Our investigation begins with the import of a microarray data set into our procedure. This microarray data set is typically a 2D array, with rows representing different genes and columns representing their intensity at various time stamps. To minimize the dimensionality of the data set, we will use Principal Component Analysis. It is a sophisticated approach used by academics to remove irrelevant data from a data set while keeping its integrity.

Then, in our data set, we run a distance metric. A distance measure, in general, calculates the similarity of 2 genes and determines how far apart they are. We employed the following 3 different distance metrics: Euclidean, Manhattan, and maximum. We chose a linkage method to connect related genes and generate a hierarchical tree after picking the distance metric. We used the following 4 linkage methods: single, complete, average, and ward linkage methods. We constructed a hierarchical tree using the distance-linkage method, where each leaf represents a gene, and the branches reflect the dissimilarity among them. The tree was then cut to various heights, resulting in several sets of genes for each cut point. Subsequently, we identified the appropriate cut point for that hierarchical tree by calculating how well those genes are clustered on different cut points. We used “Average Silhouette Width” and “Distance within Cluster” to calculate the fitness of the groups formed by different cut locations. The optimal fitness value is calculated using these fitness values. We determined the best combination of distance and linkage methods for a single data set by repeating this process with different combinations of distance and linkage methods. Figure 1 depicts the algorithm.

For a particular data set, D, optimal fitness value can be expressed by the following equations:

Where d distance methods and, I linkage methods.

We will try ensemble clustering [26] to see if it works better once we have tried different clustering combinations. Three ensemble clustering techniques were employed, which are as follows: (1) similarity partitioning based on clusters; (2) hypergraph partitioning algorithm [27-29]; (3) meta-clustering algorithm.

We identified the genes responsible for various cancer tumors from the data sets and then evaluated their expression in different patients with cancer to report their various phenotypes in order to discover the pleiotropic behavior of distinct genes. We built a secondary data set by extracting the expression data for each gene from each data set after identifying the common genes across these disorders. Every primary data set must contain an equal number of time stamp values in order to build a 2D microarray data set. The data sets, however, have different numbers of columns. Central nervous system, for example, includes 60 time stamps for a single gene, but the ALL-AML (acute lymphoblastic leukemia-acute myeloid leukemia) data set has 72 time stamps. We cannot modify or remove any columns from the data set because doing so could compromise the data’s integrity or result in the loss of valuable information. To address this issue, we estimated the mean, median, standard deviation, and variance, which may be used to summarize numerical data [30], and we used these numbers to construct our secondary data set. We will design a hierarchical tree using the perfect distance-linkage method found in the previously presented method because we have a data set for each gene with pleiotropic behavior. For that particular gene, the diseases that are closest to each other share similar summarized statistics. As a result, these trees will aid our understanding of how a single gene exhibits various phenotypes in patients with cancer. Furthermore, the gene enrichment scores of these common genes for the disorders that are frequent will be used to corroborate our findings.

Since no human or animal trial was conducted during this research, the authors did not apply for an ethical approval for the study.

We obtained gene expression data for various cancers from a publicly accessible database [31]. Every data set includes the disease-causing genes as well as their expression in various patients with the same condition. We also examined a data set from a variety of disorders to confirm that our findings were disease-agnostic. We used 7 data sets for various cancers. Table 2 lists the specifics of each data set.

The number of genes and patients, or the number of conditions for each gene, differs among these data sets. We used a diverse data set to discover the ideal metrics, which can be used to any gene expression data set. Furthermore, these databases contain certain genes that are widely used. We have created a secondary data set to explore and analyze those genes further.

In our experiment, we employed several combinations of distance measurements and connection algorithms to generate a hierarchical tree. To validate our founding, we used 3 distance metrics and 4 linking methods. We combined these 3 distance metrics and 4 linkage methods to build 12 hierarchical trees for each data set. We cut each tree on numerous cut points after building hierarchical trees. As a result, the tree has been separated into several distinct groups. We assessed the fitness value for each cut point and selected the highest as the ideal value for that hierarchical tree given that particular distance metric-linkage method combination.

A portion of a hierarchical tree of genes from the lung cancer data set is shown in Figure 2. This tree was constructed using the maximum-Ward combination. The full tree has a large number of leaves due to the data set’s 12,533 genes. All the values using Equation 13 are calculated, and the best values for each combination of distance method and linkage metric are shown in Table 3.

We chose the data set (ALL-AML) for testing and ran these 4 ensemble clustering techniques. For this data set, the maximum-average combination produced the best result, with a cluster number of 135. Table 4 displays the fitness values. We discovered that no ensemble clustering approach improves fitness value in any way.

Multiple tumors can be caused by a small number of genes. We discovered 9 genes linked to the following 3 types of cancer: central nervous system, lymphoma, and lung cancer. AFFX-TrpnX-5 at, AFFX-ThrX-5 at, AFFX-ThrX-3 at, AFFX-PheX-M at, AFFX-PheX-5 at, AFFX-PheX-3 at, AFFX-LysX-M at, AFFX-LysX-3 at, and AFFX-LysX-5 at were discovered to be common genes. We found the gene enrichment score publicly available at [32] to confirm our findings. Gene enrichment scores in various malignancies are given in Figure 3 for the discovered common genes.

