Rajesh N. Dave

Robust clustering methods: a unified view

Clustering methods need to be robust if they are to be useful in practice. In this paper, we analyze several popular robust clustering methods and show that they have much in common. We also establish a connection between fuzzy set theory and robust statistics, and point out the similarities between robust clustering methods and statistical methods such as the weighted least-squares technique, the M estimator, the minimum volume ellipsoid algorithm, cooperative robust estimation, minimization of probability of randomness, and the epsilon contamination model. By gleaning the common principles upon which the methods proposed in the literature are based, we arrive at a unified view of robust clustering methods. We define several general concepts that are useful in robust clustering, state the robust clustering problem in terms of the defined concepts, and propose generic algorithms and guidelines for clustering noisy data. We also discuss why the generalized Hough transform is a suboptimal solution to the robust clustering problem.

Characterization and detection of noise in clustering

Abstract A concept of ‘Noise Cluster’ is introduced such that noisy data points may be assigned to the noise class. The approach is developed for objective functional type (K-means or fuzzy K-means) algorithms, and its ability to detect ‘good’ clusters amongst noisy data is demonstrated. The approach presented is applicable to a variety of fuzzy clustering algorithms as well as regression analysis.

Synthesis of engineered particulates with tailored properties using dry particle coating

Abstract Dry particle coating is used to create new-generation materials by combining different powders having different physical and chemical properties to form composites, which show new functionality or improve the characteristics of known materials. Materials with relatively large particle size (1–200 μm) form a core and these core (host) particles are mechanically coated with fine submicron (guest) particles; no liquid of any kind (solvents, binders or water) is required. A number of different devices used to achieve dry particle coating are reviewed. The fundamental mechanisms by which these devices achieve coating are discussed, and many examples of coated particles produced by these methods in our laboratory, as well as by other researchers, are described. Attempts to model some of these processes, so as to be able to predict suitable operating conditions and processing times for different host and guest particle properties, are also described. A theoretical predictive capability is necessary, not only to determine which of the devices would give the best results in a specific application, but also for scale-up and optimization. Based on our research, we believe that dry coating is a viable alternative to wet coating and can be used successfully for certain applications where wet coating processes are not feasible.

Adaptive fuzzy c-shells clustering and detection of ellipses

Several generalizations of the fuzzy c-shells (FCS) algorithm are presented for characterizing and detecting clusters that are hyperellipsoidal shells. An earlier generalization, the adaptive fuzzy c-shells (AFCS) algorithm, is examined in detail and is found to have global convergence problems when the shapes to be detected are partial. New formulations are considered wherein the norm inducing matrix in the distance metric is unconstrained in contrast to the AFCS algorithm. The resulting algorithm, called the AFCS-U algorithm, performs better for partial shapes. Another formulation based on the second-order quadrics equation is considered. These algorithms can detect ellipses and circles in 2D data. They are compared with the Hough transform (HT)-based methods for ellipse detection. Existing HT-based methods for ellipse detection are evaluated, and a multistage method incorporating the good features of all the methods is used for comparison. Numerical examples of real image data show that the AFCS algorithm requires less memory than the HT-based methods, and it is at least an order of magnitude faster than the HT approach.

FUZZY SHELL-CLUSTERING AND APPLICATIONS TO CIRCLE DETECTION IN DIGITAL IMAGES

A new type of Fuzzy Clustering algorithm called Fuzzy-Shell Clustering (FSC) is introduced, The FSC algorithm seeks cluster prototypes that are p-dimensional hyper-spherical-shells. In two-dimensional data, this amounts to finding cluster prototypes that are circles. Thus the FSC algorithm can be applied for detection of circles in digital images. The algorithm does not require the data-points to be in any particular order, therefore its performance can be compared with the global transformation techniques such as Hough transforms. Several numerical examples are considered and the performance of the FSC algorithm is compared to the performance of the methods based on generalized Hough transform (HT). The FSC is shown to be superior to the HT method with regards to memory requirement and computation time. Like the HT method, the FSC is successful even if only a part of a circular shape is present in the image. Other potential applications of FSC are also considered.

Validating fuzzy partitions obtained through c-shells clustering

Validation of fuzzy partitions induced through c-shells clustering is considered. The classical validity measures based on fuzzy partition alone are shown to be inadequate in capturing the shell sub-structure imposed by the shell clustering algorithm. Therefore, performance measures specifically designed for c-shells clustering are considered. Through examples, the new set of indices are shown to be capable of validating the structure characterized by the shell clustering algorithms. The issues related to classical cluster validity versus individual cluster validity are also discussed.

