Homework Help is Here – Start Your Trial Now!
Math
Statistics
Is the average squared distance between two clusters equal to the squared distance of the difference in the two centroids? Σ E-x where C and C₂ are two different clusters. Simplify For simplicity, use the Euclidean distance for x-x¹^|| Choose all expressions below that are equal to the above expression. 0 x _L [l|m-Mall² 1 Σ Σ (x-μ₂₁) + (A^₂ -M₂) (x (¹) M₂)||² Σ Σ (x-μ₁² + M₁-M₂||²+ ||x¹M₂)||²³)

Is the average squared distance between two clusters equal to the squared distance of the difference in the two centroids? Σ E-x where C and C₂ are two different clusters. Simplify For simplicity, use the Euclidean distance for x-x¹^|| Choose all expressions below that are equal to the above expression. 0 x _L [l|m-Mall² 1 Σ Σ (x-μ₂₁) + (A^₂ -M₂) (x (¹) M₂)||² Σ Σ (x-μ₁² + M₁-M₂||²+ ||x¹M₂)||²³)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

Please help with the understanding of this concept having trouble. Provide Final answer and explanation for understanding.

Is the average squared distance between two clusters equal to the squared distance of the difference in the two centroids? 1 Simplify Σ Σxxwhere C₁ and C₂ are two different clusters. 72172₂ For simplicity, use the Euclidean distance for x - x|| Choose all expressions below that are equal to the above expression. X 1 Σ Σma-pelle 1110₂ 2020 20₂ 1 121702 1 11 12 Σ Σ(x-₂) + (1₂−µ₂) — (x(³) — µ₂)||² Σ Σ (x-μ₂||²+₂ M₂||²+ ||Xx²¹ μµ₂₁)|| ²)
Transcribed Image Text:Is the average squared distance between two clusters equal to the squared distance of the difference in the two centroids? 1 Simplify Σ Σxxwhere C₁ and C₂ are two different clusters. 72172₂ For simplicity, use the Euclidean distance for x - x|| Choose all expressions below that are equal to the above expression. X 1 Σ Σma-pelle 1110₂ 2020 20₂ 1 121702 1 11 12 Σ Σ(x-₂) + (1₂−µ₂) — (x(³) — µ₂)||² Σ Σ (x-μ₂||²+₂ M₂||²+ ||Xx²¹ μµ₂₁)|| ²)
Hierarchical Clustering Hierarchical clustering does not start with a fixed chosen number of clusters, but builds a hierarchy of clusters with different levels corresponding to different numbers of clusters. We can use a bottom-up or top-down approach: • Agglomerative clustering (Bottom-Up) • Divisive clustering (Top-down) We will only discuss the bottom-up approach. Agglomerative Clustering (Bottom-Up approach) Agglomerative clustering starts with 1 data point per cluster, and at each consequent stage, merges pairs of clusters that are the closest together according to a dissimilarity measure between clusters. This merging can be depicted by a tree, also known as a dendrogram. The bottom-most level has n clusters (of 1 observation each), and as merging occurs as the levels go up, the number of clusters decreases, and the top-most level has only 1 cluster (encompassing all observations). See the recitation in this module for an example of hierarchical clustering and the associated dendrogram. Dissimilarity between clusters In order to choose which pair of clusters to merge at each stage, we need to define a dissimilarity measure between clusters, and the dissimilarity measure between clusters is often based on dissimilarity between points. A few commonly used distances between individual points are: • -norm, i.e. the usual Euclidean distance (x,x) = √√(x − ¹)* + (x − xª)* + +...+ ¹-norm (also known as Manhattan distance) (xx) = + | − | + + | − | -norm, Le. the maximum distance among all coordinates d(x,x)= max d(x,x) 20(positivity) d(x,x!) (x²)x(i) • Other dissimilarity measures d (x,x) that do not satisfy all properties of distances, but still meet the following criteria: Now we can define dissimalarity measures between clusters: d (C₁, C₂) - d (x²), x)) d(C₁,C₂) = • Minimum distance between points in the two clusters, also known as single linkage: d(C₁,C₂) min -24 (x1) =RP) max * EDEC 1 7172 (symmetry) • Maximum distance between points in the two clusters, also known as complete linkage: d(x,x). (x²) d(x,x). • Average distance between points in the two different clusters, also known as average linkage ΣΣ d(x,x).
Transcribed Image Text:Hierarchical Clustering Hierarchical clustering does not start with a fixed chosen number of clusters, but builds a hierarchy of clusters with different levels corresponding to different numbers of clusters. We can use a bottom-up or top-down approach: • Agglomerative clustering (Bottom-Up) • Divisive clustering (Top-down) We will only discuss the bottom-up approach. Agglomerative Clustering (Bottom-Up approach) Agglomerative clustering starts with 1 data point per cluster, and at each consequent stage, merges pairs of clusters that are the closest together according to a dissimilarity measure between clusters. This merging can be depicted by a tree, also known as a dendrogram. The bottom-most level has n clusters (of 1 observation each), and as merging occurs as the levels go up, the number of clusters decreases, and the top-most level has only 1 cluster (encompassing all observations). See the recitation in this module for an example of hierarchical clustering and the associated dendrogram. Dissimilarity between clusters In order to choose which pair of clusters to merge at each stage, we need to define a dissimilarity measure between clusters, and the dissimilarity measure between clusters is often based on dissimilarity between points. A few commonly used distances between individual points are: • -norm, i.e. the usual Euclidean distance (x,x) = √√(x − ¹)* + (x − xª)* + +...+ ¹-norm (also known as Manhattan distance) (xx) = + | − | + + | − | -norm, Le. the maximum distance among all coordinates d(x,x)= max d(x,x) 20(positivity) d(x,x!) (x²)x(i) • Other dissimilarity measures d (x,x) that do not satisfy all properties of distances, but still meet the following criteria: Now we can define dissimalarity measures between clusters: d (C₁, C₂) - d (x²), x)) d(C₁,C₂) = • Minimum distance between points in the two clusters, also known as single linkage: d(C₁,C₂) min -24 (x1) =RP) max * EDEC 1 7172 (symmetry) • Maximum distance between points in the two clusters, also known as complete linkage: d(x,x). (x²) d(x,x). • Average distance between points in the two different clusters, also known as average linkage ΣΣ d(x,x).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS