## 1 Introduction  
The perfume imitation problem has become increasingly serious [1]. Counterfeit perfumes are typically made by blending ethyl alcohol, water, and cheap chemical synthetics, which can cause dizzy feelings, headaches, and skin allergies for perfume consumers. Owing to their low manufacturing cost, counterfeit perfumes are capable of undercutting certified perfumes with relatively very low prices. It is important for promoting the perfume industry to expose counterfeit perfumes. However, for common perfume consumers, it is hard to determine which perfumes are certified, since counterfeit and certified perfumes are generally enclosed in substantially identical external packings. Existing sensing instruments that can be used for PI include gas chromatography (GC) [2], mass spectrometry (MS) [3], and EN. With respect to the identification of perfume types, EN has the merits of low-cost, high time-efficiency, and portability [4]. To achieve the objective of EN-based PI, different perfume samples are dripped into the volatilization unit of an EN. Typically, the responses of gas sensors in the EN to the individual chemical constitution of a perfume are different. The response data from multiple chemical sensors contain specific 'fingerprint' information about the perfume simulant. By considering samples of perfumes in market and genuine perfumes as test and training sets, respectively, the EN-based PI problem turns into a multi-class classification problem, since the number of candidate perfume types is often larger than three. As the multiple decision boundaries interact with each other, multi-class classification problems become more challenging than binary classification [5]. Many EN-based PI results have been presented in the past twenty years. [PERSON] et al. [6] performed PI with an array of quartz-resonator sensors using neural network (NN) pattern recognition, which can achieve relatively high separation accuracies among ethanol-diluted perfume samples. [PERSON] et al. [7] proposed combining principal component analysis (PCA) and a radial basis function NN for perfume discrimination; PCA was used to extract the relevant information of perfume samples into two principal components, which were then used as the input to a radial basis function NN. [PERSON] et al. [8] achieved fragrance mixture recognition using back propagation NN and fuzzy-neuro learning vector quantization with four quartz resonator-sensitive membrane sensors. [PERSON] et al. [9] implemented the support vector machine (SVM) method for the identification of four perfume samples with an EN system containing three common gas sensors. [PERSON] et al. [10] used a \(k\)-NN kfold method with EN to identify pure and mixed agarwood oils, which can also be considered to be a specific type of perfume. However, in each of these studies, only an individual classifier was constructed to classify the features extracted from the sampling data. In the last decade, the field of machine learning (ML) has progressed significantly with many excellent new classification ML methods proposed [11; 12]. As a flourishing branch of ML, ensemble learning methods combine the results of multiple base learners. Tree ensemble learning methods, which employ the decision tree learner [13] as the base learner, can usually achieve better performance than traditional methods [14]. The motivation for this paper was to implement tree ensemble learning methods for solving the EN-based PI problem and to compare their performance. In this paper, we present EN-based PI experimental results obtained using four tree ensemble learning methods: XGBoost [14], RF [15], SAMME [16], and GBDT [17]. To obtain the experimental results, an EN system designed in the authors' laboratory was used to collect sensing data for four perfumes. The collected raw measurements were preprocessed via wavelet denoising [18] and baseline subtraction. Then, based on the preprocessed data, six empirically selected equations were used for feature extraction.