Application of Dimensionality Reduction and Machine Learning Methods for the Interpretation of Gas Sensor Array Readouts from Mold-Threatened Buildings

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The solutions presented in the work, based on the use of a multi-sensor matrix and the analysis of multidimensional data, can be used in practice for assessing the mycological risk of buildings, detecting the presence of mold in rooms and evaluating the risk of the sick building syndrome.

Abstract

Paper is in the scope of moisture-related problems which are connected with mold threat in buildings, sick building syndrome (SBS) as well as application of electronic nose for evaluation of different building envelopes and building materials. The machine learning methods used to analyze multidimensional signals are important components of the e-nose system. These multidimensional signals are derived from a gas sensor array, which, together with instrumentation, constitute the hardware of this system. The accuracy of the classification and the correctness of the classification of mold threat in buildings largely depend on the appropriate selection of the data analysis methods used. This paper proposes a method of data analysis using Principal Component Analysis, metric multidimensional scaling and Kohonen self-organizing map, which are unsupervised machine learning methods, to visualize and reduce the dimensionality of the data. For the final classification of observations and the identification of datasets from gas sensor arrays analyzing air from buildings threatened by mold, as well as from other reference materials, supervised learning methods such as hierarchical cluster analysis, MLP neural network and the random forest method were used.

1. Introduction

The presence of fungi in the indoor environment is a widespread phenomenon. It is estimated that several hundred species of fungi are present indoors, including Cladosporium sphaerospermumn, Penicillium chrysogenum, Aspergillus niger, Aspergillus versicolor, Alternaria alternata, and Stachybotrys chartarum [1]. Exposure to these fungi can lead to many adverse and serious health effects, including allergies, fungal infections, or toxic reactions [2]. High relative humidity (optimally above 70%) and adequate ambient temperature, in the range of 16–35 °C, are conducive to fungal growth [3,4].

Fungal spores are the greatest group of biological particles present in the air. They infiltrate the respiratory system with the inhaled air, which contributes to allergies. They range in size, from a few micrometers to tens of micrometers; they are smaller than pollen grains and can enter the respiratory tract more deeply [5], causing allergic reactions from both the upper and lower respiratory tracts.

It is possible to distinguish more than a few dozen species of mold, which are among the dangerous factors in building infrastructures. This is because of their low requirements for development conditions, resulting in their occurrence in many different places. The most commonly mentioned mold fungi include the genera Penicillium, Aspergillus (Aspergillus pasiticus, Aspergillus flavus, Aspergillus fumigatus, and Aspergillus niger), Strachybotrys (Stachybotrys chartarum and Stachybotrys chartarum) Cladosporium, Alternalia, and Fusarium [6,7,8].

Mold fungi are heterotrophic organisms with a eukaryotic structure. They feed on dead or living organic matter, and their enzymes enable the decomposition of complex organic compounds. Contamination of the indoor environment by fungi, and thus the increased occurrence of SBS, is mainly due to the presence of microbial volatile organic compounds (mVOCs) [9]. These substances are metabolites formed during the life processes of fungi and are volatile compounds due to their physicochemical properties [10,11]. These compounds cause the characteristic odor of mold and the sensory indications of the presence of filamentous fungi in buildings. The toxins considered most harmful to human and animal health are metabolites of fungi from the genera Stachybotrys chartarum, Fusarium, and Aspergillus versicolor [12]. The most dangerous mycotoxins produced by fungi include ochratoxin a (OT), zearalenone (ZEN), aflatoxins (AF), trichothecenes, and fumonisins (F) [13]. Other toxins produced by fungi include ketones, alcohols, esters, terpenes, and sulfur compounds, including the following [14]: ketones: 2-heptanone, 2-pentanone, and 3-octanone; alcohols: 2-methyl-1-butanol, 3-methyl-1-butanol, 2-methylpropanol, 3-octanol, 1-octen-3-ol, 1-hexanol, 1-pentanol, 2-methylisoborneol, and geosmin; terpenes and sesquiterpenes: limonene and pinene; furans: 3-methylfuran; sulfur: 296 compounds; and hydrocarbons: alkanes, olefins, dienes, and trienes. Currently, about 400 such compounds and about 350 species of fungi are known to produce them [12,15]. The intensity of mVOC production is influenced by environmental factors such as fungal species composition, substrate and nutrient availability, and thermo-humidity conditions (air temperature and relative humidity) [16,17].

