Classification and the Geometric view of data

Class 1

January 22th, 2020

Data Science: Techniques and Applications (DSTA)

Classification

Classifying iris flowers

Linear discriminant classification
high-quality, annotated dataset

technique and data are interwined!

(was 1) Classification and class probability

Definition

Instance:

datapoints over d-1 numerical dimensions $\mathcal{D_1,} \dots \mathcal{D_{d-1}}$
a classification function over k categories

Solution:

a linear combination $\mathcal{D_1} \times \mathcal{D_2} \times \dots \mathcal{D_{d-1}}\rightarrow \mathcal{D_d}$

that respects the given classification.

Instance:

datapoints over d-1 numerical dimensions $\mathcal{D_1,} \dots \mathcal{D_{d-1}}$
a classification function over k categories

Solution:

a linear combination $\mathcal{D_1} \times \mathcal{D_2} \times \dots \mathcal{D_{d-1}}\rightarrow \mathcal{D_d}$

Measure

agreement with the given classification.

Discussion

Can we accept a linear combination that gives the correct answer only 19 times over 20?

It depends on the application.

Given two putative classifiers, which is the best?

Proposed answer:

At the same level of precision, the one that ``errs’’ less on the clear-cut cases.

The Geometric view of data

An introduction

Please follow up on slides adapted from Zaki-Meira textbook.

Classification and the Geometric view of data Class 1 January 22th, 2020