Robust clusters

In hierarchical clustering one can obtain any number of clusters K,lhierarchical clustering, with the difference that there K is defined a priori by the user. The question then arises which A -clustering is significant. To introduce the problem let us first consider a technique that was proposed for the non-hierarchical method MASLOC [27], which selects so-called robust clusters. 

Sikarwar G. S. (2005). Array informatics robust clustering of cDNA microarray data. M.Tech. Thesis, IIT, Kanpur, India. 

Examples of carbyne-metal bonds in organometallic complexes, the adequate model being the framed one, a robust cluster... 

The AIM scheme is popular due to its reliability with large basis sets for which some other schemes fail. Unfortunately, the numerical surface finding and integration involved in this scheme are not completely robust. For example, nonnuclear attractor compounds like Li2 and Na clusters have maxima in the middle... 

Binary systems of ruthenium sulfide or selenide nanoparticles (RujcSy, RujcSey) are considered as the state-of-the-art ORR electrocatalysts in the class of non-Chevrel amorphous transition metal chalcogenides. Notably, in contrast to pyrite-type MS2 varieties (typically RUS2) utilized in industrial catalysis as effective cathodes for the molecular oxygen reduction in acid medium, these Ru-based cluster materials exhibit a fairly robust activity even in high methanol content environments of fuel cells. 

Fig. 30.18. Nine objects, A-I, are clustered. K=2 and K=2i clusterings are obtained. The 2-clustering is correct but not relevant. The 3-clustering is meaningful and robust.

L. Kiernan, J.D. Mason and K. Warwick, Robust initialisation of Gaussian radial basis function networks using partitioned k-means clustering. Electron. Lett., 32 (1996) 671-672. 

Kavuri, S. N., and Venkatasubramanian, V., Using fuzzy clustering with ellipsoidal units in neural networks for robust fault classification, Comput. Chem. Eng. 17(8), 765 (1993). 

We can see so many lanthanide clusters behave as efficient SMMs in those p -O-fixed complexes. Especially, the energy barrier record (530 K) for polynuclear lanthanide SMMs, held by the p5-0-fixed Dy5 with a square-based pyramid, has not been broken by the end of 2013. Such a structural characteristic should support the isolation of a robust SMM to a great extent, which provides a change to explore new methods for achieving SMMs with high barriers. 

Although most of the reported gas-phase experiments do not investigate the temporal evolution of alcohol clusters explicitly, the frequency-domain spectral information can nevertheless be translated into the time domain, making use of some elementary and robust relationships between spectral and dynamical features [289]. According to this, the 10-fs period of the hydrogen-bonded O—H oscillator is modulated and damped by a series of other phenomena. Energy flow into doorway states is certainly slower than for aliphatic C—H bonds [290] but on a time scale of a few picoseconds, energy will nevertheless have... 

FIGURE 6.26 Cluster validity measures for the glass vessels data (left) and result from model-based clustering for k = 4 (right) as a projection on the first two robust principal components (compare Figure 3.10, right). 

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