# On the Role of Clustering and Visualization Techniques in Gene Microarray Data
## 2 Clustering for Microarray Gene Expression Data
### Other Approaches  
Other several clustering approaches have been proposed. Some approaches are used not only for clustering but also for data projection and visualization. We can list the following approaches:* **Self Organizing Maps**. The k-means method is a well-known centroid approach. A neural variation that allows samples to influence the location of neighboring clusters is known as the self-organizing map (SOM) or Kohonen map [48]. Such maps, usually a \(2D\) rectangular grid of neurons, are particularly valuable for describing the relationships between clusters. The neurons of the neural network are all connected with their own reference vector, and each data point is mapped to the neuron with the closest reference vector. During the training steps, each data point directs the movement of the reference vectors towards the denser areas of the input vector space, so that those reference vectors are trained to fit the distributions of the input data set. When the training is complete, clusters are identified by mapping all data points to the output neurons. SOM was applied to gene expression data in [41] with good results over the k-means approach, nonetheless it requires an a priori clusters number and lattice structure of the neural network. * **Graph-Theoretical Clustering**. Graph-theoretical clustering techniques are explicitly presented in terms of a graph, thus converting the problem of clustering a data set into such graph theoretical problems as finding minimum cut or maximal cliques in the proximity graph G. In [49], the CLuster Identification via Connectivity Kernels (CLICK) was proposed. CLICK tries to discover highly connected components in the proximity graph as clusters. In [49], the authors applied their CLICK clustering method to public gene expression data demonstrating better quality in terms of homogeneity and separation compared with other methods. In [50], both a theoretical algorithm and a practical heuristic called CAST (Cluster Affinity Search Technique) is presented. CAST takes as input a real, symmetric, \(N\times N\) similarity matrix \(Sim(Sim(i,j)\in[0,1])\) and an affinity threshold \(\epsilon\). CAST alternates between adding high affinity samples to a given cluster and removing low affinity samples from it. CAST does not require the number of clusters and is effective in handling outliers. Nevertheless, for CAST, it is difficult to determine a proper value for the global parameter \(\epsilon\). * **Density-Based Hierarchical Approaches**. In [51], a density-based, hierarchical clustering method (DHC) was proposed in order to identify the co-expressed gene groups from gene expression data. As the name suggests, DHC combines both the the model-based and hierarchical clustering approaches. DHC is effective in detecting the co-expressed genes (which have relatively higher density) from noise (which have relatively lower density), and thus is robust in the noisy environment. However, DHC is not efficient from the computational complexity point of view and exhibits the typical difficulty to determine the appropriate value of its parameters. A different approach, called NEC, was defined in [52]. The authors argued that most of clustering algorithms proposed in the literature were based on the Euclidean metric, even though Euclidean metric is often limited and inadequate. NEC is a clustering method accomplished in two steps, where a Probabilistic Principal Surfaces approach (i.e., a density-based modelling) [2] is firstly used to find an initial rough clusterization (with a large number of clusters), and, secondly, it begins an agglomeration phase on the basis of specific non-Euclidean metric defined in terms of [PERSON]'s and Negentropy information. The computational burden of NEC is limited due to [PERSON] information and Negentropy, thus the technique can efficiently and effectively be applied to gene expression data [53; 54] and, with some generalization, to other kinds of data [55]. * **Biclustering**.