# On the Role of Clustering and Visualization Techniques in Gene Microarray Data
## 1 Introduction
### Microarray Experimental Data  
A microarray experiment typically assesses a large number of DNA sequences (genes, cDNA clones, or expressed sequence tags [ESTs]) under multiple conditions. These conditions may be a time series during a biological process (e.g., the yeast cell cycle) or a collection of different tissue samples (e.g., normal versus cancerous tissues). From now on, we will refer to gene expression data without making a distinction among DNA sequences, which will uniformly be called \"genes\". In the same way, we will refer to all kinds of experimental conditions as \"samples\". A gene expression data set from a microarray experiment can be represented by a real-valued expression matrix \(M=\{a_{ij}|1\leq i\leq n,1\leq j\leq m\}\), where the rows form the expression patterns of genes, the columns represent the expression profiles of samples, and each cell \(a_{ij}\) is the measured expression level of gene \(i\) in sample \(j\). The original gene expression matrix obtained from a scanning process contains noise, missing values, and systematic variations arising from the experimental procedure. Data preprocessing is indispensable before any cluster analysis can be performed. Some problems of data preprocessing have themselves become interesting research topics. Those questions are beyond the scope of this paper; however, the interested reader may refer to [13; 14] for an examination of the problem of missing value estimation and to [15; 16] for addressing the problem of data normalization or data compression (e.g., compressive sensing) [17; 18].  
In literature, there is a huge number of available gene expression data sets, aimed at different biological and medical goals, the most of which are publicly available for experimenting with. In the following, a description of a brief list of useful data sets (see Table 1 for a summary) for assessing the suitability and the effectiveness of various clustering, visualization and, in general, machine learning techniques. The interested reader may refer to [19] for more extensive references.  
* ALLAML [20] contains two classes of samples, namely ALL and AML, each of 47 and 25 samples, respectively, for an overall number of 72 samples. Each sample is formed by 7129 gene expression values.
* LEUKEMIA [20] contains in total 72 samples in two classes: acute lymphoblastic and acute myeloid corresponding to 7129 genes.
* CLL SUB 111 [21] dataset has gene expressions from high density oligonucleotide arrays containing genetically and clinically distinct subgroups of B-cell chronic lymphocytic leukemia (B-CLL). The dataset consists of 11,340 gene expression levels, 111 instances and three classes.
* GLIOMA [22] contains in total 50 samples in four classes: cancer glioblastomas, non-cancer glioblastomas, cancer oligodendrogliomas and non-cancer oligodendrogliomas, which have 14, 14, 7, 15 samples, respectively. Each sample is formed by 12,625 genes.
* LUNG [23] contains in total 203 samples in five classes, adenocarcinoma, squamous cell lung carcinomas, pulmonary carcinoids, small-cell lung carcinomas and normal lung, with 139, 21, 20, 6, 17 samples, respectively.
* LUNG DISCRETE [24] contains 73 samples in seven classes where each sample consists of 325 gene expressions.
* DLBCL [25] is a modified version of the original DLBCL dataset. It consists of 96 samples in nine classes, where each sample is defined by the expression of 4026 genes.
* CARCINOM [26] contains 174 samples in 11 classes, prostate, bladder/ ureter, breast, colorectal, gastroesophagus, kidney, liver, ovary, pancreas, lung adenocarcinoma and lung squamous cell carcinoma.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Size** & **\# of Features** & **\# of Classes** \\ \hline ALLAML & 72 & 7129 & 2 \\ LEUKEMIA & 72 & 7070 & 2 \\ CLL\_SUB\_111 & 111 & 11,340 & 3 \\ GLIOMA & 50 & 4434 & 4 \\ LUNG\_C & 203 & 3312 & 5 \\ LUNG\_D & 73 & 325 & 7 \\ DLBCL & 96 & 4026 & 9 \\ CAR & 174 & 9182 & 11 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Gene expression Datasets Description.