Massive dimensionality:issues and solutions

Table of Contents

Massive dimensionality:issues and solutions

Outline

Acks

Problem – Motivation

Problem – Motivation

Typical queries

what is the problem?

Solutions: dim. reduction

In more detail

In more detail

In more detail

Application: VideoTrails

Remaining problems

Common answer: fractals

Fractals

Outline

What is a fractal?

Intrinsic (‘fractal’) dimension

Sierpinsky triangle

Outline

Remaining problems

SAMs, eg: R-trees

R-trees

R-trees

Question:

Self-similarity in Real Data

Formula

Accuracy of Formula

Synthetic Data

effect of embedding dimension

Remaining problems

Outline

Feature selection

Motivation

Idea behind solution:

Eg:

Solution:

Eg:

Currency dataset

Currency dataset

self-similar?

FDR on the ‘currency’ dataset

FDR on the ‘currency’ dataset

Remaining problems

Outline

Galaxies

Brain scans

More fractals:

PPT Slide

Internet

Internet topology

More power laws

More power laws: areas – Korcak’s law

More power laws: areas – Korcak’s law

More power laws: Korcak

(Korcak’s law: Aegean islands)

More power laws

Even more power laws

Olympic medals:

Even more power laws:

Power laws on the web

Conclusions

Future research questions

Citations

Resources

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