It should be noted that the mVOCs produced by fungi can be transformed into other compounds, making their detection much more difficult. For example, alcohols are easily oxidized to aldehydes and then to carboxylic acids, whereas ketones can be transformed into aldehydes through chemical transformations [18], which can contribute to hindering the detection of the presence of mVOCs in the air and thus interfere with the effectiveness of assessing the degree of infestation of buildings by using chemical methods.

When assessing the degree of infestation of buildings, it is important to determine the concentration of fungal spores in infested buildings. This concentration is expressed in (CFU (colony-forming units)). Its permissible value in residential buildings is 50 CFU/m³ for mold fungi and 150 CFU/m³ for mixed fungi (mold and non-mold)—excluding pathogens. In contrast, according to the PN-EN 13098:2007 standard currently in force in Poland, the permissible number of indoor CFU should be less than 500 CFU/m³. Fungal colonies of the Cladosporium and Alternaria genera are allowed at 300 CFU/m³, while the presence of Aspergillus fumigatus and Stachybotrys chartarum is not allowed to any extent [19]. According to Piotrowska and Żakowska [20], the dominant genera in buildings are Aspergillus versicolor, Penicillium chrysogenum, and Cladosporium cladosporoides.

It should be noted that infested buildings can exceed as much as 1000 CFU/m³, and there have been values as high as 67,000 CFU/m³ in particularly infested areas [21], reaching up to 260,000 CFU/m³ in the carpets and bedding of infested rooms [22].

The presence of fungi can be determined using numerous techniques. As a method for the fast detection of fungal presence in buildings, it appears that e-nose devices have a significant application potential. The e-nose was successfully used to find fungi in archives and libraries [23]. E-nose devices may additionally be applied to assess the threat of mold in equipment and buildings. Literature data indicate that an array of 16 MOS (metal oxide semiconductor) sensors used indoors was sufficient to identify and classify five fungi species at a quality level of approximately 96%. Additionally, five mold-emitted microbial volatile compounds (MVOCs) were identified [24]. Two e-noses were used in other studies to detect the presence of fungi: Moses II and Kamina. The former produced more precise results. It was not possible to distinguish between species, despite the application of a sophisticated valuation model. According to M. Kuske’s research [25], using 12 MOS sensors, one of four mold species could be identified with an estimation accuracy of 80–85%, bred under laboratory conditions on the following materials: particleboard, plasterboard, oriented strand board (OSB), and wallpaper.

The functional elements of e-noses are the arrays that consist of many various sensors [26,27,28]. This hinders signal interpretation that is multidimensional and requires advanced techniques of analysis [29,30,31,32]. The MOS sensor array is made up of thin-film metal oxide semiconductor materials. In the case of the applied sensor array, this is tin dioxide (SnO₂) [26,29]. When the sensor is exposed to the sample, specific mVOCs and VOCs present in the air become adsorbed onto the surface of the sensing material [33]. Different gases will have different affinities to the sensor material, leading to varying degrees of adsorption [34]. The presence of adsorbed gases on the surface of the metal oxide semiconductor material causes a change in the electrical resistance of the material [35]. This change in resistance is directly related to the concentration of the detected gas, as well as type of sensor [36]. Individual sensors are not precisely selective, which is why they react with varying intensity to a range of different gas compounds. In the commercial market, there is a lack of MOS sensors dedicated to detecting all VOCs, especially mVOCs. However, air pollutants do not occur as single chemical compounds, and deteriorated air quality also means increased concentrations of compounds to which one of the many sensors reacts.

In order to visualize multivariate data, the following methods can be applied: principal component analysis (PCA), metric multidimensional scaling, and Kohonen self-organizing map, which are unsupervised machine-learning methods. Hierarchical cluster analysis, random forest, and MLP neural network were used to classify objects.

