arXiv subjects

William Zhu

Publications and source records attributed to William Zhu.

At least 19 recordsLinked to original sources

arXiv2026

The Structural Case for the Eco-Civilization Paradigm

This paper establishes a quantitative and structural framework for civilizational continuity under rapid, non-linear ecological transitions. Utilizing empirical data on Earth's Energy Imbalance (EEI), currently measured at 1.36 W/m^2, we demonstrate that the planetary system is on a deterministic trajectory toward a new ecological equilibrium, breaching the 1.5 degrees C thermodynamic threshold in less than 6.5 years. We show that mitigating direct anthropogenic waste heat emissions is statistically insufficient, as 35/36-ths of the annual energy imbalance stems from atmospheric radiative forcing rather than localized thermal output. Consequently, preserving legacy centralized socioeconomic frameworks is unfeasible. We present the structural case for the "Eco-Civilization Paradigm" -- a decentralized network of autonomous, modular eco-communities engineered to insulate core life-support functions, localized energy networks, and edge computation from cascading macro-system failures. Finally, we outline the systemic requirements for this transition, including the realignment of asset valuation frameworks from geography-dependent to engineering-dependent metrics, the mobilization of youth-driven innovation capital, and the strategic reallocation of global industrial manufacturing capacity to safeguard civilizational survival.

physics.soc-ph↗

arXiv2020

Hybrid Channel Based Pedestrian Detection

Pedestrian detection has achieved great improvements with the help of Convolutional Neural Networks (CNNs). CNN can learn high-level features from input images, but the insufficient spatial resolution of CNN feature channels (feature maps) may cause a loss of information, which is harmful especially to small instances. In this paper, we propose a new pedestrian detection framework, which extends the successful RPN+BF framework to combine handcrafted features and CNN features. RoI-pooling is used to extract features from both handcrafted channels (e.g. HOG+LUV, CheckerBoards or RotatedFilters) and CNN channels. Since handcrafted channels always have higher spatial resolution than CNN channels, we apply RoI-pooling with larger output resolution to handcrafted channels to keep more detailed information. Our ablation experiments show that the developed handcrafted features can reach better detection accuracy than the CNN features extracted from the VGG-16 net, and a performance gain can be achieved by combining them. Experimental results on Caltech pedestrian dataset with the original annotations and the improved annotations demonstrate the effectiveness of the proposed approach. When using a more advanced RPN in our framework, our approach can be further improved and get competitive results on both benchmarks.

cs.CV↗

arXiv2015

Dependence space of matroids and its application to attribute reduction

Attribute reduction is a basic issue in knowledge representation and data mining. Rough sets provide a theoretical foundation for the issue. Matroids generalized from matrices have been widely used in many fields, particularly greedy algorithm design, which plays an important role in attribute reduction. Therefore, it is meaningful to combine matroids with rough sets to solve the optimization problems. In this paper, we introduce an existing algebraic structure called dependence space to study the reduction problem in terms of matroids. First, a dependence space of matroids is constructed. Second, the characterizations for the space such as consistent sets and reducts are studied through matroids. Finally, we investigate matroids by the means of the space and present two expressions for their bases. In a word, this paper provides new approaches to study attribute reduction.

cs.AI↗

arXiv2015

Connectedness of graphs and its application to connected matroids through covering-based rough sets

Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data representation in data mining and covering-based rough sets provide a systematic approach to this type of representation. In this paper, we study the connectedness of graphs through covering-based rough sets and apply it to connected matroids. First, we present an approach to inducing a covering by a graph, and then study the connectedness of the graph from the viewpoint of the covering approximation operators. Second, we construct a graph from a matroid, and find the matroid and the graph have the same connectedness, which makes us to use covering-based rough sets to study connected matroids. In summary, this paper provides a new approach to studying graph theory and matroid theory.

cs.AI↗

arXiv2014

Geometric lattice structure of covering and its application to attribute reduction through matroids

