10855228
Generating Symbolic Interpolants for Scattered Data with Normal Vectors
Algorithms to generate a triangular or a quadrilateral interpolant with G1-continuity are given in this paper for arbitrary scattered data with associated normal vectors over a prescribed triangular or quadrilateral decomposition. The interpolants are constructed with a general method to generate surfaces from moving Bézier curves under geometric constraints. With the algorithm, we may obtain interpolants in complete symbolic parametric forms, leading to a fast computation of the interpolant. A dynamic interpolation solid modelling software package DISM is implemented based on the algorithm which can be used to generate and manipulate solid objects in an interactive way.
14317372
Construct piecewise Hermite interpolation surface with blending methods
Three methods are proposed to construct a piecewise Hermite interpolation surface (PHIS), which is a piecewise algebraic surface interpolating a set of given points with associated normal directions. The surface is obtained by blending together some low-degree surface patches. Both the first and the second methods are completely local and give a surface with G/sup n/-continuity. In the third construction, we reduce the number of surface patches by joining as many cubic patches as possible. This method gives a global solution with G/sup 1/-continuity. These three different methods can be used to meet different requirements of the designers.
10964754
SETRED: Self-training with Editing
Self-training is a semi-supervised learning algorithm in which a learner keeps on labeling unlabeled examples and retraining itself on an enlarged labeled training set. Since the self-training process may erroneously label some unlabeled examples, sometimes the learned hypothesis does not perform well. In this paper, a new algorithm named Setred is proposed, which utilizes a specific data editing method to identify and remove the mislabeled examples from the self-labeled data. In detail, in each iteration of the self-training process, the local cut edge weight statistic is used to help estimate whether a newly labeled example is reliable or not, and only the reliable self-labeled examples are used to enlarge the labeled training set. Experiments show that the introduction of data editing is beneficial, and the learned hypotheses of Setred outperform those learned by the standard self-training algorithm.
9175149
Generation of Comprehensible Hypotheses from Gene Expression Data
Machine learning techniques have been recognized as powerful tools for the analysis of gene expression data. However, most learning techniques used in class prediction in gene expression analysis during the past years generate black-box models. Although the prediction accuracy of these models could be very well, they provide little insight into the biological facts. This paper holds the recognition that a more reasonable role for machine learning techniques is to generate hypotheses that can be verified or refined by human experts instead of making decisions for human experts. Based on this recognition, a general approach to generate comprehensible hypotheses from gene expression data is described and applied to human acute leukemias as a test case. The results demonstrate the feasibility of using machine learning techniques to help form hypotheses on the relationship between genes and certain diseases.
14428056
Approximation algorithms for directed Steiner problems
We obtain the first non-trivial approximation algorithms for the Steiner Tree problem and the Generalized Steiner Tree problem in general directed graphs. Essentially no approximation algorithms were known for these problems. For the Directed Steiner Tree problem, we design a family of algorithms which achieve an approximation ratio of O(k^\epsilon) in time O(kn^{1/\epsilon}) for any fixed (\epsilon < 0), where k is the number of terminals to be connected. For the Directed Generalized Steiner Tree Problem, we give an algorithm which achieves an approximation ratio of O(k^{2/3}\log^{1/3} k), where k is the number of pairs to be connected. Related problems including the Group Steiner tree problem, the Node Weighted Steiner tree problem and several others can be reduced in an approximation preserving fashion to the problems we solve, giving the first non-trivial approximations to those as well.
43310555
Twist-Rotation Transformations of Binary Trees and Arithmetic Expressions
The paper studies the computational complexity and efficient algorithms for the twist?rotation transformations of binary trees, which is equivalent to the transformation of arithmetic expressions over an associative and commutative binary operation. The main results are (1) a full binary tree with n labeled leaves can be transformed into any other in at most 3nlogn+2n twist and rotation operations, (2) deciding the twist?rotation distance between two binary trees is NP-complete, and (3) the twist?rotation transformation can be approximated with ratio 6logn+4 in polynomial time for full binary trees with n uniquely labeled leaves.
54297489
Iso-Map: Energy-Efficient Contour Mapping in Wireless Sensor Networks
Contour mapping is a crucial part of many wireless sensor network applications. Many efforts have been made to avoid collecting data from all the sensors in the network and producing maps at the sink, which is proven to be inefficient. The existing approaches (often aggregation based), however, suffer from heavy transmission traffic and incur large computational overheads on each sensor node. We propose Iso-Map, an energy-efficient protocol for contour mapping, which builds contour maps based solely on the reports collected from intelligently selected ?isoline nodes? in wireless sensor networks. Iso-Map achieves high-quality contour mapping while significantly reducing the generated traffic from O(n) to O(?n), where n is the total number of sensor nodes in the field. The pernode computation overhead is also restrained as a constant. We conduct comprehensive trace-driven simulations to verify this protocol, and demonstrate that Iso-Map outperforms the previous approaches in the sense that it produces contour maps of high fidelity with significantly reduced energy cost.