Incremental Cluster Validity Indices for Online Learning of Hard Partitions: Extensions and Comparative Study

Validation is one of the most important aspects of clustering, particularly when the user is designing a trustworthy or explainable system. However, most clustering validation approaches require batch calculation. This is an important gap because of the value of clustering in real-time data streaming and other online learning applications. Therefore, interest has grown in providing online alternatives for validation. This paper extends the incremental cluster validity index (iCVI) family by presenting incremental versions of Calinski-Harabasz (iCH), Pakhira-Bandyopadhyay-Maulik (iPBM), WB index (iWB), Silhouette (iSIL), Negentropy Increment (iNI), Representative Cross Information Potential (irCIP), Representative Cross Entropy (irH), and Conn_Index (iConn_Index). This paper also provides a thorough comparative study of correct, under- and over-partitioning on the behavior of these iCVIs, the Partition Separation (PS) index as well as four recently introduced iCVIs: incremental Xie-Beni (iXB), incremental Davies-Bouldin (iDB), and incremental generalized Dunn\u27s indices 43 and 53 (iGD43 and iGD53). Experiments were carried out using a framework that was designed to be as agnostic as possible to the clustering algorithms. The results on synthetic benchmark data sets showed that while evidence of most under-partitioning cases could be inferred from the behaviors of the majority of these iCVIs, over-partitioning was found to be a more challenging problem, detected by fewer of them. Interestingly, over-partitioning, rather then under-partitioning, was more prominently detected on the real-world data experiments within this study. The expansion of iCVIs provides significant novel opportunities for assessing and interpreting the results of unsupervised lifelong learning in real-time, wherein samples cannot be reprocessed due to memory and/or application constraints

General equilibrium

Unlike partial equilibrium analysis which study the equilibrium of a particular market under the clause "ceteris paribus" that revenues and prices on the other markets stay approximately unaffected, the ambition of a general equilibrium model is to analyze the simultaneous equilibrium in all markets of a competitive economy. Definition of the abstract model, some of its basic results and insights are presented. The important issues of uniqueness and local uniqueness of equilibrium are sketched ; they are the condition for a predictive power of the theory and its ability to allow for statics comparisons. Finally, we review the main extensions of the general equilibrium model. Besides the natural extensions to infinitely many commodities and to a continuum of agents, some examples show how economic theory can accommodate the main ideas in order to study some contexts which were not thought of by the initial model.Commodity space, price space, exchange economy, production economy, feasible allocations, equilibrium, quasi-equilibrium, Pareto optimum, core, edgeworth equilibrium allocutions, time and uncertainty, continuum economies, non-convexities, public goods, incomplete markets.

Neuroengineering of Clustering Algorithms

Cluster analysis can be broadly divided into multivariate data visualization, clustering algorithms, and cluster validation. This dissertation contributes neural network-based techniques to perform all three unsupervised learning tasks. Particularly, the first paper provides a comprehensive review on adaptive resonance theory (ART) models for engineering applications and provides context for the four subsequent papers. These papers are devoted to enhancements of ART-based clustering algorithms from (a) a practical perspective by exploiting the visual assessment of cluster tendency (VAT) sorting algorithm as a preprocessor for ART offline training, thus mitigating ordering effects; and (b) an engineering perspective by designing a family of multi-criteria ART models: dual vigilance fuzzy ART and distributed dual vigilance fuzzy ART (both of which are capable of detecting complex cluster structures), merge ART (aggregates partitions and lessens ordering effects in online learning), and cluster validity index vigilance in fuzzy ART (features a robust vigilance parameter selection and alleviates ordering effects in offline learning). The sixth paper consists of enhancements to data visualization using self-organizing maps (SOMs) by depicting in the reduced dimension and topology-preserving SOM grid information-theoretic similarity measures between neighboring neurons. This visualization\u27s parameters are estimated using samples selected via a single-linkage procedure, thereby generating heatmaps that portray more homogeneous within-cluster similarities and crisper between-cluster boundaries. The seventh paper presents incremental cluster validity indices (iCVIs) realized by (a) incorporating existing formulations of online computations for clusters\u27 descriptors, or (b) modifying an existing ART-based model and incrementally updating local density counts between prototypes. Moreover, this last paper provides the first comprehensive comparison of iCVIs in the computational intelligence literature --Abstract, page iv

A taxonomy of supply chain innovations

In this paper, a taxonomy of supply chain and logistics innovations was developed and presented. The taxonomy was based on an extensive literature survey of both theoretical research and case studies. The primary goals are to provide guidelines for choosing the most appropriate innovations for a company, and help companies in positioning themselves in the supply of chain innovations landscape. To this end, the three dimensions of supply chain innovations, namely the goals, supply chain attributes, and innovation attributes were identified and classified. The taxonomy allows for the efficient representation of critical supply chain innovations information, and serves the mentioned goals, which are fundamental to companies in a multitude of industries

Elucidating the Importance of Structure, Surfaces, and Interfaces in Polymer Nanoparticles and Nanocomposites

