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Discussion on ”Exploiting Non-Linear Structure in Astronomical Data for Improved Statistical Inference” by Ann B. Lee and Peter E. Freeman Didier Fraix-Burnet

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(1)

Discussion

on

”Exploiting Non-Linear Structure in Astronomical Data for Improved Statistical Inference”

by Ann B. Lee and Peter E. Freeman

Didier Fraix-Burnet

UJF-Grenoble / CNRS / IPAG

(2)

Dimensionality Reduction and Classification

Dimensionality Reduction to ease statistical inference to simplify interpretation

Classification to ease memory

to find relationships between objects

Adanson 1763

Dimensionality reduction reduces number of parameters

Classification reduces number of objects

Par1 Par2 Par3 Par4 ...

Object1 . . . . .

Object2 . . . . .

Object3 . . . . .

Object4 . . . . .

... . . .

(3)

Dimensionality Reduction and Classification

Dimensionality Reduction to ease statistical inference to simplify interpretation

Classification to ease memory

to find relationships between objects

Adanson 1763

Dimensionality reduction reduces number of parameters

Classification reduces number of objects

Par1 Par2 Par3 Par4 ...

Object1 . . . . .

Object2 . . . . .

Object3 . . . . .

Object4 . . . . .

... . . .

Didier Fraix-Burnet (UJF/CNRS/IPAG) SCMA-V June 2011 2 / 7

(4)

Classification and the Data Space

Why should we care about structures in the data space?

= ⇒

Object comparison

. &

Distance-based assume a metrics

Parameter-based explore the metrics

(5)

Classification and the Data Space

Why should we care about structures in the data space?

= ⇒

Object comparison

. &

Distance-based assume a metrics

Parameter-based explore the metrics

Didier Fraix-Burnet (UJF/CNRS/IPAG) SCMA-V June 2011 3 / 7

(6)

Classification and the Data Space

Why should we care about structures in the data space?

= ⇒

Object comparison

. &

Distance-based assume a metrics

Parameter-based explore the metrics

(7)

Classification and Structures in the Data Space

Continuous data space

−→

classifying

=

organizing, ordering

Tree or split-network

⇐⇒

Convexity

(cf salesman problem) Thuillard & Fraix-Burnet 2009

Didier Fraix-Burnet (UJF/CNRS/IPAG) SCMA-V June 2011 4 / 7

(8)

Finding the Right Data Space

(9)

A New Era for Astrophysics

Observation Huge databases

Theory

Huge numerical simulations

Didier Fraix-Burnet (UJF/CNRS/IPAG) SCMA-V June 2011 6 / 7

(10)

Population Analyses

Complex objects

= ⇒

Model fitting = population comparison

a new way of thinking...

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