Density-based clustering

The nature of the low-conducting states at low ion densities has been treated both by cluster theories [141, 207, 256, 257] and MC simulations [208, 258, 259]. There is no doubt that in this regime neutral (1,1) pairs prevail, and there is some evidence for neutral (2, 2) clusters (a cluster s, t comprises s cations and t anions). Near the critical density, higher clusters come into play, and eventually the cluster representation becomes inappropriate [141]. Simulations indicate the importance of intercluster interactions that are unsatisfactorily described [208] by MSA-based estimates [141],... 

A density-based method clusters gene expression data based on the notion of density. It grows clusters either according to the density of neighborhood clusters or according to some estimated density functions.55... 

Clustering algorithms can be classified into four major approaches hierarchical methods, partitioning-based methods, density-based methods, and grid-based methods. Here, we will focus on the hierarchical cluster approach because it is often used in the context of structure-activity analysis. Recent research has suggested that hierarchical methods perform better than the more commonly used nonhierarchical methods in separating known actives and inactives [41]. 

Figure 3. Energy levels and total density of states at E for the Si 14 based clusters. From left to the right fully hydrogenated (a), with 1 (b), 2 (c), 3 (d), 4 (e) and 6 (f) double-bonded O atoms.

Jiang, D., Pei, J., and Zhang, A. (2003). DHC A density-based hierarchical clustering method for time-series gene expression data. In Proceedings of BIBE2003 3rd IEEE International Symposium on Bioinformatics and Bioengineering, March 10—12, 2003, Bethesda, MD. 

Density-based embeddings This approach starts with a calculation on the whole system to construct an approximate yet accurate representation of the total density Plot by performing a periodic DFT calculation. Then, a guess density of the cluster is constructed from a calculation on the isolated unit or using some simple embedding scheme as described above. The total density is now divided in two parts ptot = Pi+ P2 and the one-electron embedding potential is constructed from the functional derivative of interaction energy with respect to the cluster density pi. 

---