## 4 Materials and Methods
### Radiomics-Based Semi-Supervised Slice Selection  
CT scan volumes can be of large number of slices, which leads to high computation time and complexity. Aside from the high computation complexity, another critical issue is the information content of the slices. CT volumes comprise slices of the whole thoracic cavity area. It includes discriminative and non-discriminative lung slices. Figure 4 shows sample slices, exemplar slices in Figure 4 is of low value to the current study as it will not give any additional information to the learning model. In fact, these slices may add noise degrading the performance of the classification model. On the contrary, the exemplar slices in Figure 4 are the ones that need to be selected as they show lung tissue clearly. Another issue is that the exact location (index) of informative slices varies individually per patient, which means that manual selection would be time consuming. Also, static predefined range for the targeted slices will hinder the learning process as the range of informative slices varies considerably. Hence, the slice selection is required to input informative slices to the classifications' models. The slices are not labelled as discriminative and non-discriminative lung slices; hence, unsupervised clustering is used to group the slices based on a set of extracted features. Unsupervised learning provides an adequate solution to the issue of unlabeled slices, as it divides the slices into their natural groupings based on the extracted features. For the purpose of feature extraction, Haralick texture features [28] and Histogram-based features [29] are extracted from each slice and its binary mask. The features capture the structural and spatial characteristics of the slices. The extracted features help differentiate between discriminative and non-discriminativelung slices. Haralick features are extracted from the normalized Gray-Level Co-occurrence Matrix (GLCM). Each GLCM element \(p(i,i)\) represents the co-occurrence of a pair of grey levels \((i,j,d,\theta)\) in neighboring pixels, where \(i\) denotes the grey level in the reference pixel, \(j\) denotes the grey level in the neighbor pixel, \(d\) is the interpixel distance set to one and \(\theta\) is the angle of offset between neighbouring pixels set to zero. The number of (quantized) grey levels is denoted as \(G\). Five features are extracted from the produced GLCM, namely Angular Second Moment  
Figure 4: Various exemplars of slices (views) from different positions of different CT volumes. (\(ASM\)), contrast (C), Sum Entropy (\(SE\)), Homogeneity (\(H\)) and Energy (\(E\)). The equations given below present the calculation of the Haralick features. \[ASM=\sum_{i=1}^{G}\sum_{j=1}^{G}p(i,j)^{2} \tag{3}\] \[C=\sum_{i=1}^{G}\sum_{j=1}^{G}(i-j)^{2}p(i,j)^{2}\] (4) \[SE=-\sum_{i=1}^{G}\sum_{j=1}^{G}p(i,j)\log_{2}p(i,j)\] (5) \[H=\sum_{i=1}^{G}\sum_{j=1}^{G}\frac{p(i,j)}{1+(i-j)^{2}}\] (6) \[E=\sqrt{ASM} \tag{7}\]  
For Histogram-based features, three descriptive statistical measures are computed for each histogram. Histogram Entropy (\(Ent_{H}\)) measuring the uncertainty and disagreement of the distribution is calculated according to the equation shown below. Kurtosis (\(K_{H}\)) and Skewness (\(Sk_{H}\)) measures are calculated. Kurtosis (\(K_{H}\)) detect whether the data are heavy-tailed or light-tailed relative to a normal distribution. Skewness (\(Sk_{H}\)) checks the lack of symmetry. The measures are evaluated given the following equations, where \(N\) is the number if bins, \(w\) is the bin width, \(pr\) is the bin probability and \(Ct\) is the bin count. \[En_{H}= -\sum_{i=1}^{N}pr_{i}\log(pr_{i}/w_{i}) \tag{8}\] \[K_{H}= \sum_{i=1}^{N}\frac{(Ct_{i}-Ct_{i})^{4}/N}{\sigma^{4}}\] (9) \[Sk_{H}= \sum_{i=1}^{N}\frac{(Ct_{i}-Ct_{i})^{3}/N}{\sigma^{3}} \tag{10}\]  
After feature extraction, a range of clustering algorithms, such as modified k-means variant [30], agglomerative [31], Spectral [32], and BIRCH [33] are applied to create different data partitions (clusters).