The maximum distance method combined with the average linkage method produces better hierarchical trees in 4 data sets (central nervous system, leukemia, lymphoma, and SRBCT), according to the fitness values provided in Table 3. These data sets are medium in size, with 60-80 rows and 2000-7000 columns, as shown in Table 2. In the Spellmen data set, however, the maximum-average combination also excels. The other 4 data sets reflect human genes that are responsible for specific tumors, whereas Spellmen is a microarray data set of bacteria. However, the maximum distance approach with ward linkage method constructs a superior hierarchical tree compared with the other methods in 2 of the largest data sets, lung and ovarian. These 2 data sets are larger than the others, and they share no genes with the others.

The maximum distance metric outperforms the other 2 distance methods among the 3 most commonly used distance metrics. Maximum distance considers only 1 column where those 2 genes have the most variance when calculating distance between them. The Euclidean and Manhattan distance methods, on the other hand, would have taken distances across all columns. As a result, the dissimilarity values for the Euclidean and Manhattan distances are approaching the maximum distance. As a result, in clustering, the Euclidean and Manhattan distances place points slightly farther apart than the Maximum distance. Furthermore, because all the columns indicate the same features of a gene evaluated at different time stamps, we can analyze the worst scenario (ie, the greatest differential in the expression of 2 genes at a certain moment). This is the most significant difference between these 2 genes. To put it another way, maximum distance calculates only the difference that matters. The Euclidean and Manhattan distances, on the other hand, are becoming buried in the massive amount of data. The maximum distance, on the other hand, may create undesirable clusters in a different data set with uniform variation across all columns.

When the data set is small, the average linkage approach performs well, and when the data set is huge, the ward method performs well. The single linkage approach may be faster than the average method for joining clusters, but it is not necessarily better. When determining the proximity of 2 clusters, it always considers only 2 points and ignores all others. The average linkage approach, on the other hand, considers all the points in the cluster when determining relatedness. When using the ward technique, the sum square error is used to determine similarity. When working with small or medium-sized data sets, the average linkage approach outperforms the ward linkage method, but as the data sets grow larger, the sum square error values take over and produce superior results compared with the average linkage method.

We tried to identify the optimal combination in our research and found that the maximum distance method performs better on hierarchical clustering when column variance is not uniform across the data set. However, if the data set is medium in size, with around 2000-7000 rows and 60-80 columns, the average linkage technique will outperform other linkage methods, and if the data set is very large, with 12,000-15,000 rows and 100-200 columns, the ward linkage approach will outperform other linkage methods. Furthermore, it has been discovered that ensemble clustering can improve performance by a very little amount at the cost of extra work.

We discovered 9 common genes that cause the following 3 diseases: lymphoma, central nervous system cancer, and lung cancer. We tried to figure out how these genes play a role in these 3 diseases using the data provided in the data sets. The maximum-average hierarchical clustering technique was chosen since it performed the best in the first experiment. We used gene enrichment score to confirm our findings on whether the 9 genes discovered have an impact on these 3 conditions. Figure 3 shows the gene enrichment scores for these genes. We can see that 8 of the 9 genes are important for all 3 cancers. Only 1 gene (AFFX-PheX-3 at) is more important than the other 2 in lung cancer. However, it is clear that our discovered genes have a significant impact on these 3 cancer forms.

Bioinformatics is becoming more and more involved in health sectors, such as disease detection and individualized medicine recommendation, as computational technology advances. Clustering techniques are becoming increasingly important in these industries. We investigated several distance-linkage combinations and attempted to find a solution. We hope that other researchers who use hierarchical clustering will profit from our findings and apply what they have learned to their own study. We also discovered common genes with multiple symptoms, which we confirmed using gene enrichment profiling. Knowing the pleiotropic nature of these genes will help scientists work on them to combat cancer.

In this study, we discovered a set of measures that will yield higher-quality clusters for gene expression data. Pleiotropic behavior of common genes for many disorders was also discovered. To validate our findings, we used a variety of data sets that varied in size and richness. We used a fitness function to compare cluster quality between sets of clusters while assessing cluster quality. For medium-sized data sets, we discovered that the maximum distance metric combined with average linkage works best. Ward linkage also works better with huge data sets. Furthermore, due to data dimension differences, we had to preprocess data while identifying common genes for various disorders. It is critical to identify genes with similar symptoms more precisely and to separate those genes more effectively. Furthermore, detecting a gene by applying the clustering technique to find comparable genes is a critical work for researchers, and if done correctly, might save countless lives. For all these reasons, correct clustering is becoming increasingly important in bioinformatics. Therefore, if their data set resembles our microarray data, researchers from other fields can employ this technology.