This dissertation details research conducted to elucidate the importance of structure, surfaces, and interfaces in both polymeric nanoparticles and polymer nanocomposites. The fundamental understanding that is garnered in these studies provides a foundation to rationally develop nanocomposites tailored for unique functionalities, performance and applications. Soft polymeric nanoparticles, have shown to imbue non-traditional diffusive properties, the strength of which decreases with crosslinking density of the nanoparticle. The crosslinking dependent morphology of these nanoparticles is first characterized in a dilute solution of good solvent (Chapter 2). The scattering results revealed that the structure ranges from a swollen polymer in good solvent (0% XL), to a collapsed polymer in theta solvent (0.4%XL), to unequivocally particle-like ( ≥ 0.8%XL). The transition to a particle-like morphology hinges on the clear presence of a measurable surface. To better understand the mechanisms behind their non-traditional diffusive properties, the internal dynamics of these nanoparticles were probed (Chapter 3). While globally exhibiting Zimm-like dynamics, the nanoparticles showed a heterogeneity of local internal dynamics, exhibiting significantly slowed dynamics on length scales that contained crosslinks and linear-like dynamics over length scales where crosslinks were mostly absent. The clear separation of internal dynamics magnifies the importance of the nanoparticle’s core-shell structure. The consequences of surfaces and interfaces within polymer nanocomposites is also explored. The permanency of a bound polymer layer is characterized by monitoring the time evolution of the volume fraction profile of an adsorbed polymer layer (Chapter 4). While the total thickness of the layer remained unchanged, the composition varied indicating that individual chains are not necessarily “irreversibly” adsorbed. Additionally, the molecular weight dependence on the kinetics of chain desorption are studied, finding that desorption in the melt transitions from diffusion limited to a combination of diffusion and surface detachment limited with increasing molecular weight. Finally interfaces between a fire-retardant small molecule and polymer is compatibilized using a polymeric dispersant (Chapter 5). The average and homogeneity of particle size is improved in melt mix blends of the three components as the polymer dispersant can disrupt the intramolecular hydrogen bonding within the flame-retardant with intermolecular interactions

IR Colors and Sizes of Faint Galaxies

We present J and Ks band galaxy counts down to J=24 and Ks=22.5 obtained with the new infrared imager/spectrometer, SOFI, at the ESO New Technology Telescope. The co-addition of short, dithered, images led to a total exposure time of 256 and 624 minutes respectively, over an area of $\sim20$ arcmin$^2$ centered on the NTT Deep Field. The total number of sources with S/N$>5$ is 1569 in the J sample and 1025 in the Ks-selected sample. These are the largest samples currently available at these depths. A d$logN$/d$m$ relation with slope of $\sim0.36$ in J and $\sim0.38$ in Ks is found with no evident sign of a decline at the magnitude limit. The observed surface density of ``small'' sources is much lower than ``large'' ones at bright magnitudes and rises more steeply than the large sources to fainter magnitudes. Fainter than $J\sim22.5$ and Ks$\sim21.5$, small sources dominate the number counts. Galaxies get redder in J-K down to J$\sim20$ and Ks$\sim19$. At fainter magnitudes, the median color becomes bluer with an accompanying increase in the compactness of the galaxies. We show that the blue, small sources which dominate the faint IR counts are not compatible with a high redshift ($z>1$) population. On the contrary, the observed color and compactness trends, together with the absence of a turnover at faint magnitudes and the dominance of small sources, can be naturally explained by an increasing contribution of sub-$L^*$ galaxies when going to fainter apparent magnitudes. Such evidence strongly supports the existence of a steeply rising ($\alpha\ll-1$) faint end of the local infrared luminosity function of galaxies - at least for luminosities $L<0.01L^*$.Comment: Accepted for publication on A&A; 15 pages, 13 figure

Ligand-based design of dopamine reuptake inhibitors : fuzzy relational clustering and 2-D and 3-D QSAR modleing

As the three-dimensional structure of the dopamine transporter (DAT) remains undiscovered, any attempt to model the binding of drug-like ligands to this protein must necessarily include strategies that use ligand information. For flexible ligands that bind to the DAT, the identification of the binding conformation becomes an important but challenging task. In the first part of this work, the selection of a few representative structures as putative binding conformations from a large collection of conformations of a flexible GBR 12909 analogue was demonstrated by cluster analysis. Novel structurebased features that can be easily generalized to other molecules were developed and used for clustering. Since the feature space may or may not be Euclidean, a recently-developed fuzzy relational clustering algorithm capable of handling such data was used. Both superposition-dependent and superposition-independent features were used along with region-specific clustering that focused on separate pharmacophore elements in the molecule. Separate sets of representative structures were identified for the superpositiondependent and superposition-independent analyses. In the second part of this work, several QSAR models were developed for a series of analogues of methylphenidate (MP), another potent dopamine reuptake inhibitor. In a novel method, the Electrotopological-state (B-state) indices for atoms of the scaffold common to all 80 compounds were used to develop an effective test set spanning both the structure space as well as the activity space. The utility of B-state indices in modeling a series of analogues with a common scaffold was demonstrated. Several models were developed using various combinations of 2-D and 3-D descriptors in the Molconn-Z and MOE descriptor sets. The models derived from CoMFA descriptors were found to be the most predictive and explanatory. Progressive scrambling of all models indicated several stable models. The best models were used to predict the activity of the test set analogues and were found to produce reasonable residuals. Substitutions in the phenyl ring of MP, especially at the 3- and 4-positions, were found to be the most important for DATbinding. It was predicted that for better DAT-binding the substituents at these positions should be relatively bulky, electron-rich atoms or groups