## 4 Results
### Comparative Analysis of Dimensionality Reduction Results  
After performing feature selection, the size of the data dimensions obtained, as mentioned earlier, was 384. With such large data dimensions, data clustering required much  
Figure 3: Different selected programming language demand changes over time. larger resources. Several methods, such as CBMIDE, are not adapted to such dimensions. The following work uses data dimensionality reduction methods based on these insights. Different data dimensionality reduction methods have different properties and perform differently depending on the dataset. In order to properly evaluate data dimensionality reduction, metrics were needed to enable this. Estimating the dimensions of the data allow for determining which new dataset was the best, and how many new dimensions were needed to retain the maximum amount of information possible. One of the possible evaluation metrics is the trustworthiness metric [73]. This metric assesses how well the information and relationships between observations in the original and reduced dimensions are preserved. The computation of this metric was accomplished by utilizing the following formula:  
\[T(k)=1-\frac{2}{nk(2n-3k-1)}\sum_{i=1}^{n}\sum_{j\in N_{i}^{k}}\max(0,(r(i,j)- k)) \tag{3}\]  
where for each observation \(i\), \(N_{i}^{k}\) are its \(k\) nearest neighbors (the output space obtained after applying the methods), and for each observation \(j\), \(r(i,j)\) was its original data space. In the event of a random observation appearing in the output space, it incurred a penalty. At the same time, the study employed a set of five neighbors. During data dimensionality reduction in this work, different data dimensionality reduction methods were used, and their hyperparameters were changed. For all data dimensionality reduction methods, the number of new dimensions varied from two to fifty. In the case of PCA, only the number of dimensions was varied. In the case of UMAP, the parameters and their values were changed: \(n\) neighbors hyperparameter set {5, 10, 20, 30, 50, 100}, minimum distance set {0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 0.75, 1}, and distance metrics (euclidean, cosine, and manhattan). ISOMAP parameters and their values: n neighbors hyperparameter set {5, 10, 20, 30, 50, 100}, and the distance metric hyperparameter set {manhattan, cosine, manhattan, and minkowski}. T-SNE parameters and their values: learning rate {10, 50, 100, 500, and 1000}, and perplexi-ty {5, 10, 20, 30, 40, 50}. Trimap parameters and their values: number of inliers hyperparameter set {5, 10, 12, 20, 30, 50}, and the number of outliers hyperparameter set {2, 3, 4, 5, 10}. Below is a table of the best model results (see Table 1). More than 11,000 models were created to evaluate the best dimensionality reduction method for the current task. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Components** & **PCA** & **UMAP** & **Trimap** & **t-SNE** & **ISOMAP** \\ \hline
2 & 0.756 & 0.933 & 0.831 & 0.871 & 0.748 \\
3 & 0.805 & 0.950 & 0.882 & 0.881 & 0.821 \\
4 & 0.844 & 0.955 & 0.908 & 0.883 & 0.859 \\
5 & 0.876 & 0.961 & 0.931 & 0. Based on the results of data reduction, it can be observed that all the methods performed quite similarly for a larger number of components. All studied methods became fairly stable from 15 dimensions. A higher number of dimensions was found to not improve the results of the models. Given that the results are important to consider the training time of the models, it was noticeable that the t-SNE models were trained longer compared to others as the Barnes-Hut algorithm was not used. The ISOMAP method also had quite a higher computational time compared with the other methods. It is important to note that the PCA method has a high trustworthiness value. However, after further analysis, it was noticed that the work profiles created using the PCA method were more complicated to interpret, and therefore this method was abandoned in further work.