The principal component analysis method was first formalized in 1901 by Pearson [37], and then in 1933 by Hotteling [38]. The main purpose of PCA is to reduce the dimensionality of the data, that is, to extract the information contained in n variables and store it in the form of a new system of orthogonal variables—principal components [39]. The PCA algorithm seeks a linear combination of the variables contained in dataset X with the greatest variance. If the mean variables of X are stored in the vector $\mu$, while $\Sigma$ denotes its covariance matrix, then the following matrix is sought:

$$Y={\Gamma }^T\left(X-\mu \right),$$

(1)

where $\Gamma$ is an orthogonal matrix. In turn:

$$\Lambda ={\Gamma }^T\Sigma \Gamma ,$$

(2)

is a diagonal matrix with eigenvalues on the main diagonal that have a relationship with each other:

$${\lambda }_1\ge {\lambda }_2\ge \dots \ge {\lambda }_n\ge 0.$$

(3)

Thus, the i-th principal component is the i-th column of the matrix Y given by the equation

$$Y_i={\Gamma }_i^T\left(X-\mu \right),$$

(4)

where ${\Gamma }_i$ is the i-th column of the matrix $\Gamma$, which is also called the factor charge vector [40].

Dimensionality reduction, which is the main goal of PCA, is usually used to represent multidimensional data in a two- or three-dimensional space. It is a very common technique used in visualization, including environmental engineering works [41,42], but also for imaging electronic sense readings [28,31,43].

Multidimensional scaling was created by Torgerson and described in 1952 [44]; this method was designed to detect similarity between observations. In multidimensional scaling, a distinction is made between metric and non-metric methods. The non-metric method is used when the dataset under consideration contains variables measured in different units, which prevents the calculation of the Euclidean distance between them. Metric scaling, on the other hand, is employed when all measurements are made in the same unit. In the dataset considered in this work, all measurements were made in one unit, so it was acceptable to use metric scaling.

This method aims to preserve the distance between points in the reduced space. The algorithm is based on minimizing the difference between the points in the original space, and the reduced one. Thus, the stress function relying on these distances is minimized:

$$STRESS=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^{N-1}{{\displaystyle \sum }}_{j=i+1}^N{\left({\Vert x_i-x_j\Vert }_2-{\Vert y_i-y_j\Vert }_2\right)}^2}{{{\displaystyle \sum }}_{i=1}^{N-1}{{\displaystyle \sum }}_{j=i+1}^N{\Vert x_i-x_j\Vert }_2^2}},$$

(5)

where ${\Vert .\Vert }_2$ denotes the Euclidean norm, $x_i$ is the i-th observation in the original dataset, while $y_i$ is the i-th observation in the reduced space [45,46].

Although this algorithm is called a metric, its solution is not obtained in a linear fashion. The model’s answer is obtained iteratively—in a k-dimensional space, where $1\le k\le n-1$, and the points are moved to minimize the STRESS function [47].

Multidimensional metric scaling such as PCA can be used to visualize data in low-dimensional space. Among other things, it has been used in the past to study the distribution patterns of phyto- and bacterio-plankton in different seasons [48], as well as to identify the most important habitats of endangered and endemic fish inhabiting coral reefs [49].

Self-organizing maps were presented in 1982 by Kohonen in [50]. These are a type of neural network used to create a transformation that preserves the features of objects in a multidimensional space into a map. These maps are usually represented as a two-dimensional grid on which observations from the multidimensional space are marked. As this is intended to be a transformation that preserves the characteristics of objects, the data that are similar in the original space are represented close together in a self-organizing map [51]. The Kohonen map consists of $p\cdot q$ neurons, where the numbers p and q are the dimensions of this map. These numbers are established in advance at the beginning of the algorithm. Each neuron is an n-element vector (where n is the number of explanatory variables in the original set). Usually, neurons in Kohonen maps have a rectangular, hexagonal, or circular topology. Training a self-organizing map involves reducing the direct neighborhood of each neuron while reducing the weights assigned to individual neurons, which are randomly assigned at the start of the algorithm [52]. Kohonen networks have been used to visualize, cluster, and analyze multivariate environmental engineering data, among others, in [53,54,55].

