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for people with large data sets

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One way to find tools suited to your task is to browse galleries of innovative visualizations such as Visual Complexity and Infosthetics. Longer lists of tools appear at WikiViz and AI3. What is Advertising SomeVisits

Maps

Google Maps: This classic solution adds spice to any geographic data.

modest maps: an open source Flash mapping solution that works with most major mapping backends.

Open Layers: An open-source Google Maps clone.

Mapstraction: An abstraction layer for different JS mapping tools including Google Maps, OpenLayers/OpenStreetMap, poly9 FreeEarth, and more.

Math

R and ggplot2

SOCR Tools: Web-based applets, computational libraries, educational and data resources

Matplotlib: Python 2D plotting library. Useful for generating all sorts of graphs/plots/charts. Highly recommended.

Matplotlib: Information visualization toolkit in Java, and its fellow Flare built in Flex. Very nice examples, good architecture.

pygooglechart: is a complete Python wrapper for the Google Chart API.

Charts

Chart Chooser recommends chart formats based on the type of thing you're trying to show.

SOCR_Charts: The largest openly web-accessible collection of tools for Exploratory Data Analysis (EDA)

Excel Chart Cleaner removes chartjunk from Excel spreadsheets.

Web apps

Simile Timeline: Great for visualizing time-based data.

many eyes: While they require you to upload your data to them, this site makes getting some good visualizations off the ground quite fast.

Swivel: Another site to upload your data and generate some basic graphs.

Graphs

Most graph tools seem to concentrate on making cluster-tree graphs, using some form of ball-and-spring model.

Interactive, Standalone (non browser-based)

The best option for visualizing massive network graphs appears to be Cytoscape, a Java-based Open Source graph visualizer that scales well and has a flexible plugin structure. It maintains interactivity to the 100,000+ nodes and edges level.

Non-interactive tools for huge (n > 107 nodes+edges) network graphs:

These tools will scale efficiently for massive graphs that call for parallel processing across computer clusters:

In-browser tools for graph exploration

These are typically written in Flash or Java and typically let you explore small local slices from a much larger remote graph.

Toolkits

Eye-Sys: Windows visualization app launched in late 2007; offers a building-block approach for creating a huge variety of visualization systems. Version 2.0 released in Sept. 2008 includes a suite of graph theory objects, enabling faster and more customizable graphing in 2D & 3D

Processing: This classic workhorse will let you browse through linked RDF data from the comfort of your browser. While I admit most of its examples seem overly artsy, Processing can genuinely be used on real data sets -- indeed, there's a whole book on it.

ProcessingJS: This is the JavaScript port of Processing using Canvas Elements. With this you can render/view processing applications in a web browser without the need of installing plug-ins and alike.

nodebox: A Mac OS X application, similar to Processing, but using Python as a basis.

prefuse: A visualization toolkit for the Java programming language.

prefuse flare: provides much of the same functionality for Actionscript 3.

Google Visualization API: Embed visualizations directly into your website: Display attractive data on your website by choosing from a vast array of visualizations created by the developer community.

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last modified October 3, 2012