimating

the inverse of covariance matrix, Σ

−1

, sparsely by

applying a lasso penalty (Tibshirani, 1996). In Fig-

ure 2 (right panel), the undirected graph connects two

variables which are conditionally correlated given all

other attributes. For instance, the sensors 9, 10, and

11 are conditionally correlated with each other. This

also agrees with the heatmap of the correlation ma-

trix Figure 2 (left panel). Thus, this dependence must

be taken into account while modeling data. Another

vital assumption that should be veriﬁed is the Gaus-

sianity of the data. The non-Gaussianity of the sensor

values is established using various methods such as

analyzing the distribution of individual sensor values,

scatter plot of the linear projection of data using prin-

cipal components, estimating the multivariate kurtosis

and skewness, and also multivariate Mardia test, see

Figure 3.

ICPRAM 2016 - International Conference on Pattern Recognition Applications and Methods

408

−1

−0.8

−0.6

−0.4

−0.2

0.2

0.4

0.6

0.8

Figure 2: Left panel, heatmap of the correlation matrix of the sensor values (s

–s

). Right panel, the undirected graph

of partial correlation using the graphical lasso. The undirected graph of the right panel approves the block structure of the

heatmap of the left panel.

0 200 400 600 800 1000

10 20 30 40

Squared Mahalanobis Distance

Chi−Square Quantile

× 10

−4

35 40 45 50

0246

× 10

Density

× 10

−4

35 40 45 50

0246

× 10

Density

× 10

−4

35 40 45 50

0246

× 10

Density

Figure 3: Left panel, the Q-Q plot of squared Mahalanobis distance supposed to follow chi-square distribution for Gaussian

data. Right panel, the marginal density for some randomly chosen sensor values. Both graphs conﬁrm the non-Gaussianity of

data.

4 METHODOLOGY

In order to demonstrate the validity of the e-nose mea-

surements, we aim to allocate each sample to different

zones. To be able to verify the validity of the measure-

ments, it is necessary to have some reference samples

for the purpose of comparison. These reference sam-

ples are collected while the e-nose is at its best per-

formance, and the conditions are fully under control.

For the data set under the study, there are two distinct

reference sets. Reference 1 is constituted of data in a

period of sampling deﬁned by an expert after installa-

tion of the e-nose. We call the data in this period of

sampling as proposed set. Reference 2, upon its avail-

ability, is manually gathered samples from the ﬁeld

and brought to the laboratory to quantify the odor con-

centration. We call the latter data, calibration set to

emphasize that it can be used for data modeling us-

ing supervised learning. If new data diverge greatly

from the overall pattern of data previously seen, then

it is marked as an outlier and is allocated to the red

zone. This zone represents a dramatic change in the

pattern of samples and refer to “risky” samples. If

new data is non-outlier and it is also located within the

data polytope of the Reference 1 or the Reference 2, it

is assigned to green or blue zone respectively. These

zones represent the “safe” samples. If new data is

non-outlier, but outside of the area of green and blue

zones, it is assigned to yellow zone. This zone dis-

plays potentially “critical” samples.

Producing many samples belonging to the yellow

and the red zones is an indication of a major ﬂaw in

the system. Physical complications, such as sensor

loss in the e-nose, or sudden changes in the chem-

ical pattern of the environment, account for all un-

desirable measurements. Zone assignment, therefore,

require some outlier detection algorithms. To de-

ﬁne the green and the blue zones, the new samples

Statistical Measurement Validation with Application to Electronic Nose Technology

409

Table 1: Description of each zones in validity assessment procedure.

Zone Description

Red Observations that are outliers in terms of AO measure.

Green

Observations that are non-outliers in terms of AO measure. Moreover, they fall into the polytope

of the Reference 1.

Blue

Observations that are non-outliers in terms of AO measure. Moreover, they fall into the polytope

of the Reference 2.

Orange

Observations that are non-outliers in terms of AO measure. Moreover, they fall into the polytopes

of both the Reference 1 and the Reference 2.

Yellow

Observations that are non-outliers in terms of AO measure. Moreover, they do not fall into the

polytope of neither the Reference 1 nor the Reference 2.

44 48 52

36 37 38 39

× 10

0.5

1.5

× 10

−7

Figure 4: Validity assessment for about 700 samples based on 2 sensor values. Left panel, the plot illustrates the contour map

of estimated density function for the 2 sensors. Right panel, the density function of the samples demonstrated in 3D with

zones identiﬁed for each of the samples in the sensor 1 (s

) versus sensor 2 (s

) plane. Higher density is assigned to green,

blue, and orange zones compared to yellow and red zones.

are projected onto a lower dimension subspace. Di-

mension reduction methods such as principal compo-

nent analysis (PCA) can serve this purpose (Jolliffe,

2002). PCA transforms a collection of possibly corre-

lated attributes into a set of linearly uncorrelated axes

through orthogonal linear transformations. The ﬁrst k

(k < p) principal components are the eigenvectors of

the covariance matrix Σ associated with the k largest

eigenvalues. PCA exploits empirical covariance ma-

trix,

Σ, which is extremely sensitive to outliers (Pren-

dergast, 2008). Since the data contain many outliers,

robust covariance estimation must be applied to avoid

misleading results. Robust principal component anal-

ysis (Hubert et al., 2005) is employed for dimension

reduction purpose throughout this paper. This robust

PCA computes the covariance matrix through projec-

tion pursuit (Li and Chen, 1985) and minimum co-

variance determinant (Croux and Haesbroeck, 2000)

methods. The robust PCA procedure can be summa-

rized as follows:

1. The matrix of data is pre-processed such that the

data spread in the subspace of at most min(n −

1, p).