There are many algorithms for hierarchical clustering, the main differences between them are the choice of the metric in which the distances between the observed objects are calculated and the choice of the method for determining clusters. The most commonly used metric is Euclidean, which was also used in this work; the distance between two vectors x, y of length n is determined using the formula:

$$d\left(x,y\right)=\sqrt{{\displaystyle \sum }_{i=1}^n{\left(x_i-y_i\right)}^2}.$$

(6)

There are many methods for determining clusters, for example, Ward’s method presented in [56], as well as clustering by single [57] and full linkage methods [58]. In this paper, the full linkage method, which is an agglomerative method, was used. It relies on the fact that at the beginning of the algorithm, each observation is in a separate cluster. The distances between clusters A and B are calculated as follows:

$$D\left(A,B\right)=\underset{x\in A, y\in B}{\max }d\left(x,y\right).$$

(7)

Thus, joining of two clusters depends on the farthest pair of observations. In this method of object clustering, as the cluster grows in size, it becomes increasingly difficult to attach more objects to the cluster, because the increase in cluster size automatically distances it from other observations and clusters considered in the analysis [59]. The hierarchical clustering method was used in [41] to classify the water quality in the Fuji River and in [60] to assess the sources of heavy metal contamination in water.

In an MLP (multilayer perceptron) neural network, the results are obtained not only through a set of n explanatory variables derived from the input data, but also through a set of auxiliary variables, which are latent units. Each of them is a linear combination of the original variables, usually transformed with a hidden g function, which is not linear in nature:

$$h_k\left(x\right)=g\left({\beta }_{0k}+{\displaystyle \sum }_{i=1}^n{x}_j{\beta }_{jk}\right).$$

(8)

The coefficient ${\beta }_{jk}$ denotes the effect of the j-th variable on the formation of the k-th hidden unit. Assuming that there are H hidden units in the network, the result of the neural network will be a linear combination of the following form:

$$f\left(x\right)={\gamma }_0+{\displaystyle \sum }_{i=1}^H{\gamma }_k{h}_k.$$

(9)

Optimization of the coefficients of such a network involves minimizing the sum of squares of the errors with an additional correction attaching a predetermined regularization parameter $\lambda$ to control the overfitting of the model to the training data. Thus, minimized, it is the sum of:

$${\displaystyle \sum }_{i=1}^N{\left(y_i-f\left(x_i\right)\right)}^2+\lambda \left({\displaystyle \sum }_{k=1}^H{\displaystyle \sum }_{j=1}^n{\beta }_{jk}^2+{\displaystyle \sum }_{k=0}^H{\gamma }_k^2\right),$$

(10)

where N is the number of observations in the learning set. The larger the regularization parameter, the lower the chance of model overfitting [61].

MLP neural networks are widely used in various scientific fields, including predicting ozone and nitrogen dioxide levels in the air [62], assessing the toxicity of ionic liquids in cell lines of rats suffering from leukemia [63], or predicting the diameter of TiO₂ nanotubes [64].

Although random forests can be created using a variety of algorithms presented in different papers [65,66,67], among others, the most widely used one at present is one developed in 1999. This algorithm for learning a random forest begins by selecting the number of m trees from which a forest will be created. For each of the m trees, to begin with, a bootstrap sample of data is drawn on which the tree will be trained. Next, $1\le k\le n-1$ is drawn, which is a fixed number of variables on which the splitting rules in the tree under consideration will be created [61]. According to Breiman [68], the number k for classification tasks should be equal to the rounded down root of the number of explanatory variables, while for regression it should be one-third of the number of such variables.

Random forests have been used in the past to estimate atmospheric aerosol concentrations [69], to spatially interpolate environmental variables using mud samples [70], to classify VOC vapors [71], or to detect mycophenolic acid in silage [72].

In the literature, one can find the works in which gas sensor arrays were used with the aforementioned methods, and there are also works in which gas sensor arrays were applied to the buildings affected by sick-building syndrome. However, there are a lack of works that present an effective step-by-step procedure for analyzing data from mold-infested buildings with the methods used within this paper.

