## 2 **Introduction**  
Lung cancer is the worldwide leading cause of death among all cancers, and one of the top four causes of overall mortality in people under 70 years of age in nearly every nation in the world outside of sub-Saharan Africa [1]. Lung cancer is the most common neoplasm in men (14.3%) and the third most common in women (8.4%), where its incidence is exceeded by breast (24.5%) and colorectal (9.4%) cancers. When treatment is available, mortality strongly depends upon the stage at which the cancer is detected. Early detection of lung cancer improves clinical outcomes, raising the five-year survival rate from 17.7% to 55.2% [2]. Unfortunately, the majority of patients present with lung cancer having already reached third or fourth stages, in which treatment options are limited, and the mortality rate is high [3]. A chest X-ray is most commonly used for lung cancer screening; thus, the first indication that cancer may be present is an abnormal finding on an X-ray. These findings are non-specific and must be followed up by other techniques. More sophisticated imaging modalities, such as computed tomography (CT), magnetic resonance imaging (MRI) and positron emission tomography (PET), are far more sensitive than the chest X-ray, and their usefulness has been enhanced by a number of computer-assisted detection (CAD) algorithms that automatically identify malignant lung nodules [4; 5; 6; 7; 8; 9; 10; 11]. CT is the most informative modality for detecting lung cancer, and, if used for screening, it can decrease mortality by 20% [12]. The greatest drawback of its use as a screening tool is that it is quite expensive. Furthermore, detection of malignancy using a single CT scan has a high false-positivity rate. More accurate detection uses a track-and-trace approach that considers a nodule's growth rate, which requires multiple CT scans over a period of time and thus incurs an even greater cost. These considerations have motivated research into relatively inexpensive, non-invasive approaches to lung cancer screening. These look for the biomarkers of cancer in a patient's blood (e.g., [13]), urine (e.g., [14; 15; 16]), saliva (e.g., [17; 18]) or exhaled breath. Volatile organic compounds (VOCs) are a class of biomarker associated with cancer. The fluctuating redox environment within cancer cells is thought to cause oxidative stress, which increases the synthesis of numerous VOCs [19; 20]. These are released into the extracellular environment and pass into the bloodstream. Exhaled breath analysis is a method for identifying VOCs at very low concentrations. Breath analysis studies have supported the hypothesis that the VOCs profile is altered in the presence of lung cancer [21; 22; 23; 24; 25]. The quantitative measurement of carbonyl VOCs in exhaled breath has recently been pursued as a method for early lung cancer detection [26; 27; 28; 29; 30]. Studies of note include that of [PERSON] et al. [31], who used thermal desorption comprehensive two-dimensional gas chromatography time of flight mass spectrometry (TD-GC \(\times\) GC-TOFMS) to analyze VOCs. Out of six VOCs' chemical families (aldehydes, alcohols, hydrocarbons, nitrogen-containing compounds, ketones and fatty acid methyl esters [FAME]), a principal component analysis and random forest (RF) identified ketones and FAME as the most indicative of cancer. The study data was quite small, however, with only 15 lung cancer patients and 14 healthy participants. [PERSON] et al. [32] used a set of 19 VOCs to diagnose lung cancer. Data from 51 lung cancer patients and 38 cancer-free patients with abnormal CTs were used to train a random forest classifier that achieved 84% accuracy and an area under the curve (AUC) of 0.94. [PERSON] et al. [28] looked at six carbonyl VOCs gathered from 34 individuals with benign pulmonary nodules, 85 lung cancer patients and 85 healthy participants. They tested several classification algorithms and employed dimensionality reduction via recursive feature elimination (RFE).