Robust fuzzy clustering of relational data

Popular relational-data clustering algorithms, relational dual of fuzzy c-means (RFCM), non-Euclidean RFCM (NERFCM) (both by Hathaway et al), and FANNY (by Kaufman and Rousseeuw) are examined. A new algorithm, which is a generalization of FANNY, called the fuzzy relational data clustering (FRC) algorithm, is introduced, having an identical objective functional as RFCM. However, the FRC does not have the restriction of RFCM, which is that the relational data is derived from Euclidean distance as the measure of dissimilarity between the objects, and it also does not have limitations of FANNY, including the use of a fixed membership exponent, or a fuzzifier exponent, m. The FRC algorithm is further improved by incorporating the concept of Daves object data noise clustering (NC) algorithm, done by proposing a concept of noise-dissimilarity. Next, based on the constrained minimization, which includes an inequality constraint for the memberships and corresponding Kuhn-Tucker conditions, a noise resistant, FRC algorithm is derived which works well for all types of non-Euclidean dissimilarity data. Thus it is shown that the extra computations for data expansion (/spl beta/-spread transformation) required by the NERFCM algorithm are not necessary. This new algorithm is called robust non-Euclidean fuzzy relational data clustering (robust-NE-FRC), and its robustness is demonstrated through several numerical examples. Advantages of this new algorithm are: faster convergence, robustness against outliers, and ability to handle all kinds of relational data, including non-Euclidean. The paper also presents a new and better interpretation of the noise-class.

Mixing and characterization of nanosized powders: An assessment of different techniques

The objective of this paper was to gain an understanding of the mixing and characterization of nanosized powders. Three different nanosized material systems were selected based on their physical and chemical properties. Mixing experiments of the selected nanopowders were performed using a variety of environmentally friendly dry powder processing devices and the rapid expansion of supercritical CO2 suspensions (RESS process) and compared with solvent-based methods coupled with ultrasonic agitation. A number of imaging techniques, including FESEM, AFM, TEM, EELS and EDS were used to characterize the degree of mixing or homogeneity of the mixtures obtained.The results indicate that only some of the imaging techniques are capable of determining the quality of nanoparticle mixing, depending on the physical and chemical properties of the nanopowders. For example, field emission scanning electron microscope (FESEM) is suitable for characterizing powder mixtures having a distinct difference in particle shape, or with a large difference in atomic number of the metallic element of the two constituents. Only electron energy loss spectroscopy (EELS) was able to fully characterize nanopowder mixtures of SiO2 and TiO2 at the nanoscale. Energy dispersive X-ray spectroscopy (EDS) provided information on mixing quality, but only on a scale of about 1 μm. The results also show that solvent-based mixing methods coupled with ultrasonic agitation, and RESS generally perform better than dry powder processing systems, with the exception of the hybridizer, in generating a homogeneous mixture.

Preparation and characterization of hydroxypropyl methyl cellulose films containing stable BCS Class II drug nanoparticles for pharmaceutical applications.

The design and feasibility of a simple process of incorporating stable nanoparticles into edible polymer films is demonstrated with the goal of enhancing the dissolution rate of poorly water soluble drugs. Nanosuspensions produced from wet stirred media milling (WSMM) were transformed into polymer films containing drug nanoparticles by mixing with a low molecular weight hydroxylpropyl methyl cellulose (HPMC E15LV) solution containing glycerin followed by film casting and drying. Three different BCS Class II drugs, naproxen (NPX), fenofibrate (FNB) and griseofulvin (GF) were studied. The influence of the drug molecule on the film properties was also investigated. It was shown that film processing methodology employed has no effect on the drug crystallinity according to X-ray diffraction (XRD) and Raman spectroscopy. Differences in aggregation behavior of APIs in films were observed through SEM and NIR chemical imaging analysis. NPX exhibited the strongest aggregation compared to the other drugs. The aggregation had a direct effect on drug content uniformity in the film. Mechanical properties of the film were also affected depending on the drug-polymer interaction. Due to strong hydrogen bonding with the polymer, NPX exhibited an increase in Youngs Modulus (YM) of approximately 200%, among other mechanical properties, compared to GF films. A synergistic effect between surfactant/polymer and drug/polymer interactions in the FNB film resulted in an increase of more than 600% in YM compared to the GF film. The enhancement in drug dissolution rate of films due to the large surface area and smaller drug particle size was also demonstrated.

Generalized fuzzy c-shells clustering and detection of circular and elliptical boundaries

Abstract The Fuzzy c -Shells (FCS) algorithm and its adaptive generalization, called the Adaptive Fuzzy c -Shells (AFCS) algorithm, are considered for detection of curved boundaries, specifically circular and elliptical. The FCS algorithms utilize hyper-spherical-shells as cluster prototypes. Thus in two dimensions, the prototypes are circles. The AFCS algorithms consider hyper-ellipsoidal-shells as prototypes, hence the ability to characterize elliptical boundaries. The generalization is achieved by allowing the distances to be measured through a norm inducing matrix that is symmetric, positive definite. Each cluster is allowed to have a different matrix, which is made a variable of optimization. The ability of the algorithms to detect circular and elliptical boundaries in two-dimensional data is illustrated through several examples.