The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially greedy algorithm design which plays an important role in the reduction problems. Therefore, it is meaningful to combine coverings with geometric lattices to solve the optimization problems. In this paper, we obtain geometric lattices from coverings through matroids and then apply them to the issue of attribute reduction. First, a geometric lattice structure of a covering is constructed through transversal matroids. Then its atoms are studied and used to describe the lattice. Second, considering that all the closed sets of a finite matroid form a geometric lattice, we propose a dependence space through matroids and study the attribute reduction issues of the space, which realizes the application of geometric lattices to attribute reduction. Furthermore, a special type of information system is taken as an example to illustrate the application. In a word, this work points out an interesting view, namely, geometric lattice to study the attribute reduction issues of information systems.

cs.AI↗

arXiv2013

Closed-set lattice of regular sets based on a serial and transitive relation through matroids

Rough sets are efficient for data pre-processing in data mining. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. Both rough sets and matroids are closely related to lattices. For a serial and transitive relation on a universe, the collection of all the regular sets of the generalized rough set is a lattice. In this paper, we use the lattice to construct a matroid and then study relationships between the lattice and the closed-set lattice of the matroid. First, the collection of all the regular sets based on a serial and transitive relation is proved to be a semimodular lattice. Then, a matroid is constructed through the height function of the semimodular lattice. Finally, we propose an approach to obtain all the closed sets of the matroid from the semimodular lattice. Borrowing from matroids, results show that lattice theory provides an interesting view to investigate rough sets.

cs.AI↗

arXiv2013

Rough matroids based on coverings

The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving them are usually greedy. Matroid, as a generalization of linear independence in vector spaces, it has a variety of applications in many fields such as algorithm design and combinatorial optimization. An excellent introduction to the topic of rough matroids is due to Zhu and Wang. On the basis of their work, we study the rough matroids based on coverings in this paper. First, we investigate some properties of the definable sets with respect to a covering. Specifically, it is interesting that the set of all definable sets with respect to a covering, equipped with the binary relation of inclusion $\subseteq$, constructs a lattice. Second, we propose the rough matroids based on coverings, which are a generalization of the rough matroids based on relations. Finally, some properties of rough matroids based on coverings are explored. Moreover, an equivalent formulation of rough matroids based on coverings is presented. These interesting and important results exhibit many potential connections between rough sets and matroids.

cs.AI↗

arXiv2013

Connectivity for matroids based on rough sets

In mathematics and computer science, connectivity is one of the basic concepts of matroid theory: it asks for the minimum number of elements which need to be removed to disconnect the remaining nodes from each other. It is closely related to the theory of network flow problems. The connectivity of a matroid is an important measure of its robustness as a network. Therefore, it is very necessary to investigate the conditions under which a matroid is connected. In this paper, the connectivity for matroids is studied through relation-based rough sets. First, a symmetric and transitive relation is introduced from a general matroid and its properties are explored from the viewpoint of matroids. Moreover, through the relation introduced by a general matroid, an undirected graph is generalized. Specifically, the connection of the graph can be investigated by the relation-based rough sets. Second, we study the connectivity for matroids by means of relation-based rough sets and some conditions under which a general matroid is connected are presented. Finally, it is easy to prove that the connectivity for a general matroid with some special properties and its induced undirected graph is equivalent. These results show an important application of relation-based rough sets to matroids.

cs.AI↗

arXiv2013

A necessary and sufficient condition for two relations to induce the same definable set family

In Pawlak rough sets, the structure of the definable set families is simple and clear, but in generalizing rough sets, the structure of the definable set families is a bit more complex. There has been much research work focusing on this topic. However, as a fundamental issue in relation based rough sets, under what condition two relations induce the same definable set family has not been discussed. In this paper, based on the concept of the closure of relations, we present a necessary and sufficient condition for two relations to induce the same definable set family.

cs.AI↗

arXiv2013

Granular association rule mining through parametric rough sets for cold start recommendation

