Matrix Decomposition Methods for Data Mining : Computational Complexity and Algorithms

Matrix decompositions, where a given matrix is represented as a product of two other matrices, are regularly used in data mining. Most matrix decompositions have their roots in linear algebra, but the needs of data mining are not always those of linear algebra. In data mining one needs to have results that are interpretable -- and what is considered interpretable in data mining can be very different to what is considered interpretable in linear algebra. --- The purpose of this thesis is to study matrix decompositions that directly address the issue of interpretability. An example is a decomposition of binary matrices where the factor matrices are assumed to be binary and the matrix multiplication is Boolean. The restriction to binary factor matrices increases interpretability -- factor matrices are of the same type as the original matrix -- and allows the use of Boolean matrix multiplication, which is often more intuitive than normal matrix multiplication with binary matrices. Also several other decomposition methods are described, and the computational complexity of computing them is studied together with the hardness of approximating the related optimization problems. Based on these studies, algorithms for constructing the decompositions are proposed. Constructing the decompositions turns out to be computationally hard, and the proposed algorithms are mostly based on various heuristics. Nevertheless, the algorithms are shown to be capable of finding good results in empirical experiments conducted with both synthetic and real-world data.

Applicability of pebble matrix filtration for the pre-treatment of surface waters containing high turbidity and NOM

Purification of drinking water is routinely achieved by use of conventional coagulants and disinfection procedures. However, there are instances such as flood events when the level of turbidity reaches extreme levels while NOM may be an issue throughout the year. Consequently, there is a need to develop technologies which can effectively treat water of high turbidity during flood events and natural organic matter (NOM) content year round. It was our hypothesis that pebble matrix filtration potentially offered a relatively cheap, simple and reliable means to clarify such challenging water samples. Therefore, a laboratory scale pebble matrix filter (PMF) column was used to evaluate the turbidity and natural organic matter (NOM) pre-treatment performance in relation to 2013 Brisbane River flood water. Since the high turbidity was only a seasonal and short term problem, the general applicability of pebble matrix filters for NOM removal was also investigated. A 1.0 m deep bed of pebbles (the matrix) partly in-filled with either sand or crushed glass was tested, upon which was situated a layer of granular activated carbon (GAC). Turbidity was measured as a surrogate for suspended solids (SS), whereas, total organic carbon (TOC) and UV Absorbance at 254 nm were measured as surrogate parameters for NOM. Experiments using natural flood water showed that without the addition of any chemical coagulants, PMF columns achieved at least 50% turbidity reduction when the source water contained moderate hardness levels. For harder water samples, above 85% turbidity reduction was obtained. The ability to remove 50% turbidity without chemical coagulants may represent significant cost savings to water treatment plants and added environmental benefits accrue due to less sludge formation. A TOC reduction of 35-47% and UV-254 nm reduction of 24-38% was also observed. In addition to turbidity removal during flood periods, the ability to remove NOM using the pebble matrix filter throughout the year may have the benefit of reducing disinfection by-products (DBP) formation potential and coagulant demand at water treatment plants. Final head losses were remarkably low, reaching only 11 cm at a filtration velocity of 0.70 m/h.

Studies on electrical conductivity of insulator-conductor composites

The variation of electrical resistivity of an insulator-conductor composite, namely, wax-graphite composite, with parameters such as volume fraction, grain size, and temperature has been studied. A model is proposed to explain the observed variations, which assumes that the texture of the composite consists of insulator granules coated with conducting particles. The resistivity of these materials is controlled mainly by the contact resistance between the conducting particles and the number of contacts each particle has with its neighbors. The variation of resistivity with temperature has also been explained with the help of this model and it is attributed to the change in contact area. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Velocity ratio-cum-transfer matrix method for the evaluation of a muffler with mean flow

The paper deals with a method for the evaluation of exhaust muffers with mean flow. A new set of variables, convective pressure and convective mass velocity, have been defined to replace the acoustic variables. An expression for attenuation (insertion loss) of a muffler has been proposed in terms of convective terminal impedances and a velocity ratio, on the lines of the one existing for acoustic filters. In order to evaluate the velocity ratio in terms of convective variables, transfer matrices for various muffler elements have been derived from the basic relations of energy, mass and momentum. Finally, the velocity ratiocum-transfer matrix method is illustrated for a typical straight-through muffler.

On the transfer matrix for a uniform tube with a moving medium

Abstract is not available.

Optimal iterative schemes for computing the Moore-Penrose matrix inverse

Among the iterative schemes for computing the Moore — Penrose inverse of a woll-conditioned matrix, only those which have an order of convergence three or two are computationally efficient. A Fortran programme for these schemes is provided.