2. Materials and Methods

2.1. Materials

To carry out the research, a mobile measurement device was developed. The main component of the measuring device was a sensor array consisting of eight MOS-type gas sensors, presented in Figure 1. Figaro 2600 series gas sensors were used together with TO-5 metal housing and a maximum power of less than 300 mW. The physical and chemical parameters of the gas sensors used in the study are summarized in

Table 1. Parameters of the gas sensors used in the 8 × MOS array.

No.	Sensor Type	Purpose	Measurement Range [ppm]
1	TGS2600-	Air pollution sensor	1 ÷ 30 (for H2)
2	TGS2602-	General air pollution sensor	1 ÷ 30 (for ethanol)
3	TGS2610-	Propane sensor	500 ÷ 10,000
4	TGS2610-	Propane and butane sensor with carbon filter	500 ÷ 10,000
5	TGS2611-	Methane and natural gas sensor	500 ÷ 10,000
6	TGS2611-	Methane sensor with carbon filter	500 ÷ 10,000
7	TGS2612-	Methane, propane and isobutane sensor	1 ÷ 25% (explosive)
8	TGS2620-	Ethyl alcohol and solvent vapor sensor	50 ÷ 5000

. The sensors planted in the bases were arranged in a circular array. Additional temperature and humidity measurements were carried out using Maxim-Dallas DS18B20 and Honeywell HIH-4000 sensors.

2.2. Measurement Protocol

Before each measurement session, the sensors were flushed with clean air for 10 min. The specified time for the initial cleaning of the sensor array using dry air before each measurement session was based on calibration studies of the device. A period of 10 min was sufficient to stabilize the resistances of individual sensors. However, the shorter flushing time (2 min) before each measurement was due to the relatively low level of VOC air contamination. The initial flushing was necessary because during the periods when the meter was not in use between measurement sessions, ambient air could enter the sensor chamber. After each measurement session, the process of flushing the sensor array was also performed with clean air flow of 200 cm³/min. The first resistance measurement of individual sensors in the array was performed for a blank sample without added chemicals (sample bag background). Resistance measurements were then carried out for the reference gases, starting with the sample with the lowest concentration.

Each reference gas measurement included a zero air flush phase for $t^0=2$ min and a measurement phase for $t^{samp}=5$ min. During the initial $t^{samp}$ phase of the sample measurement, there was a rapid decrease in the resistance of the sensor, proportional to the concentration of impurities in the test sample. At the end of the $t^{samp}$ period of exposure to a given sample, the sensor resistance values stabilized and the average resistance value of the $R_S^{samp}$ period could be determined. An example of a graph of resistance changes for the sensors is shown in Figure 2.

For each sensor, the relative resistance was determined according to the following formula:

$$R_w=R_S{}^{samp}/R_S{}^0,$$

(11)

where $R_S^{samp}$ is the stable value of sensor resistance for the sample under test and $R_S^0$ is the baseline (sensor resistance for zero air). The baseline $R_S^0$ was taken as the average value of the resistance of a given sensor from the final phase of flushing the sensors with zero air before the measurements.

The phenomenon of drift was investigated during the initial flushing of the sensor array. Measurements were performed over a short period of time, and during this period, no drift in the sensor responses caused by aging of the sensor’s detection elements was observed. The relatively low air pollution in the tested rooms also did not lead to excessive poisoning of the sensors.

2.3. Applied Software and Packages

The statistical analyses and graphs included in this paper were performed using the interpreted R programming language version 4.2.1 [73] with RStudio environment version 2022.7.0.548 [74]. The functions found in the aforementioned libraries of the software were used for the calculations presented below. The tidyverse package was created by Wickham and Team Rstudio in 2016 [75], whereas tidymodels was used to support machine learning models and employed the tidyverse philosophy [76]. The kohonen package allowed for learning and visualization of self-organizing Kohonen maps [77]. The ggfortify [78] and ggplot2 [79] libraries enabled creating consistent graphs. The factoextra package [80] allowed for applying the hierarchical clustering algorithm and creating a scatter plot for the PCA model.

