*Tid:* **14 april 2015 kl 13.15-14.00.**
**Seminarierummet 3721, Institutionen för Matematik, KTH, Lindstedtsvägen 25, plan 7.**
Karta!
*Föredragshållare:*
Joakim Wininger
**Titel:**
Estimating the intrinsic dimensionality of high-dimensional data (exjobb)
**Abstract**
This report presents a review of some methods for estimating what is known as intrinsic
dimensionality (ID). The principle behind intrinsic dimensionality estimation is that
frequently, it is possible to find some structure in data which makes it possible to
re-express it using a fewer number of coordinates (dimensions). The main objective of
the report is to solve a common problem: Given a (typically high-dimensional) dataset,
determine whether the number of dimensions are redundant, and if so, find a lower
dimensional representation of it.
We introduce different approaches for ID estimation, motivate them theoretically and
compare them using both synthetic and real datasets. The first three methods estimate
the ID of a dataset while the fourth finds a low dimensional version of the data. This
is a useful order in which to organize the task, given an estimate of the ID of a
dataset, construct a simpler version of the dataset using this number of dimensions.
The results show that it is possible to obtain a remarkable decrease in
high-dimensional data. The different methods give similar results despite their
different theoretical backgrounds and behave as expected when using them on synthetic
datasets with known ID.
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