Starch composites with aconitic acid

The aim of this project is to examine the effectiveness of using aconitic acid (AcA), a tricarboxylic acid which contains a carbon/carbon double bond (C=C), to enhance the properties of starch-based films. Starch/glycerol cast films were prepared with 0, 2, 5, 10 and 15 wt% AcA (starch wt% basis) and the properties analysed. It was shown that AcA acted as both a cross-linking agent and also a strong plasticising agent. The 5 wt% AcA derived starch films were the most effectively cross-linked having the lowest solubility (28 wt%) and decreased swelling coefficient (35 vol.%) by approximately 3 times and 2.4 times respectively compared to the control film submerged in water (23 °C). There was also a significant increase in the film elongation at break by approximately 35 times (compared to the control) with the addition of 15 wt% AcA, emphasising the plasticising effect of AcA. However, generally there was a reduced tensile strength, softening of the film, and reduced thermal stability with increased amounts of AcA.

Rank-Augmented LU-Algorithm for Computing Generalized Matrix Inverses

A rank-augmnented LU-algorithm is suggested for computing a generalized inverse of a matrix. Initially suitable diagonal corrections are introduced in (the symmetrized form of) the given matrix to facilitate decomposition; a backward-correction scheme then yields a desired generalized inverse.

Studies on transport phenomena during solidification of an aluminum alloy in the presence of linear electromagnetic stirring

Numerical and experimental studies on transport phenomena during solidification of an aluminum alloy in the presence of linear electromagnetic stirring are performed. The alloy is electromagnetically stirred to produce semisolid slurry in a cylindrical graphite mould placed in the annulus of a linear electromagnetic stirrer. The mould is cooled at the bottom, such that solidification progresses from the bottom to the top of the cylindrical mould. A numerical model is developed for simulating the transport phenomena associated with the solidification process using a set of single-phase governing equations of mass. momentum, energy. and species conservation. The viscosity variation of the slurry, used in the model, is determined experimentally using a rotary viscometer. The set of governing equations is solved using a pressure-based finite volume technique, along with an enthalpy based phase change algorithm. The numerical study involves prediction of temperature, velocity, species and solid fraction distribution in the mould. Corresponding solidification experiments are performed, with time-temperature history recorded at key locations. The microstructures at various temperature measurement locations in the solidified billet are analyzed. The numerical predictions of temperature variations are in good agreement with experiments, and the predicted flow field evolution correlates well with the microstructures observed at various locations.

Electrical Percolation studies of Polystyrene-multi wall carbon nanotubes Composites

Composites of Polystyrene-multi wall carbon nanotubes (PS-MWNTs) were prepared with loading up to 7 wt% of MWNTs by simple solvent mixing and drying technique. MWNTs with high aspect ratio similar to 4000 were used to make the polymer composites. A very high degree of dispersion of MWNTs was achieved by ultrasonication technique. As a result of high dispersion and high aspect ratio of the MWNTs electrical percolation was observed at rather low weight fraction similar to 0.0021. Characterization of the as prepared PS-MWNTs composites was done by Electron microscopy (EM), X-ray diffraction technique (XRD) and Thermogravimetery analysis (TGA).

Acoustic emission source location and damage detection in a metallic structure using a graph-theory-based geodesic pproach

A geodesic-based approach using Lamb waves is proposed to locate the acoustic emission (AE) source and damage in an isotropic metallic structure. In the case of the AE (passive) technique, the elastic waves take the shortest path from the source to the sensor array distributed in the structure. The geodesics are computed on the meshed surface of the structure using graph theory based on Dijkstra's algorithm. By propagating the waves in reverse virtually from these sensors along the geodesic path and by locating the first intersection point of these waves, one can get the AE source location. The same approach is extended for detection of damage in a structure. The wave response matrix of the given sensor configuration for the healthy and the damaged structure is obtained experimentally. The healthy and damage response matrix is compared and their difference gives the information about the reflection of waves from the damage. These waves are backpropagated from the sensors and the above method is used to locate the damage by finding the point where intersection of geodesics occurs. In this work, the geodesic approach is shown to be suitable to obtain a practicable source location solution in a more general set-up on any arbitrary surface containing finite discontinuities. Experiments were conducted on aluminum specimens of simple and complex geometry to validate this new method.

Structural, dielectric, impedance and optical properties of CaBi2B2O7 glasses and glass-nanocrystal composites

Optically clear glasses were fabricated by quenching the melt of CaCO3-Bi2O3-B2O3 (in equimolecular ratio). The amorphous and glassy characteristics of the as-quenched samples were confirmed via the X-ray powder diffraction (XRD) and differential scanning calorimetric (DSC) studies These glasses were found to. have high thermal stability parameter (S). The optical transmission studies carried out in the 200-2500 nm wavelength range confirmed both the as-quenched and heat-treated samples to be transparent between 400 nm and 2500 nm. The glass-plates that were heat-treated just above the glass transition temperature (723 K) for 6 h retained approximate to 60% transparency despite having nano-crystallites (approximate to 50-100 nm) of CaBi2B2O7 (CBBO) as confirmed by both the XRD and transmission electron microscopy (TEM) studies. The dielectric properties and impedance characteristics of the as-quenched and heat-treated (723 K/6 h) samples were studied as a function of frequency at different temperatures. Cole-Cole equation was employed to rationalize the impedance data.