2.4. Measured Objects

Research was conducted in nine selected rooms with different levels of mold threat. A short presentation of each object is shown in

Table 2. Features of the analyzed objects and reference samples.

Sample Name	Mold Bloom	Odor Nuisance	Object Features	Type of Object
B1	Visible	Plain	Roof construction failure	House, day room
B2	None	Perceptible	No thermal insulation	House, day room
B3	None	Plain	Incorrect thermal insulation	House, wainscot
B4	Significant	High	No thermal and water insulation	House, basement
B5	None (salt efflorescence)	None	Incorrect water isolation	House, basement
B6	None	None	Poor ventilation	Multifamily, bedroom
B7	Significant	High	Incorrect insulation	House, living room
B8	None	None	None	House, living room
B9	Fine Stains	None	Poor ventilation	Multifamily, wardrobe
Air	-	-	-	Clean air
DT	Totally stricken	High	Fully covered in mold	Decayed timber

. The flux of the sampled air was equal to 200 cm³/min and sampling was conducted close to the building barriers with visible mold bloom. Additionally, the decayed wood and clean air were selected as the reference samples.

3. Results

The data from the last 30 s of readings from the facilities were involved in model development. Principal component analysis was performed on the full dataset. According to the scatter plot shown in Figure 3, the appropriate number of principal components was equal to 2 or 3, but the percentage of explained variance by the first two components was almost 85%. For this reason, only the first two components were chosen to visualize the data.

This decision turned out to be the right one, as the groups delineated by observations derived from the samples pertaining to other objects formed distinct, homogeneous clusters that did not overlap with the observations derived from other samples in the main component space in Figure 4. The visibly separable groups were the clean air and decayed wood samples, which are located in the upper left and upper right corners of the graph, respectively. This agrees with intuition, as the air was completely uncontaminated by mold, while the tested wood was entirely covered with it. The remaining observations from the other samples were grouped mainly in the right half-plane. Furthest from the decayed wood sample were the data from samples B5 and B9, which, according to Table 2, were characterized by the absence of odor nuisance, but in sample B9, the experts noted a minor mold bloom. The remaining data were grouped into two clusters B1, B2, B3, and B4 in the first quadrant and B6, B7, and B8 in the fourth quadrant of the system. The indicated clusters did not represent groups with the same degree of mold infestation, but the closest relative to the reference wood sample was sample B4, in which significant mold bloom and high odor nuisance were also observed.

The result of the multidimensional scaling metric can be found in Figure 5; again, the greatest difference was between the measurements from the decayed wood sample and the clean air sample. The closest to air was the B5 sample, which was characterized only by salt efflorescence. In contrast, the closest to decayed wood were the measurements from sample B7, which was characterized by significant mold bloom and a high odor nuisance, similar to the previously mentioned sample B4. The remaining results were arranged in a similar manner, as shown in Figure 4.

The Kohonen map was made in a hexagonal topology, on a 20 × 20 grid of neurons. The observations from the analyzed dataset were mapped onto the grid and labeled according to the sample to which they belonged, as can be observed in Figure 6. The map shows that all groups of observations separated from each other and formed disjoint groups. The observations from the clean air sample were not located in close proximity to those from the decayed wood sample. However, other groups of observations were not particularly well placed on the map, as, for example, the B9 measurements were next to those from the clean air reference sample.

The hierarchical clustering method grouped the observations from the original dataset into six homogeneous clusters. There were six clusters due to the fact that the analyzed objects were rated by experts according to the degree of mold bloom. This enabled verifying the correctness of the clusters created by the algorithm. The dendrogram in Figure 7a shows the differences between the groups of observations allowing for the creation of clusters. Meanwhile, Figure 7b shows where the observations belonging to each of the created clusters are located on the PCA plane. The observations from each sample are all assigned to one of the clusters, so they are homogeneous. According to

Table 3. Classification of objects into individual clusters formed by hierarchical clustering.

