# miRNA-Gene Association Prediction Method Based on Deep Learning Model
## 2 Materials and Methods
### Negative Dataset  
As mainstream biological research has moved from wet labs to groundbreaking bioinformatic-based models, one of the major challenges has been negative data. Most association-prediction studies that employ deep learning are binary classification problems. Although there is considerable experimentally validated and open positive data, there are very limited validated negative data (no interaction) [33]. However, to optimize the performance of a binary classification deep learning model, having a balanced dataset is often highly beneficial. Most related studies use random pairs that do not exist in positive pairs and consider them as negative data. However, we introduced a distance-based filtering method to generate a sophisticated negative dataset. In a recent study [4], negative data were generated using the Euclidean distance and cosine similarity as the distance criteria. Our study introduces the Mahalanobis distance [34] as an additional criterion building upon this concept. The data in this study comprised miRNA-gene pairs, all of which existed in a vector space through embedding. The miRNAs and genes that spread in the vector space are separated by a distance, which is an important metric. In natural language processing, the distance in this vector space is considered a measure of similarity. The following three distances were used to construct sophisticated negative data: (1) The Euclidean distance, which represents the straight-line distance between two points and is the shortest distance between two points. It is frequently used to compare the similarity between two data points, with a lower distance indicating a higher similarity. (2) The cosine similarity that measures the cosine angle between two vectors. It is frequently used in text analytics to measure document similarities. (3) The Mahalanobis distance measures the distance between two points, considering the covariance structure of the data. Euclidean distance treats all dimensions equally, while Mahalanobis distance takes into account the variance and correlation of the data to calculate the distance. This is useful for detecting outliers or clustering in multivariate data. We utilized these three distance criteria to calculate the distances between miRNA and gene pairs in the positive set. The average of these calculated distances was then used as a threshold for constructing the negative dataset:  
\[(A,B)=\sqrt{(A_{1}-B_{1})^{2}+(A_{2}-B_{2})^{2}+\cdots+(A_{n}-B_{n})^{2}}= \sqrt{(A_{i}-B_{i})^{2}}, \tag{1}\]  
\[\cos(A,B)=\frac{A\cdot B}{||A||\ ||B||}=\frac{\sum_{i=0}^{n}A_{i}B_{i}}{\sqrt{ \sum_{i=0}^{n}A_{i}^{2}\cdot\sum_{i=0}^{n}B_{i}^{2}}}, \tag{2}\]  
\[D^{2}(A,B)=(A-B)^{T}(A-B)^{\sum^{-1}}. \tag{3}\]  
Based on these three distance criteria, the negative dataset was constructed as follows: First, 2656 miRNAs and 14,319 genes in the positive dataset were matched for all the cases. A total of 38,031,264 datasets (2656 \(\times\) 14,319) were generated, and 358,864 positive datasets were removed. Then, we removed pairs that were closer than the three average distances calculated earlier (smaller values for the Euclidean distance and Mahalanobis distance and higher values for the cosine similarity) because we assumed that they did not show the characteristics of negative data (Figure 2). After filtering, we obtained a set of 4,932,554 negative candidates. We have illustrated the counts of instances filtered as negative candidates through each of the three distance criteria using a Venn diagram (Figure 3). From this set of negative candidates, we randomly selected 358,864 values as negative data to balance the quantity of positive data (Figure 4 and Table 3). These negative data exhibited negative features that are more distant than the average distance of the positive dataset on the three distance measures of similarity. Figure 3: To construct a sophisticated negative set, we utilized three distinct distance measures for filtering within the Unknown Data Pool.