Granular association rules reveal patterns hide in many-to-many relationships which are common in relational databases. In recommender systems, these rules are appropriate for cold start recommendation, where a customer or a product has just entered the system. An example of such rules might be "40% men like at least 30% kinds of alcohol; 45% customers are men and 6% products are alcohol." Mining such rules is a challenging problem due to pattern explosion. In this paper, we propose a new type of parametric rough sets on two universes to study this problem. The model is deliberately defined such that the parameter corresponds to one threshold of rules. With the lower approximation operator in the new parametric rough sets, a backward algorithm is designed for the rule mining problem. Experiments on two real world data sets show that the new algorithm is significantly faster than the existing sandwich algorithm. This study indicates a new application area, namely recommender systems, of relational data mining, granular computing and rough sets.

cs.DB↗

arXiv2013

Applications of repeat degree on coverings of neighborhoods

In covering based rough sets, the neighborhood of an element is the intersection of all the covering blocks containing the element. All the neighborhoods form a new covering called a covering of neighborhoods. In the course of studying under what condition a covering of neighborhoods is a partition, the concept of repeat degree is proposed, with the help of which the issue is addressed. This paper studies further the application of repeat degree on coverings of neighborhoods. First, we investigate under what condition a covering of neighborhoods is the reduct of the covering inducing it. As a preparation for addressing this issue, we give a necessary and sufficient condition for a subset of a set family to be the reduct of the set family. Then we study under what condition two coverings induce a same relation and a same covering of neighborhoods. Finally, we give the method of calculating the covering according to repeat degree.

cs.AI↗

arXiv2013

Unique expansion matroids and union minimal matroids

The expansion axiom of matroids requires only the existence of some kind of independent sets, not the uniqueness of them. This causes that the base families of some matroids can be reduced while the unions of the base families of these matroids remain unchanged. In this paper, we define unique expansion matroids in which the expansion axiom has some extent uniqueness; we define union minimal matroids in which the base families have some extent minimality. Some properties of them and the relationship between them are studied. First, we propose the concepts of secondary base and forming base family. Secondly, we propose the concept of unique expansion matroid, and prove that a matroid is a unique expansion matroid if and only if its forming base family is a partition. Thirdly, we propose the concept of union minimal matroid, and prove that unique expansion matroids are union minimal matroids. Finally, we extend the concept of unique expansion matroid to unique exchange matroid and prove that both unique expansion matroids and their dual matroids are unique exchange matroids.

cs.DM↗

arXiv2013

Test-cost-sensitive attribute reduction of data with normal distribution measurement errors

The measurement error with normal distribution is universal in applications. Generally, smaller measurement error requires better instrument and higher test cost. In decision making based on attribute values of objects, we shall select an attribute subset with appropriate measurement error to minimize the total test cost. Recently, error-range-based covering rough set with uniform distribution error was proposed to investigate this issue. However, the measurement errors satisfy normal distribution instead of uniform distribution which is rather simple for most applications. In this paper, we introduce normal distribution measurement errors to covering-based rough set model, and deal with test-cost-sensitive attribute reduction problem in this new model. The major contributions of this paper are four-fold. First, we build a new data model based on normal distribution measurement errors. With the new data model, the error range is an ellipse in a two-dimension space. Second, the covering-based rough set with normal distribution measurement errors is constructed through the "3-sigma" rule. Third, the test-cost-sensitive attribute reduction problem is redefined on this covering-based rough set. Fourth, a heuristic algorithm is proposed to deal with this problem. The algorithm is tested on ten UCI (University of California - Irvine) datasets. The experimental results show that the algorithm is more effective and efficient than the existing one. This study is a step toward realistic applications of cost-sensitive learning.

cs.AI↗

arXiv2013

Minimal cost feature selection of data with normal distribution measurement errors

