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Abstract

Techniques for multidimensional scaling visualize objects as points in a low-dimensional metric map. As a result, the visualizations are subject to the fundamental limitations of metric spaces. These limitations prevent multidimensional scaling from faithfully representing non-metric similarity data such as word associations or event co-occurrences. In particular, multidimensional scaling cannot faithfully represent intransitive pairwise similarities in a visualization, and it cannot faithfully visualize "central" objects. In this paper, we present an extension of a recently proposed multidimensional scaling technique called t-SNE. The extension aims to address the problems of traditional multidimensional scaling techniques when these techniques are used to visualize non-metric similarities. The new technique, called multiple maps t-SNE, alleviates these problems by constructing a collection of maps that reveal complementary structure in the similarity data. We apply multiple maps t-SNE to a large data set of word association data and to a data set of NIPS co-authorships, demonstrating its ability to successfully visualize non-metric similarities.

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Abstract

The paper investigates the acceleration of t-SNE-an embedding technique that is commonly used for the visualization of high-dimensional data in scatter plots-using two tree-based algorithms. In particular, the paper develops variants of the Barnes-Hut algorithm and of the dual-tree algorithm that approximate the gradient used for learning t-SNE embeddings in O(N*logN). Our experiments show that the resulting algorithms substantially accelerate t-SNE, and that they make it possible to learn embeddings of data sets with millions of objects. Somewhat counterintuitively, the Barnes-Hut variant of t-SNE appears to outperform the dual-tree variant.

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Abstract

We present a new technique called "t-SNE" that visualizes high-dimensional data by giving each datapoint a location in a two or three-dimensional map. The technique is a variation of Stochastic Neighbor Embedding (Hinton and Roweis, 2002) that is much easier to optimize, and produces significantly better visualizations by reducing the tendency to crowd points together in the center of the map. t-SNE is better than existing techniques at creating a single map that reveals structure at many different scales. This is particularly important for high-dimensional data that lie on several different, but related, low-dimensional manifolds, such as images of objects from multiple classes seen from multiple viewpoints. For visualizing the structure of very large data sets, we show how t-SNE can use random walks on neighborhood graphs to allow the implicit structure of all of the data to influence the way in which a subset of the data is displayed. We illustrate the performance of t-SNE on a wide variety of data sets and compare it with many other non-parametric visualization techniques, including Sammon mapping, Isomap, and Locally Linear Embedding. The visualizations produced by t-SNE are significantly better than those produced by the other techniques on almost all of the data sets.

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Content

"An einem trüben Novembertag 2008 sitzen zwei Männer an einem ovalen Konferenztisch. Sie befinden sich wie die meisten Geschäftstreibenden im Strudel der Finanzmärkte. Ihr Tisch steht im einzigen mehrstöckigen Nachwendebau der Berliner Karl-Marx-Allee. Links vom Fenster leuchtet die Spitze des Fernsehturms, rechts fällt der Blick auf kilometerlange Kachelfassaden. Die Verhandlungen mit den Investoren ziehen sich seit Wochen hin. Ein rhetorisches Ringen. Der Hirnforscher fragt: "Ist Wissen mit großem 'W' und wissen mit kleinem 'w' für Sie das Gleiche?" Der Vertriebsmann sagt: "Learntainment", "Knowledge Nuggets", "Mindmapping". Am Ende liegt ein unterschriebener Vertrag auf dem Tisch - an einem Tag, an dem Daimler laut über Kurzarbeit nachdenkt. Martin Hirsch und Ralf von Grafenstein genehmigen sich einen Piccolo. In der schwersten Wirtschaftskrise der Bundesrepublik haben sie für "eyePlorer" einen potenten Investor gefunden. Er hat die Tragweite ihrer Idee verstanden, und er hat begriffen: Die Welt ist eine Scheibe.
Wenn die Maschine denkt Zur Hybris des Projekts passt, dass der eyePlorer ursprünglich HAL heißen sollte - wie der außer Rand und Band geratene Bordcomputer aus Kubricks "2001: Odyssee im Weltraum". Wenn man die Buchstaben aber jeweils um eine Alphabetposition nach rechts verrückt, ergibt sich IBM. Was passiert mit unserem Wissen, wenn die Maschine selbst anfängt zu denken? Ralf von Grafenstein macht ein ernstes Gesicht. "Es ist nicht unser Ansinnen, sie alleinzulassen. Es geht bei uns ja nicht nur darum, zu finden, sondern auch mitzumachen. Die Community ist wichtig. Der Dialog ist beiderseitig." Der Lotse soll in Form einer wachsamen Gemeinschaft also an Bord bleiben. Begünstigt wird diese Annahme auch durch die aufkommenden Anfasstechnologien, mit denen das iPhone derzeit so erfolgreich ist: "Allein zehn Prozent der menschlichen Gehirnleistung gehen auf den Pinzettengriff zurück." Martin Hirsch wundert sich, dass diese Erkenntnis von der IT-Branche erst jetzt berücksichtigt wird. Auf berührungssensiblen Bildschirmen sollen die Nutzer mit wenigen Handgriffen bald spielerisch Inhalte schaffen und dem System zur Verfügung stellen. So wird aus der Suchmaschine ein "Sparringspartner" und aus einem Informationsknopf ein "Knowledge Nugget". Wie auch immer man die Erkenntniszutaten des Internetgroßmarkts serviert: Wissen als Zeitwort ist ein länglicher Prozess. Im Moment sei die Maschine noch auf dem Stand eines Zweijährigen, sagen ihre Schöpfer. Sozialisiert werden soll sie demnächst im Internet, ihre Erziehung erfolgt dann durch die Nutzer. Als er Martin Hirsch mit seiner Scheibe zum ersten Mal gesehen habe, dachte Ralf von Grafenstein: "Das ist überfällig! Das wird kommen! Das muss raus!" Jetzt ist es da, klein, unschuldig und unscheinbar. Man findet es bei Google."

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Content

Vortrag anlässlich des Workshops: "Extending the multilingual capacity of The European Library in the EDL project Stockholm, Swedish National Library, 22-23 November 2007".

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Content

As the team describe in a paper posted (http://arxiv.org/abs/1605.04951) on arXiv, they found that figures did indeed matter-but not all in the same way. An average paper in PubMed Central has about one diagram for every three pages and gets 1.67 citations. Papers with more diagrams per page and, to a lesser extent, plots per page tended to be more influential (on average, a paper accrued two more citations for every extra diagram per page, and one more for every extra plot per page). By contrast, including photographs and equations seemed to decrease the chances of a paper being cited by others. That agrees with a study from 2012, whose authors counted (by hand) the number of mathematical expressions in over 600 biology papers and found that each additional equation per page reduced the number of citations a paper received by 22%. This does not mean that researchers should rush to include more diagrams in their next paper. Dr Howe has not shown what is behind the effect, which may merely be one of correlation, rather than causation. It could, for example, be that papers with lots of diagrams tend to be those that illustrate new concepts, and thus start a whole new field of inquiry. Such papers will certainly be cited a lot. On the other hand, the presence of equations really might reduce citations. Biologists (as are most of those who write and read the papers in PubMed Central) are notoriously mathsaverse. If that is the case, looking in a physics archive would probably produce a different result.