Optimal Lower Bound for Generalized Median Problems in Metric Space

Jiang, Xiaoyi; Bunke, Horst

doi:10.1007/3-540-70659-3_14

Cited by 18 publications

(15 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The main idea of the genetic search-based algorithm proposed by Jiang et al (2001) and Jiang and Bunke (2002) is to represent, by a chromosome, the transformations from a candidate graph g to each graph in the set S. This representation is followed by a labeling process for nodes and the specification of edges and their labeling. We compared our algorithm with this algorithm in four tests, in each of which the number of graphs in the set S was varied from 5 to 20.…”

Section: Comparison With the Genetic Median Graph Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Median graph computation for graph clustering

Hlaoui

Wang

2005

Soft Comput

View full text Add to dashboard Cite

In this paper, we are interested in the problem of graph clustering. We propose a new algorithm for computing the median of a set of graphs. The concept of median allows the extension of conventional algorithms such as the k-means to graph clustering, helping to bridge the gap between statistical and structural approaches to pattern recognition. Experimental results show the efficiency of the new median graph algorithm compared to the (only) existing algorithm in the literature. We also show its effective use in clustering a set of random graphs and in a content-based synthetic image retrieval system.

show abstract

Section: Comparison With the Genetic Median Graph Algorithmmentioning

confidence: 99%

“…This type of approach has not yet been widely explored, partly due to the lack of efficient algorithms for computing the median graph. Recently, Jiang et al (2001) and Jiang and Bunke (2002) proposed a genetic solution to the median graph problem.…”

Section: Introductionmentioning

confidence: 99%

Median graph computation for graph clustering

Hlaoui

Wang

2005

Soft Comput

View full text Add to dashboard Cite

show abstract

“…Instead, we employ the lower bounding ideas in [9] to model the distance of every graph, G i to the generalized median by an unknown variable, x i . Therefore, x i = d(G * , G i ).…”

Section: Generalized Median Graphsmentioning

confidence: 99%

“…Spatial proximity (adjacency) between chromosomes is expressed as an edge between vertices. We focus on 8 pairs of the larger chromosomes (numbers 1, 2, 3, 4, 6,7,8,9) from the human lung fibroblast cell line. The acquisition process was repeated for 37 cells overall.…”

Section: Chromosomal Organization Mapsmentioning

confidence: 99%

See 1 more Smart Citation

Generalized Median Graphs: Theory and Applications

Mukherjee

Singh

Peng

et al. 2007

2007 IEEE 11th International Conference on Computer Vision

View full text Add to dashboard Cite

We study the so-called Generalized Median graph problem where the task is to to construct a prototype (i.e., a 'model') from an input set of graphs. The problem finds applications in many vision (e.g., object recognition) and learning problems where graphs are increasingly being adopted as a representation tool. Existing techniques for this problem are evolutionary search based; in this paper, we propose a polynomial time algorithm based on a linear programming formulation. We present an additional bi-level method to obtain solutions arbitrarily close to the optimal in non-polynomial time (in worst case). Within this new framework, one can optimize edit distance functions that capture similarity by considering vertex labels as well as the graph structure simultaneously. In context of our motivating application, we discuss experiments on molecular image analysis problems -the methods will provide the basis for building a topological map of all pairs of the human chromosome.

show abstract

A Class of Generalized Median Contour Problem with Exact Solution

Wattuya

Jiang

2006

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

The ability to find the average of a set of contours has several applications in computer vision including prototype formation and computational atlases. While contour averaging can be handled in an informal manner, the formal formulation within the framework of generalized median as an optimization problem is attractive. In this work we will follow this line. A special class of contours is considered, which start from the top, pass each image row exactly once, and end in the last row of an image. Despite of the simplicity they frequently occur in many applications of image analysis. We propose a dynamic programming approach to exactly compute the generalized median contour in this domain. Experimental results will be reported on two scenarios to demonstrate the usefulness of the concept of generalized median contours. In the first case we postulate a general approach to implicitly explore the parameter space of a (segmentation) algorithm. It is shown that using the generalized median contour, we are able to achieve contour detection results comparable to those from explicitly training the parameters based on known ground truth. As another application we apply the exact median contour to verify the tightness of a lower bound for generalized median problems in metric space.

show abstract

Optimal Lower Bound for Generalized Median Problems in Metric Space

Cited by 18 publications

References 15 publications

Median graph computation for graph clustering

Median graph computation for graph clustering

Generalized Median Graphs: Theory and Applications

A Class of Generalized Median Contour Problem with Exact Solution

Contact Info

Product

Resources

About