Hyperbolic Tree Research Articles

Integrating information visualization and retrieval for WWW information discovery

An important technology in knowledge discovery is to access the desired information from the large amount of data stored on the WWW. At present, such information can be accessed by a browser itself or by using a keyword search function. However, browsing is a time consuming task where a user must access individual pages one by one. Furthermore, in keyword searches, it is difficult for users to provide reasonable keywords in knowledge discovery processes. This paper outlines an approach for integrating information visualization and retrieval into WWW information discovery. In this approach, the link structure of a web site is displayed in a 3-D hyperbolic tree in which the height of a node (corresponding to a web page) within the tree indicates a user's “interest” for each page. Here, interest is calculated by a fitting function between a page and a user-supplied query (nested keywords). This measure can be used to filter uninteresting pages, reducing the size of the link structure. Furthermore, each web page is modeled as semi-structured data and can also be displayed as a hyperbolic tree in which the result of query evaluation is visible. Such functions are incorporated within our browser, allowing us to interactively discover desired pages from a large web site. We selected typical web sites to show the performance of the proposed method with improved accuracy and efficiency in WWW information discovery. Here, accuracy indicates how surely the user accesses his/her desired documents, and efficiency indicates how quickly the user reaches the documents.

Network Map: visualizing telecommunications service

In order to propose an evolutionary path for a large business’ telecommunications service, one needs a synoptic view of that customer’s existing services suitable for systemic analysis. Only with such a view can a telecommunications provider enter into a truly consultative relation with large customers. The Network Map application provides such a view by displaying service information contained in a conventional relational database through a Hyperbolic Tree viewer.

The metrical interpretation of superreflexivity in banach spaces

The main result is a metrical characterization of superreflexivity in Banach spaces. A Banach spaceX is not superreflexive if and only ifX contains hyperbolic trees as a metric space. The notion of non-linear cotype in discussed.

Hyperbolic trees

Hyperbolic trees