	Predicted	Cluster 1	Cluster 2	Cluster 3	Cluster 4	Cluster 5	Cluster 6
Observed
Air		0	0	0	0	0	174
None		162	176	178	352	0	0
Fine Stains		0	0	0	177	0	0
Visible		35	0	0	0	0	0
Significant		0	176	0	0	176	0
Totally stricken		0	0	0	0	66	0

, cluster 6 containing the observations from the clean air sample and cluster 3 with the B5 sample did not contain elements from the other observed groups. Cluster 5 contained the observations from the wood sample and object B7, which was significantly infested by mold. In cluster 4, there were observations from samples B6, B8, and B9, some of which were non-molded objects and some had light mold bloom. It can be seen that the worst classified group comprised the non-molded objects, which were classified into four different clusters. The overall correctness of the classification by hierarchical clustering could be assumed as 48.2%.

Thus, the dataset consisted of 1672 observations, which were randomly divided in a 2:1 ratio, where $\frac{2}{3}$ of the data were used in teaching supervised learning models, and the remainder became the training set for the models. The hyperparameters of the neural network were tuned using a five-fold cross-validation. The grid was three-level for each hyperparameter, and the tuned values, when possible, were equidistant from each other. The parameters tuned were the number of hidden units at levels $1, 5, \mathrm{and} 10$; the number of epochs at levels $50, 125, \mathrm{and} 200$; and the value of the regularization parameter at levels ${10}^{-10}, {10}^{-5}, \mathrm{and} 1$. The result of model tuning can be seen in Figure 8. The model with the number of hidden units equal to 5, 125 training iterations, and a regularization parameter equal to 1 turned out to be the most optimal. On the training set, it achieved 100% correctness in classifying samples into the classes determined by the degree of mold bloom. The neural network achieved the same correctness for a model with 10 hidden units and two models with 200 iterations of training, but a model that was less computationally complex was chosen. The selected model on the test set also achieved perfect classification in all of the samples considered, as it can be observed in Figure 9, which shows the diagonal classification error matrix.

The random forest model was supposed to be tuned based on a grid of hyperparameters, but it turned out that regardless of their selection, all of the models had 100% classification accuracy. Therefore, a model with default parameter values was used, i.e., 500 trees built in the forest, 3 variables possible to divide at each node, and a minimum of 1 observation at each tree node. Such a model also achieved the maximum possible classification quality on both the training set and the test set, as shown in Figure 10, which presents the error matrix on the test set. Figure 11 demonstrates the ROC curves for each of the fungus infestation classes in the dataset. They had an ideal shape due to the 100% correctness of the classification.

4. Discussion

The principal component analysis method is used to analyze the sick-building syndrome in order to visualize the position of the test samples in low-dimensional space. An example of such an application of the PCA method is the work of [81]. The data analyzed therein came from samples of building materials and rooms tested for fungal contamination using an electronic nose. The data were visualized on a PCA plane; in the case of this work, the first two principal components explained 96.5% of the variance of the original variables. In the plot, only the reference samples were distinguished by their distribution; the other samples did not group into distinct clusters. The article [23] analyzed the samples of three types of paper, on which three different types of fungi were observed. The paper samples were examined using an electronic nose. The two-dimensional graph created by the PCA method for all data apparently discriminated the samples into three clusters, corresponding to the three paper types considered. The paper also produced additional graphs using this method, which highlighted the samples relating to only one of the paper types at 75% or 100% relative humidity. An additional method used in the paper was cluster analysis, which was also applied to the sets containing only one type of paper at 75% or 100% humidity. In the PCA charts, superior results were obtained at 100% RH, while the cluster analysis in each case distinguished between the paper samples from the control sample and those in which any type of fungus was observed.

In the present study, similar results to the articles considered above were observed, as the percentage of explained variance by the first two principal components allowed for visualization of the results in two-dimensional space. In addition, in this case, the samples constituting the control observations in the PCA plot were distinguished from the others by being distinct clusters.

The multidimensional scaling method is used to visualize the dissimilarity between the studied objects. In the paper [82], it was employed to show the differences between bacterial communities in three different moving bed bioreactors. The method showed that the samples from each reactor were clustered together and separated from the others on a plane. Therefore, it could be concluded that the three reactors contained different bacterial communities.

