Loading in 5 sec....

Minkowski (Family of) DistancesPowerPoint Presentation

Minkowski (Family of) Distances

- By
**flo** - Follow User

- 152 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Minkowski (Family of) Distances' - flo

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Minkowski (Family of) Distances

Put in eqn (for cluster and mds, or just mds?)

- Minkowski distances
- i&j are stimuli, k=dims (r of them)
- q=2? Euclidean distance (as the crow flies)
- model of psych processing? No, but easy & useful w data
- q=1 “city block” distance
- model? More compensatory
- q=∞ “dominance” distanc
- largest diff betw 2 points on any dim is the only relevant one.
- psych processing? Maybe, e.g., “diet drink vs. not” >important than other qualities. Least compensatory.

Family of Distances

Minkowski distances

i&j are stimuli, k=dims (r of them)

q=2? Euclidean distance (as the crow flies)

model of psych processing? No, but easy & useful w data

q=1 “city block” distance

model? More compensatory

q=∞ “dominance” distance

largest diff betw 2 points on any dim is the only relevant one.

psych processing? Maybe, e.g., “diet drink vs. not” >important than other qualities. Least compensatory.

Dissimilarities // Distance, So…

Stimulus: point A has coordinates (XA1, XA2).

point B has coordinates (XB1, XB2)

(subscripts are: first=stimulus, second=dimension)

Define

for r > 2 dimensions:

#dimensions

Distances

j

i

j

k

i

k

P

2

2

DP

C

- Non-negativity & equivalence
- dij>0
- dii = djj = 0
- dij = 0 only if points i&j coincide (on all r dims)

- Symmetry
- dij = dji
- Ok in geometry, but in data, ?
- E.g., How similar is Cuba to Russia? How similar is Russia to Cuba?
- E.g., How similar is store-brand to Coke? How similar is Coke to store-brand?
- Fix: “How similar are Coke and Pepsi”

- Triangle Inequality
- dik<dij + djk
- dik=dij + djk
- dik<dij + djk
- > is not possible
- Will it hold in data? Not necessarily: Pepsi & Coke 2, Pepsi & DietPepsi 2, Coke & DietPepsi 5

5>2+2

Download Presentation

Connecting to Server..