2. In the spanned subspace, the most obvious out-

liers are diagnosed and removed from data. The

covariance matrix is calculated for the remaining

data,

is used to decide about the number of principal

components to be retained in the analysis, say k

< p).

4. The data are projected onto the subspace spanned

by the ﬁrst k

eigenvectors of

5. The covariance matrix of the projected points is

estimated robustly using minimum covariance de-

terminant method and its k leading eigenvalues are

computed. The corresponding eigenvectors are

the robust principal components.

To deﬁne the red zone, it is required to ﬁnd the

outliers of data as it is being measured by the e-nose

through time. As the data fail to follow a Gaussian

distribution, outlier detection methods that rely on the

assumption of elliptical contoured distribution should

be avoided. Here, outliers are ﬂagged by means of ad-

justed outlyingness (AO) criterion (Brys et al., 2006).

If a sample is detected as an outlier by AO measure,

it belongs to the red zone. For the speciﬁcation of the

ICPRAM 2016 - International Conference on Pattern Recognition Applications and Methods

410

remaining zones, we need to deﬁne the polytopes of

the samples in Reference 1 and Reference 2. These

polytopes are built using the convex hull of the ro-

bust principal component scores. More speciﬁcally,

the boundary of the green zone is deﬁned by com-

puting the convex hull of the robust principal compo-

nent scores of the Reference 1. A short description of

each zone is provided in Table 1. Before determin-

ing the color tag for each new data, the samples are

checked for missing values and are imputed in case

needed by multivariate imputation methods such as

Josse et al. (2011). The idea behind the validity as-

sessment is visualized in Figure 4. For simplicity,

only 2 sensors are used for all computations in Fig-

ure 4 and a 2D presentation of zones is plotted using

the sensors’ coordinates. Suppose that X

N×11

repre-

sents the matrix of sensor values for N samples, y

the vector of corresponding odor concentration val-

ues and x

is the lth row of X

N×11

, l = 1, 2, . . . , N.

Furthermore, suppose that n

refers to the number of

samples in the proposed set of the sampling and n

refers to the number of samples in the calibration set.

The samples of the proposed set are always available,

but not necessary the calibration set. Two different

scenarios occur based on the availability of the cali-

bration set. If the calibration set is accessible, then

Scenario 1 happens. Otherwise, we only deal with

Scenario 2. Scenario 1 is a general case which is

explained more in details. The data undergo a pre-

processing stage, including imputation and outlier de-

tection, before any further analyses. Having done the

pre-processing stage, data are stored as Reference 1,

×11

, and Reference 2, X

×11

. The ﬁrst k, e.g.

k = 2, 3, robust principal components of X

×11

are

calculated and the corresponding loading matrix is

Sub-Algorithm: (Scenario 1).

1: if the point x

, l = 1, 2, . . . , N is identiﬁed as an

outlier by AO measure then

2: x

is in red zone,

3: else if x

∈ ConvexHull

(1)

AND x

6∈

ConvexHull

(2)

then

4: x

is in green zone,

5: else if x

6∈ ConvexHull

(1)

AND x

∈

ConvexHull

(2)

then

6: x

is in blue zone,

7: else if x

∈ ConvexHull

(1)

AND x

∈

ConvexHull

(2)

then

8: x

is in orange zone,

9: else

10: x

is in yellow zone.

11: end if

denoted by L

. The pseudo code of two algorithms

for Scenario 1 is provided below. Scenario 2 is a spe-

cial case of Scenario 1 in which Sub-Algorithm (Sce-

nario 1) is used with ConvexHull

(2)

= ∅ that elimi-

nates the blue and the orange zones. Consequently,

there is no model for odor concentration prediction in

the Main Algorithm.

Main Algorithm: (Scenario 1).

Require: X

×11

, X

×11

, and the loading matrix L

using robust PCA over Reference 1, X

×11

1: ConvexHull

(1)

← the convex hull of the projected

values of the Reference 1, X

×11

2: Train a supervised learning model on Refer-

ence 2, X

×11

, and its odor concentration vector,

3: ConvexHull

(2)

← the convex hull of the projected

values of the Reference 2, X

×11

4: Do Sub-Algorithm for new data x

∗

5: Predict the odor concentration for new data x

∗

us-

ing the trained supervised learning model.

The above steps are implemented over 8 months

of data collected by the e-nose in Section 6. In order

to justify our choice of statistical techniques, the pro-

posed methodology is run over a set of simulated data

in a following section.

