Computing fuzzy rough approximations in large scale information systems

Rough set theory is a popular and powerful machine learning tool. It is especially suitable for dealing with information systems that exhibit inconsistencies, i.e. objects that have the same values for the conditional attributes but a different value for the decision attribute. In line with the emerging granular computing paradigm, rough set theory groups objects together based on the indiscernibility of their attribute values. Fuzzy rough set theory extends rough set theory to data with continuous attributes, and detects degrees of inconsistency in the data. Key to this is turning the indiscernibility relation into a gradual relation, acknowledging that objects can be similar to a certain extent. In very large datasets with millions of objects, computing the gradual indiscernibility relation (or in other words, the soft granules) is very demanding, both in terms of runtime and in terms of memory. It is however required for the computation of the lower and upper approximations of concepts in the fuzzy rough set analysis pipeline. Current non-distributed implementations in R are limited by memory capacity. For example, we found that a state of the art non-distributed implementation in R could not handle 30,000 rows and 10 attributes on a node with 62GB of memory. This is clearly insufficient to scale fuzzy rough set analysis to massive datasets. In this paper we present a parallel and distributed solution based on Message Passing Interface (MPI) to compute fuzzy rough approximations in very large information systems. Our results show that our parallel approach scales with problem size to information systems with millions of objects. To the best of our knowledge, no other parallel and distributed solutions have been proposed so far in the literature for this problem

A comparative study of the AHP and TOPSIS methods for implementing load shedding scheme in a pulp mill system

The advancement of technology had encouraged mankind to design and create useful equipment and devices. These equipment enable users to fully utilize them in various applications. Pulp mill is one of the heavy industries that consumes large amount of electricity in its production. Due to this, any malfunction of the equipment might cause mass losses to the company. In particular, the breakdown of the generator would cause other generators to be overloaded. In the meantime, the subsequence loads will be shed until the generators are sufficient to provide the power to other loads. Once the fault had been fixed, the load shedding scheme can be deactivated. Thus, load shedding scheme is the best way in handling such condition. Selected load will be shed under this scheme in order to protect the generators from being damaged. Multi Criteria Decision Making (MCDM) can be applied in determination of the load shedding scheme in the electric power system. In this thesis two methods which are Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) were introduced and applied. From this thesis, a series of analyses are conducted and the results are determined. Among these two methods which are AHP and TOPSIS, the results shown that TOPSIS is the best Multi criteria Decision Making (MCDM) for load shedding scheme in the pulp mill system. TOPSIS is the most effective solution because of the highest percentage effectiveness of load shedding between these two methods. The results of the AHP and TOPSIS analysis to the pulp mill system are very promising

Surface Tension, Surface Stiffness, and Surface Width of the 3-dimensional Ising Model on a Cubic Lattice

We compute properties of the interface of the 3-dimensional Ising model for a wide range of temperatures, covering the whole region from the low temperature domain through the roughening transition to the bulk critical point. The interface tension sigma is obtained by integrating the surface energy density over the inverse temperature beta. We use lattices of size L x L x T, with L up to 64, and T up to 27. The simulations with antiperiodic boundary conditions in T-direction are done with the Hasenbusch-Meyer interface cluster algorithm that turns out to be very efficient. We demonstrate that in the rough phase the large distance behavior of the interface is well described by a massless Gaussian dynamics. The surface stiffness coefficient kappa is determined. We also attempt to determine the correlation length xi and study universal quantities like xi^2 * sigma and xi^2 * kappa. Results for the interfacial width on lattices up to 512 x 512 x 27 are also presented.Comment: 33 pages, 5 figures, report MS-TPI-92-2

Data granulation by the principles of uncertainty

Researches in granular modeling produced a variety of mathematical models, such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets, which are all suitable to characterize the so-called information granules. Modeling of the input data uncertainty is recognized as a crucial aspect in information granulation. Moreover, the uncertainty is a well-studied concept in many mathematical settings, such as those of probability theory, fuzzy set theory, and possibility theory. This fact suggests that an appropriate quantification of the uncertainty expressed by the information granule model could be used to define an invariant property, to be exploited in practical situations of information granulation. In this perspective, a procedure of information granulation is effective if the uncertainty conveyed by the synthesized information granule is in a monotonically increasing relation with the uncertainty of the input data. In this paper, we present a data granulation framework that elaborates over the principles of uncertainty introduced by Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is possible to apply such principles regardless of the input data type and the specific mathematical setting adopted for the information granules. The proposed framework is conceived (i) to offer a guideline for the synthesis of information granules and (ii) to build a groundwork to compare and quantitatively judge over different data granulation procedures. To provide a suitable case study, we introduce a new data granulation technique based on the minimum sum of distances, which is designed to generate type-2 fuzzy sets. We analyze the procedure by performing different experiments on two distinct data types: feature vectors and labeled graphs. Results show that the uncertainty of the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference

Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies

In motion analysis and understanding it is important to be able to fit a suitable model or structure to the temporal series of observed data, in order to describe motion patterns in a compact way, and to discriminate between them. In an unsupervised context, i.e., no prior model of the moving object(s) is available, such a structure has to be learned from the data in a bottom-up fashion. In recent times, volumetric approaches in which the motion is captured from a number of cameras and a voxel-set representation of the body is built from the camera views, have gained ground due to attractive features such as inherent view-invariance and robustness to occlusions. Automatic, unsupervised segmentation of moving bodies along entire sequences, in a temporally-coherent and robust way, has the potential to provide a means of constructing a bottom-up model of the moving body, and track motion cues that may be later exploited for motion classification. Spectral methods such as locally linear embedding (LLE) can be useful in this context, as they preserve "protrusions", i.e., high-curvature regions of the 3D volume, of articulated shapes, while improving their separation in a lower dimensional space, making them in this way easier to cluster. In this paper we therefore propose a spectral approach to unsupervised and temporally-coherent body-protrusion segmentation along time sequences. Volumetric shapes are clustered in an embedding space, clusters are propagated in time to ensure coherence, and merged or split to accommodate changes in the body's topology. Experiments on both synthetic and real sequences of dense voxel-set data are shown. This supports the ability of the proposed method to cluster body-parts consistently over time in a totally unsupervised fashion, its robustness to sampling density and shape quality, and its potential for bottom-up model constructionComment: 31 pages, 26 figure