Minimal cost feature selection is devoted to obtain a trade-off between test costs and misclassification costs. This issue has been addressed recently on nominal data. In this paper, we consider numerical data with measurement errors and study minimal cost feature selection in this model. First, we build a data model with normal distribution measurement errors. Second, the neighborhood of each data item is constructed through the confidence interval. Comparing with discretized intervals, neighborhoods are more reasonable to maintain the information of data. Third, we define a new minimal total cost feature selection problem through considering the trade-off between test costs and misclassification costs. Fourth, we proposed a backtracking algorithm with three effective pruning techniques to deal with this problem. The algorithm is tested on four UCI data sets. Experimental results indicate that the pruning techniques are effective, and the algorithm is efficient for data sets with nearly one thousand objects.

cs.AI↗

arXiv2013

Cost-Sensitive Feature Selection of Data with Errors

In data mining applications, feature selection is an essential process since it reduces a model's complexity. The cost of obtaining the feature values must be taken into consideration in many domains. In this paper, we study the cost-sensitive feature selection problem on numerical data with measurement errors, test costs and misclassification costs. The major contributions of this paper are four-fold. First, a new data model is built to address test costs and misclassification costs as well as error boundaries. Second, a covering-based rough set with measurement errors is constructed. Given a confidence interval, the neighborhood is an ellipse in a two-dimension space, or an ellipsoidal in a three-dimension space, etc. Third, a new cost-sensitive feature selection problem is defined on this covering-based rough set. Fourth, both backtracking and heuristic algorithms are proposed to deal with this new problem. The algorithms are tested on six UCI (University of California - Irvine) data sets. Experimental results show that (1) the pruning techniques of the backtracking algorithm help reducing the number of operations significantly, and (2) the heuristic algorithm usually obtains optimal results. This study is a step toward realistic applications of cost-sensitive learning.

cs.LG↗

arXiv2013

Mining top-k granular association rules for recommendation

Recommender systems are important for e-commerce companies as well as researchers. Recently, granular association rules have been proposed for cold-start recommendation. However, existing approaches reserve only globally strong rules; therefore some users may receive no recommendation at all. In this paper, we propose to mine the top-k granular association rules for each user. First we define three measures of granular association rules. These are the source coverage which measures the user granule size, the target coverage which measures the item granule size, and the confidence which measures the strength of the association. With the confidence measure, rules can be ranked according to their strength. Then we propose algorithms for training the recommender and suggesting items to each user. Experimental are undertaken on a publicly available data set MovieLens. Results indicate that the appropriate setting of granule can avoid over-fitting and at the same time, help obtaining high recommending accuracy.

cs.IR↗

arXiv2013

Granular association rules for multi-valued data

Granular association rule is a new approach to reveal patterns hide in many-to-many relationships of relational databases. Different types of data such as nominal, numeric and multi-valued ones should be dealt with in the process of rule mining. In this paper, we study multi-valued data and develop techniques to filter out strong however uninteresting rules. An example of such rule might be "male students rate movies released in 1990s that are NOT thriller." This kind of rules, called negative granular association rules, often overwhelms positive ones which are more useful. To address this issue, we filter out negative granules such as "NOT thriller" in the process of granule generation. In this way, only positive granular association rules are generated and strong ones are mined. Experimental results on the movielens data set indicate that most rules are negative, and our technique is effective to filter them out.

cs.IR↗

arXiv2013

Cold-start recommendation through granular association rules

Recommender systems are popular in e-commerce as they suggest items of interest to users. Researchers have addressed the cold-start problem where either the user or the item is new. However, the situation with both new user and new item has seldom been considered. In this paper, we propose a cold-start recommendation approach to this situation based on granular association rules. Specifically, we provide a means for describing users and items through information granules, a means for generating association rules between users and items, and a means for recommending items to users using these rules. Experiments are undertaken on a publicly available dataset MovieLens. Results indicate that rule sets perform similarly on the training and the testing sets, and the appropriate setting of granule is essential to the application of granular association rules.

cs.IR↗