5 SIMULATION

To emphasize on the importance of the assump-

tions such as non-eliptical contoured distribution and

robust estimation considered in our methodology,

we examine the methodology on a set of simu-

lated data. Assume the matrix of data X

N×2

, where

= (x

, x

); l = 1, 2, . . . , N, are generated accord-

ing to the mixture of Gaussian and the Student’s t-

distributions, Figure 5 (top left panel). Ignoring the

distribution of data and seeking for any classical ap-

proach toward outlier detection, renders some ob-

servations as outliers mistakenly, Figure 5 (top right

panel). The parameters of interest, the mean vector

and the covariance matrix, need to be estimated ro-

bustly, otherwise the conﬁdence region misrepresents

the underlying distribution. In Figure 5 (bottom left

panel), the classical conﬁdence region is pulled to-

ward the outlier observations. On the contrary, the

robust conﬁdence region perfectly unveil the distri-

bution of the majority of observations because of the

robust and efﬁcient estimation of the mean and the

covariance matrix. Consequently, the classical prin-

cipal components are affected by the inefﬁcient esti-

Statistical Measurement Validation with Application to Electronic Nose Technology

411

Figure 5: Top left panel, the simulated data from the mixture distribution f (x) = (1 − ε) f

(x) + ε f

(x) with contamination

proportion of ε =

, and f

and f

being the Gaussian and Student’s t-distribution respectively. The data from f

, and f

are plotted in triangles and crosses correspondingly. Top right panel, the outliers of data are identiﬁed and highlighted with

red using the classical Mahalonobis distance and 95th percentile of the Chi-square distribution with two degrees of freedom.

Bottom left panel, the 95% conﬁdence region for the data is computed using the classical estimates of parameters (solid line)

and the robust estimates (dashed line). Bottom right panel, the Main Algorithm is implemented and the zones are graphed by

colors described in Table 1.

mation of the covariance matrix. We proposed using

methods which deal with contaminated data appropri-

ately. Adjusted outlyingness (AO) measure identiﬁes

the outliers of the data correctly. In the Main Algo-

rithm, suppose we take the Gaussian sub-sample as

the Reference 1. Figure 5 (bottom right panel) shows

the result of our algorithm on the simulated data.

6 APPLICATION

For the easy visualization, the ﬁrst 3 robust princi-

ple components of the data are used, PC1, PC2, PC3.

These components correspond to the 3 largest eigen-

values of the covariance matrix. In case of sensor

failures, the data contain missing values that need to

be imputed. First, data are imputed to replace all the

missing values, and then the validity of the measure-

ments are identiﬁed over the 8 months sampling. Only

a subset of 500 samples out of 200 thousands of obser-

vations are plotted to make the graphs more readable.

In Figure 6, the sample points are drawn in gray and

each zone is highlighted using its corresponding color

of Table 1. The circles in Figure 6 are also illustrated

on PC1 and PC2 plane for a better demonstration of

the zones.

The zones’ deﬁnition is helpful in interpreting the

results. As an example, the green or the blue zone re-

veals the fact that the sampling points are very close

to the samples that have already been observed in ei-

ther Reference 1 or Reference 2. The observations in

reference sets were entirely under control, therefore,

the blue and green zones justify the validity of sam-

ples. Consequently, the prediction obtained over these

samples is expected to be more accurate. On the con-

trary, the prediction values for the points in the yel-

low zone are less accurate compared with the green

ICPRAM 2016 - International Conference on Pattern Recognition Applications and Methods

412

PC1

PC2

PC3

PC1

PC2

PC3

PC1

PC2

PC3

PC1

PC2

PC3

Figure 6: A random sample of size N = 500 is plotted over the ﬁrst three robust principal components coordinates. From top

left panel to bottom right panel, the colored blobs represent green, blue, yellow, and red zones respectively.

and the blue zones. In other words, the data that are

dissimilar to the already observed data deserve further

attention. These points are the potential outliers and

are reported in the red zone. Additionally, this also re-

veals that the predictions values associated with such

data can be misleading. Producing a noticeable per-

centage of samples belonging to the yellow and the

red zones referring to the possible failure of the e-nose

equipment.

7 CONCLUSION

Electronic nose devices have received continuous at-

tention in the ﬁeld of sensor technology recently. Ap-

plications of the e-nose appear in industrial produc-

tion, processing, and manufacturing including quality

control, grading, processing controls, gas leak detec-

tion, and monitoring odors. The measurement qual-

ity of the e-nose depends on its sensor’s performance.

Due to the high variability of the gases in the air

and the sensitivity of the sensor values, e-nose mea-

surements can ﬂuctuate very often and fail to main-

tain a certain level of precision. An automatic pro-

cedure that detects the samples’ validity in an online

fashion has been a technical shortage and was ad-

dressed in this work. This allows administrators to

take the subsequent steps like sampling new observa-

tions from the ﬁeld or re-calibrating the system if nec-

essary. Equipping the e-nose device with a comput-

ing server that performs the measurement validation

and odor concentration prediction in real time, initi-

ates a new era to automatic odor detection. Develop-

ing a suitable model for predicting odor concentration

might be the next challenge of this emerging technol-

ogy. We follow this direction in our future work.

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