## 2 Materials and Methods
### Algorithm Overview  
Clustering Creation and Customization:1. Initial clusters were generated for genetic groupings using a few test methods: A. Binary Matrix Factorization: Binary matrix factorization was used to generate initial clusters, which generated a large m \(\times\) n matrix of multiple genes as columns per subject where genetic activation was displayed as 0/1 for 'not activated' or 'activated'. B. Random Assignment: Initial clusters were also randomly initialized such that initial clusters of genetic groups would have equal distributions of patients in each. C. K-Means: Initial clusters were also grouped using a k-means clustering process across the 100 columns to generate a set of 5 initial clusters. Genetic data for the patients in the 0/1 matrix were grouped into these genetic groups using the aforementioned methods. This study used 5 initial groupings to simply the analysis. However, number of genes and total clusters were easily scalable based on user preference. 2. Next, a deep learning image classification algorithm was run on the medical imaging data for each subject with the outcome pointed at the generated genetic clusters. Standard Accuracy, AUC, and loss were generated to identify accuracy of model. Loss metric utilized a proposed deep clustering metric (Ratio of Training Loss/Testing Loss). This proposed algorithm used single-slice CT data for each patient, where each CT slice was confirmed to have lung tumor present. Overview: This study used a standard Convolutional Neural Network process to build the deep learning algorithm to classify inputs:  
1. Kernel Normalization: Standard CNN kernel with gradient calculation and sliding technique was used to identify initial features. DICOM data are unique in that the values of the Hounsfield units from CT scans or MRI intensity values often vary from pixel to pixel. Standard feature selection and edge detection techniques often evaluate the gradient between pixels. To ensure that small fluctuations in DICOM pixel data do not generate false-positive features based on perceived large changes in the gradient between neighboring pixels, the pixels will first be averaged for each receptive field according to the kernel. Gaussian blur is avoided to not lose info and edge detection is avoided on the raw data to not generate false edges or messy images. 2. Pooling and Final Fully Connected Layers: Each of these shapes was then fed into a pooling layer. A standard nonlinear function (ReLU) was applied. 3. Activation Function: These feature maps were passed through a final layer to determine class scores. A final activation function such as a Softmax function would be used to normalize the input into a probability distribution based on [PERSON]'s choice axiom
4. Output: Thus, the final output of a model, similar to other model outputs, was a ranked probability score and corresponding classification that identified whether a series of shapes identified from a DICOM image corresponded to one class or another based on the presence or absence of similar shapes in other images of that class. For this experiment, custom classification method in addition to standard preset model layer groupings available within the Tensorflow applications package were experimented upon to determine optimal accuracy for model. Residual Neural Network (ResNet) framework was selected as the ultimate model of choice for the classification layer due to its ready availability, popularity in literature, ability to perform well on small datasets, and speed. Models were trained \"from-scratch\" wherein every layer was retrained, using a \"transfer learning process\", where weights from a separate dataset were used to initialize the model and only the final layer was retrained on the lung image data, and a hybrid process, where a transfer learning process was used to train the first layers and 5 additional dense and drop out layers were added at the end to also leverage the \"from-scratch\" aspect of customization on the data.