Generalized Discernibility Function Based Attribute Reduction in Incomplete Decision Systems

A rough set approach for attribute reduction is an important research subject in data mining and machine learning. However, most attribute reduction methods are performed on a complete decision system table. In this paper, we propose methods for attribute reduction in static incomplete decision systems and dynamic incomplete decision systems with dynamically-increasing and decreasing conditional attributes. Our methods use generalized discernibility matrix and function in tolerance-based rough sets

Parametric matroid of rough set

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set family, with any subset of a universe as its parameter, to connect rough sets and matroids. On the one hand, for a universe and an equivalence relation on the universe, a parametric set family is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore it can generate a matroid, called a parametric matroid of the rough set. Three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, since partition-circuit matroids were well studied through the lower approximation number, we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.Comment: 15 page

A Distance-Based Method for Attribute Reduction in Incomplete Decision Systems

There are limitations in recent research undertaken on attribute reduction in incomplete decision systems. In this paper, we propose a distance-based method for attribute reduction in an incomplete decision system. In addition, we prove theoretically that our method is more effective than some other methods

Search Efficient Binary Network Embedding

Traditional network embedding primarily focuses on learning a dense vector representation for each node, which encodes network structure and/or node content information, such that off-the-shelf machine learning algorithms can be easily applied to the vector-format node representations for network analysis. However, the learned dense vector representations are inefficient for large-scale similarity search, which requires to find the nearest neighbor measured by Euclidean distance in a continuous vector space. In this paper, we propose a search efficient binary network embedding algorithm called BinaryNE to learn a sparse binary code for each node, by simultaneously modeling node context relations and node attribute relations through a three-layer neural network. BinaryNE learns binary node representations efficiently through a stochastic gradient descent based online learning algorithm. The learned binary encoding not only reduces memory usage to represent each node, but also allows fast bit-wise comparisons to support much quicker network node search compared to Euclidean distance or other distance measures. Our experiments and comparisons show that BinaryNE not only delivers more than 23 times faster search speed, but also provides comparable or better search quality than traditional continuous vector based network embedding methods

Adaptive Multidimensional Scaling: The Spatial Representation of Brand Consideration and Dissimilarity Judgments

We propose Adaptive Multidimensional Scaling (AMDS) for simultaneously deriving a brand map and market segments using consumer data on cognitive decision sets and brand dissimilarities.In AMDS, the judgment task is adapted to the individual respondent: dissimilarity judgments are collected only for those brands within a consumers' awareness set.Thus, respondent fatigue and subjects' unfamiliarity with any subset of the brands are circumvented; thereby improving the validity of the dissimilarity data obtained, as well as the multidimensional spatial structure derived.Estimation of the AMDS model results in a spatial map in which the brands and derived segments of consumers are jointly represented as points.The closer a brand is positioned to a segment's ideal brand, the higher the probability that the brand is considered and chosen.An assumption underlying this model representation is that brands within a consumers' consideration set are relatively similar.In an experiment with 200 subjects and 4 product categories, this assumption is validated.We illustrate adaptive multidimensional scaling on commercial data for 20 midsize car brands evaluated by 212 members of a consumer panel.Potential applications of the method and future research opportunities are discussed.scaling;brands;market segmentation

A metric to represent the evolution of CAD/analysis models in collaborative design

Computer Aided Design (CAD) and Computer Aided Engineering (CAE) models are often used during product design. Various interactions between the different models must be managed for the designed system to be robust and in accordance with initially defined specifications. Research published to date has for example considered the link between digital mock-up and analysis models. However design/analysis integration must take into consideration the important number of models (digital mock-up and simulation) due to model evolution in time, as well as considering system engineering. To effectively manage modifications made to the system, the dependencies between the different models must be known and the nature of the modification must be characterised to estimate the impact of the modification throughout the dependent models. We propose a technique to describe the nature of a modification which may be used to determine the consequence within other models as well as a way to qualify the modified information. To achieve this, a metric is proposed that allows the qualification and evaluation of data or information, based on the maturity and validity of information and model