| Summary: | Clustering is a mathematical approach that allows one to find a group of data with similar attributes. This approach is also often used in the field of computer science to group a large amounts of data. Triclustering analysis is an analysis technique on 3D data (observation—attribute—context). Triclustering analysis can group observations on several attributes and contexts simultaneously. Triclustering analysis has been frequently applied to analyze microarray gene expression data. We proposed the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-Trimax method to perform triclustering analysis on microarray gene expression data. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-Trimax method aims to find a tricluster that has a mean square residual smaller than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> and a maximum volume. Tricluster is obtained by deleting nodes from 3D data using multiple node deletion and single node deletion algorithms. The tricluster candidates that have been obtained are checked again by adding some previously deleted nodes using the node addition algorithm. In this research, the program improvement of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-Trimax method was carried out and also the calculation of the resulting tricluster evaluation result. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-Trimax method is implemented in two microarray gene expression data. The first implementation was carried out on gene expression data from the differentiation process of human-induced pluripotent stem cells (HiPSCs) from patients with heart disease, resulting in the best simulation when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi><mo>=</mo><mn>0.0068</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>=</mo><mn>1.2</mn></mrow></semantics></math></inline-formula>, and obtained five tricluster, which are considered as characteristics of heart disease. The second implementation was implemented on HIV-1 data, best simulation when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi><mo>=</mo><mn>0.0046</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>=</mo><mn>1.25</mn></mrow></semantics></math></inline-formula> and produced three genes as biomarkers, with the gene names <i>AGFG1</i>, <i>EGR1</i> and <i>HLA-C</i>. This gene group can be used by medical experts in providing further treatment.
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