In this study, the result of metric multidimensional scaling was similar to that obtained using the principal component analysis method, i.e., the reference samples differed from the other types of samples.

The paper [83] used the Kohonen self-organizing map to represent the classification of facilities into groups characterized by six levels of mold infestation risk to analyze the sick building syndrome. In addition, in the paper [84], the authors used self-organizing maps to build an odor control map using the data taken with an electronic nose, from environmental odor monitoring systems. A classification into three groups created using the k-means method was overlaid on the map. Further in the article, a supervised Kohonen network was also used to predict the quantitative concentration of odor.

Only observations mapped to a self-organizing map are presented in this paper. The development of the aspect related to the location of clusters on the map and the application of the supervised Kohonen network will be a further subject of research.

Hierarchical cluster analysis was used in [81], where the data on mold contamination of building materials and buildings were classified into four groups. This work also investigated and classified the facilities affected by sick building syndrome. The observations from clean air samples were classified into a separate cluster. In addition, in the work in question, a separate group was formed by the observations from a decayed wood sample, while the remaining observations were assigned to the clusters that were not consistent with the degree of contamination of the samples belonging to them. The article [85] also used this method to group indoor air pollutants into three classes, corresponding to high, moderately high, and moderate frequency of reporting by workers in non-industrial work environments.

The results on the hierarchical cluster analysis presented in this paper resemble those presented in the article [81], in that apart from the cluster into which the observations from the clean air sample were classified, other groups contained observations from the samples with varying degrees of mold infestation.

The random forest model has been used in the past to classify the readings obtained from an electronic nose. In the paper [30], the random forest model was used in the classification of samples for different stages of wastewater treatment. In this work, the model achieved 97.5% correctness on the training set and 100% on the test set. In [86], the task was to detect different gases and the changes in their concentrations. The model in the aforementioned work obtained 99.75% correct classifications, but this was not the best possible quality for the classification obtained. For the data considered by the authors, the best classifier turned out to be the one obtained by the k-nearest neighbors method (which obtained a perfect classification).

The presented paper and the above-mentioned works allowed for concluding that random forests usually perform well in classifying objects from multidimensional gas sensor arrays. They are cited as one of the better or best applied classifiers.

On the other hand, the MLP neural network shows varying results in object classification. In the aforementioned work [86], it produced a result of only 9.6% correct classifications. Interestingly, this work also used an SLP (single-layer perceptron) network, which achieved 62.78% accurate classifications. However, these results were significantly worse than those obtained by the random forest.

In turn, in [87], an MLP neural network was used to predict the thermal performance in buildings. The dataset on which the authors worked was divided into training, testing, and validation. In this work, a neural network with 50 neurons was used. The mean squared error on the training and test set was 0, while on the validation set it was 0.0004.

The results obtained in the articles discussed were similar to those obtained in the present work, especially in [87], because it was an object classification task. However, the neural network trained in this work had only five hidden units, so it was much less complex than the one discussed in [87]. It also obtained 100% classification accuracy, so it was much better than both networks trained in the work [86].

5. Summary and Conclusions

In line with the analyses carried out using machine learning models, the following can be concluded:

• The collected data allow for the classification of the considered samples into groups determined by the degree of mold infestation;
• Although the data visualization shown by the SOM and PCA models and metric multidimensional scaling did not do a perfect job of showing the differences between the samples under consideration, the graphs determined by PCA and metric scaling showed these differences better, where first two PCA components explained almost 85% of the data variance;
• Classification by an unsupervised algorithm, such as the hierarchical clustering algorithm, yielded a low accuracy of 48.2% when classifying objects;
• Supervised learning methods performed much better on a given task, as both algorithms used classified objects into mold infestation groups 100% correctly, and this classification was correct for both the training set and the test set;
• The random forest turned out to be the better of the two models in terms of the fact that no tuning of the model’s hyperparameters was needed, and even the model used with their default values classified all of the objects correctly.

This paper presents the results of classification on one dataset, while the results of the experiments on completely new datasets, to which the learned models will be applied, are already in development. Given that the measurements themselves are calibrated, it is expected that the classification results on the new datasets will confirm the generalization abilities of the obtained models.