## 4 Discussion  
In the present work, we investigated for the first time the presence of globally up- and down-regulated genes in UBC. Microarray experiments consist of a series of experimental and analysis steps, among which, the clustering of the data at hand is of major importance. Clustering is one of the most important functions in data analysis [32]. Some of the main tasks that clustering algorithms are called upon to solve, is gaining insight into data, classifying, and compressing them [33]. Clustering approaches aim to extract sets of genes with similar expression profiles across all samples, or in a subset of them [34]. This is mainly accomplished by using 2D matrices of the form _Genes_\(\times\)_Samples_, on which appropriate clustering algorithms are applied. The k-means or bi-clustering techniques are good examples of such algorithms [35; 36; 37; 38; 39; 40; 41]. There are also numerous proposals in the literature regarding the analysis of time-series microarray data. In such cases, a series of cDNA microarray experiments are performed in different time points, and then clustering techniques on a 3D matrix of the form _Time_\(\times\)_Genes_\(\times\)_Samples_ are applied [34; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51]. In the present study, our main approach was to use different clustering methods. We focused, however, on the k-means algorithm, since it is very efficient for grouping expression patterns. It is also relatively easy to implement, it can be used for large datasets, and has the significant advantage of calculating data trends by estimating the centroids [52; 53; 54; 55]. For small cluster numbers (\(k\) values), it converges very quickly to the local optimal, allowing a sufficient number of initializations to be used [56; 57; 58; 59; 60]. An important methodological parameter is the number of clusters. It is considered a difficult task since it influences the final outcome, i.e., which genes will be clustered together. A frequent approach is to test several appropriate values of \(k\), in order to find patterns in expression data. In the present work, the Davies-Bouldin criterion helped in this direction, which successfully gave the optimal \(k\) clusters [61]. Unlike k-means, hierarchical clustering algorithms do not offer user-defined configuration options. The only option that can be made is to calculate the distance between clusters. In this case, we chose to use the UPGMA method, which defines the distance between two blocks as the average distance between all elements. Therefore, we used UPGMA in combination with k-means clustering. It has been previously shown that HCL groupings based on k-means clusters, perform well [18]. A major disadvantage of the HCL algorithm is that it requires large amounts of memory in order to store the \"Dissimilarity Matrix\", making it difficult to implement when the number of data is large. This mode of analysis led us to the identification of 36 globally down-regulated and 30 globally up-regulated DEGs. The co-up-regulated genes could pose a more interesting therapeutic target since gene inhibition is probably easier, compared to the induction of gene expression. The genes YES1 and PMM1 were the ones with the highest percentage of up-regulation among all tumor samples. To our knowledge, there is no known relation between YES1 or PMM1 and UBC. In addition, no known relations were found for the role of _IRF3_, _ARL6 IP1_, _CYTH2_, _PSMD2_, _PSMD7_, _NDUFV2_, _RALY_, _ADRM1_, _RPN1_, _TYK2_, _UNG_, _EBNA1 BP2_, _SNRPB_, and _VDAC1_ in UBC; therefore, these genes could be the topic of future studies. Among the co-upregulated genes, we found CDC20, which was also previously reported to be deregulated in urinary bladder cancer [20]. The rest genes were not previously identified as co-DEGs in UBC. CDC20 encodes the cell-division cycle protein 20, a regulatory protein that interacts with several other proteins at multiple points in the cell cycle [62].