A sequential fitting procedure for linear data analysis models

A particular factor analysis model with parameter constraints is generalized to include classification problems definable within a framework of fitting linear models. The sequential fitting (SEFIT) approach of principal component analysis is extended to include several nonstandard data analysis and classification tasks. SEFIT methods attempt to explain the variability in the initial data (commonly defined by a sum of squares) through an additive decomposition attributable to the various terms in the model. New methods are developed for both traditional and fuzzy clustering that have useful theoretic and computational properties (principal cluster analysis, additive clustering, and so on). Connections to several known classification strategies are also stated.The author is grateful to P. Arabie and L. J. Hubert for editorial assistance and reviewing going well beyond traditional levels.     

Intelligent Choice of the Number of Clusters in K-Means Clustering: An Experimental Study with Different Cluster Spreads

The issue of determining “the right number of clusters” in K-Means has attracted considerable interest, especially in the recent years. Cluster intermix appears to be a factor most affecting the clustering results. This paper proposes an experimental setting for comparison of different approaches at data generated from Gaussian clusters with the controlled parameters of between- and within-cluster spread to model cluster intermix. The setting allows for evaluating the centroid recovery on par with conventional evaluation of the cluster recovery. The subjects of our interest are two versions of the “intelligent” K-Means method, ik-Means, that find the “right” number of clusters by extracting “anomalous patterns” from the data one-by-one. We compare them with seven other methods, including Hartigan’s rule, averaged Silhouette width and Gap statistic, under different between- and within-cluster spread-shape conditions. There are several consistent patterns in the results of our experiments, such as that the right K is reproduced best by Hartigan’s rule – but not clusters or their centroids. This leads us to propose an adjusted version of iK-Means, which performs well in the current experiment setting.     

Chemically tailorable colloidal particles from infinite coordination polymers

Micrometre- and nanometre-sized particles play important roles in many applications, including catalysis, optics, biosensing and data storage. Organic particles are usually prepared through polymerization of suitable monomers or precipitation methods. In the case of inorganic materials, particle fabrication tends to involve the reduction of a metal salt, or the controlled mixing of salt solutions supplying a metal cation and an elemental anion (for example, S2-, Se2-, O2-), respectively; in some instances, these methods even afford direct control over the shape of the particles produced. Another class of materials are metal-organic coordination polymers, which are based on metal ions coordinated by polydentate organic ligands and explored for potential use in catalysis, gas storage, nonlinear optics and molecular recognition and separations. In a subset of these materials, the use of organometallic complexes as ligands (so-called metalloligands) provides an additional level of tailorability, but these materials have so far not yet been fashioned into nano- or microparticles. Here we show that simple addition of an initiation solvent to a precursor solution of metal ions and metalloligands results in the spontaneous and fully reversible formation of a new class of metal-metalloligand particles. We observe initial formation of particles with diameters of a few hundred nanometres, which then coalesce and anneal into uniform and smooth microparticles. The ease with which these particles can be fabricated, and the ability to tailor their chemical and physical properties through the choice of metal and organic ligand used, should facilitate investigations of their scope for practical applications.     

DNA-programmable nanoparticle crystallization

It was first shown more than ten years ago that DNA oligonucleotides can be attached to gold nanoparticles rationally to direct the formation of larger assemblies. Since then, oligonucleotide-functionalized nanoparticles have been developed into powerful diagnostic tools for nucleic acids and proteins, and into intracellular probes and gene regulators. In contrast, the conceptually simple yet powerful idea that functionalized nanoparticles might serve as basic building blocks that can be rationally assembled through programmable base-pairing interactions into highly ordered macroscopic materials remains poorly developed. So far, the approach has mainly resulted in polymerization, with modest control over the placement of, the periodicity in, and the distance between particles within the assembled material. That is, most of the materials obtained thus far are best classified as amorphous polymers, although a few examples of colloidal crystal formation exist. Here, we demonstrate that DNA can be used to control the crystallization of nanoparticle-oligonucleotide conjugates to the extent that different DNA sequences guide the assembly of the same type of inorganic nanoparticle into different crystalline states. We show that the choice of DNA sequences attached to the nanoparticle building blocks, the DNA linking molecules and the absence or presence of a non-bonding single-base flexor can be adjusted so that gold nanoparticles assemble into micrometre-sized face-centred-cubic or body-centred-cubic crystal structures. Our findings thus clearly demonstrate that synthetically programmable colloidal crystallization is possible, and that a single-component system can be directed to form different structures.     

Chemical probing of homopurine-homopyrimidine mirror repeats in supercoiled DNA

We have recently shown that under superhelical stress and/or acid pH the homopurine-homopyrimidine tracts conforming to the mirror symmetry (H palindromes) form a novel DNA structure, the H form. According to our model, the H form includes (1) a triplex formed by half of the purine strand and by the homopyrimidine hairpin and (2) the unstructured other half of the purine strand. We used four specially designed sequences to demonstrate that, in accordance with our model, the mirror symmetry is essential for facile formation of the H form detected by two-dimensional gel electrophoresis. Here we report that, under conditions favouring the H-form extrusion, guanines of the 3' half of the purine strand are protected against alkylation by dimethylsulphate, whereas adenines of the 5' half of the purine strand react with diethyl pyrocarbonate. These data indicate that the 3' half of the homopurine strand is within the triplex whereas the 5' half is unstructured, in full agreement with our model.     

Additive clustering and qualitative factor analysis methods for similarity matrices

We review methods of qualitative factor analysis (QFA) developed by the author and his collaborators over the last decade and discuss the use of QFA methods for the additive clustering problem. The QFA method includes, first, finding a square Boolean matrix in a fixed set of Boolean matrices with simple structures to approximate a given similarity matrix, and, second, repeating this process again and again using residual similarity matrices. We present convergence properties for three versions of the method, provide cluster interpretations for results obtained from the algorithms, and give formulas for the evaluation of factor shares of the initial similarities variance.I am indebted to Professor P. Arabie and the referees for valuable comments and editing of the text.     

Controlling anisotropic nanoparticle growth through plasmon excitation

Inorganic nanoparticles exhibit size-dependent properties that are of interest for applications ranging from biosensing and catalysis to optics and data storage. They are readily available in a wide variety of discrete compositions and sizes. Shape-selective synthesis strategies now also yield shapes other than nanospheres, such as anisotropic metal nanostructures with interesting optical properties. Here we demonstrate that the previously described photoinduced method for converting silver nanospheres into triangular silver nanocrystals--so-called nanoprisms--can be extended to synthesize relatively monodisperse nanoprisms with desired edge lengths in the 30-120 nm range. The particle growth process is controlled using dual-beam illumination of the nanoparticles, and appears to be driven by surface plasmon excitations. We find that, depending on the illumination wavelengths chosen, the plasmon excitations lead either to fusion of nanoprisms in an edge-selective manner or to the growth of the nanoprisms until they reach their light-controlled final size.