TDA Mapper algorithm

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말뭉치

1. The company Ayasdi is based on the Mapper algorithm.
2. During the first 8 weeks we will introduce the TDA mapper algorithm including all needed background (e.g, clustering, PCA, some graph theory, etc.).
3. In weeks 9 - 12, we will compare TDA mapper to other data analysis/visualization software.
4. Mapper is a combination of dimensionality reduction, clustering and graph networks techniques used to get higher level understanding of the structure of data.
5. In this article we will briefly describe what Mapper technically is, reveal the advantages that it carries and show some applications as well as an exploratory case study.
6. The advantage of Mapper is that, after choosing the lens, the covering in the projected space is pulled back to the original high dimensional space and clustering happens here.
7. Another winning aspect of Mapper is to help selecting features that best discriminate data.
8. I am confused about the Mapper for Python as I can’t find any tutorial documentation about using Mapper for Python on Jupyter notebook.
9. We can also get an interactive representation of the mapper graph using the networkD3 package.
10. This example illustrates the interest of the Mapper algorithm when some topological information can not be identified by a standard principal component analysis.
11. One way in which we wish to use Mapper is as an automatic tool for detecting such flares in the data, even in situations where projections into two or three dimensional.
12. I did not manage to obtain the same mapper graph as in the original paper, probably because of the clustering algorithm which is probabply different.
13. # Initialize mapper = km .
14. # Fit to and transform the data projected_data = mapper .
15. # Visualize it mapper .
16. This is a library implementing the Mapper algorithm in Python.
17. Mathematically speaking, MAPPER is a variation of the Reeb graph.
18. A free implementation of MAPPER is available online written by Daniel Müllner and Aravindakshan Babu.
19. This is motivated by theoretical work in TDA, since the Reeb graph is related to Morse theory and MAPPER is derived from it.
20. The Mapper algorithm is a method for topological data analysis invented by Gurjeet Singh, Facundo Mémoli and Gunnar Carlsson.
21. Python Mapper is a realization of this toolchain, written by Daniel Müllner and Aravindakshan Babu.
22. There is also a company, Ayasdi, which was founded by Gurjeet Singh, Gunnar Carlsson and Harlan Sexton and whose main product, the Ayasdi Iris software, has the Mapper algorithm at its core.
23. While open-source implementations of the core TDA Mapper algorithm exist, they have been implemented in languages such as R, MATLAB, and Python.
24. In our talk, we present the first open-source scalable implementation of the Mapper algorithm for topological data analysis using Spark.
25. The TDA Mapper Max device receives OSC data directly from TouchDesigner and assigns values to selected Live Parameters.
26. To select a parameter to control, click a MAP button on the TDA Mapper device, then click the parameter you want to control in Live.
27. The abletonMapper component has a CHOP input and an OSC Input CHOP parameter for sending data to the mapper in a highly efficient manner.
28. In this work, we merge the Mapper algorithm with the expressive power of graph neural networks to produce topologically-grounded graph summaries.
29. We demonstrate the suitability of Mapper as a topological framework for graph pooling by proving that Mapper is a generalisation of pooling methods based on soft cluster assignments.
30. This data can then be analyzed using other TDA methods, such as mapper or persistent homology, to gain insights into the mechanism of periodicity.