Great, I will look to implement TCIE then and get back in touch when I have
some finalized code. Ideally I will try and structure it so that it
integrates the small additional step as an improvement to the existing
algorithms, rather than creating it as a standalone function.
Best,
Daniel
On Thu, Apr 28, 2016 at 10:12 AM, Matthieu Brucher <
matthieu.bruc...@gmail.com> wrote:
> Hi,
>
> TCIE is interesting because it's the small additional step that is
> relevant IMHO. With this additional step, you can build Sammon mapping on
> top of it (basically just switch step 4 for Sammon optimization). I would
> cite here my paper on different cost functions
> https://www.researchgate.net/publication/220058500_A_Metric_Multidimensional_Scaling-Based_Nonlinear_Manifold_Learning_Approach_for_Unsupervised_Data_Reduction?ev=prf_pub
> All cost function based dimensionality reduction algorithms could be
> enhanced with the TCIE step, so definitely something to try out.
>
> Cheers,
>
> Matthieu
>
>
> 2016-04-26 6:52 GMT+02:00 Daniel McNeela <daniel.mcne...@gmail.com>:
>
>> Thank you Matthieu and Olivier for your help.
>>
>> It sounds like, based on what Olivier said, that a good approach would be
>> for me to implement the algorithms in a way that ensures compatibility with
>> scikit-learn and then submit them for consideration for inclusion once they
>> are fully completed.
>>
>> Matthieu, my original reasoning behind implementing Sammon mapping was
>> that it seemed to be relatively intuitive to understand to the point where
>> people using the software could modify it and devise their own metrics to
>> suit the needs of their research. Having gone back today and given it a
>> second look, it does seem rather crude as you mentioned, so maybe it would
>> be best if I hold off on that.
>>
>> As far as Principle Curve Analysis, I liked that it was well established
>> (I believe it was one of the earlier manifold learning algorithms
>> introduced) and that it intuitively generalizes Principle Component
>> Analysis to account for nonlinearity. Since Principle Component Analysis is
>> widely used and implemented, Principle Curve Analysis seemed like a natural
>> algorithm to include for nonlinear cases.
>>
>> I was looking at some of the other Manifold Learning algorithms currently
>> in use, and it appears that Topologically Constrained Isometric Embedding
>> offers improvements over many of the algorithms currently in scikit-learn,
>> such as Isomap, LLE, and Eigenmapping. In particular, it seems to perform
>> more robustly in response to noisy and non-convex data. This paper offers a
>> nice comparison between TCIE and the existing algorithms.
>>
>> http://people.csail.mit.edu/rosman/tcie_ijcv.pdf
>>
>> I would certainly be interested in implementing TCIE if there's any
>> interest in having it included in scikit-learn.
>>
>> Cheers,
>>
>> Daniel
>>
>> On Mon, Apr 25, 2016 at 9:11 AM, Matthieu Brucher <
>> matthieu.bruc...@gmail.com> wrote:
>>
>>> Hi Daniel,
>>>
>>> I think in the original scikit pull request on my PhD thesis almost 10
>>> years ago, there may have been some Sammon mapping code. IIRC, the mapping
>>> is really crude and not robust. I think there are other cost functions for
>>> dimensionality reduction that are far more efficient and do not have the
>>> same drawbacks than Sammon mapping.
>>> I don't remember my position on PCA, I know that I had a look at it but
>>> never implemented it. What is the purpose of implementing this one in
>>> particular?
>>>
>>> Cheers,
>>>
>>> Matthieu
>>>
>>> 2016-04-25 7:59 GMT+02:00 Daniel McNeela <daniel.mcne...@gmail.com>:
>>>
>>>> Hi All,
>>>>
>>>> My name is Daniel McNeela, and I am a student at UC Berkeley
>>>> participating in Google Summer of Code 2016. I am working on the Fovea
>>>> project under the umbrella of the International Neuroinformatics
>>>> Coordinating Facility. The abstract for my project can be found here:
>>>> https://summerofcode.withgoogle.com/projects/#5940697098092544
>>>>
>>>> To be brief, Fovea is a Python tool for visualizing dynamical systems
>>>> and associated data, and an integral part of the back end for the software
>>>> involves performing both linear and nonlinear dimensionality reduction on
>>>> data sets. My project mentor would like to add scikit-learn as a dependency
>>>> since it already has a number of manifold learning algorithms implemented.
>>>> However, I am planning on using two additional algorithms that are not
>>>> currently implemented in scikit-learn, namely Sammon Mapping and Principal
>>>> Curve Analysis, and I was wondering whether the developer team would be
>>>> interested in incorporating these two algorithms into scikit-learn's
>>>> existing Manifold Learning package.
>>>>
>>>> Please let me know your thoughts. Information regarding these two
>>>> algorithms can be found at the following links:
>>>>
>>>>
>>>> http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/AV0910/henderson.pdf
>>>>
>>>> https://web.stanford.edu/~hastie/Papers/Principal_Curves.pdf
>>>>
>>>> <https://web.stanford.edu/~hastie/Papers/Principal_Curves.pdf>
>>>> Thanks for your time, and looking forward to hearing from you!
>>>>
>>>>
>>>> - Daniel
>>>>
>>>>
>>>>
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>>>
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