Linked Questions
21 questions linked to/from k-means implementation with custom distance matrix in input
3
votes
1
answer
1k
views
Can I use k-means with a distance matrix composed of percentages? [duplicate]
I have objects o1, o2,...,on and for each pair I calculate a value that measures the pair's difference. This is a percentage, so for example o1o2 differ by 56%. Now I want to cluster this data. I can ...
- 143
97
votes
6
answers
172k
views
Why does k-means clustering algorithm use only Euclidean distance metric?
Is there a specific purpose in terms of efficiency or functionality why the k-means algorithm does not use for example cosine (dis)similarity as a distance metric, but can only use the Euclidean norm? ...
- 1,111
112
votes
5
answers
237k
views
Loadings vs eigenvectors in PCA: when to use one or another?
In principal component analysis (PCA), we get eigenvectors (unit vectors) and eigenvalues. Now, let us define loadings as $$\text{Loadings} = \text{Eigenvectors} \cdot \sqrt{\text{Eigenvalues}}.$$
I ...
- 1,429
62
votes
4
answers
73k
views
Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite?
I have been researching the meaning of positive semi-definite property of correlation or covariance matrices.
I am looking for any information on
Definition of positive semi-definiteness;
Its ...
- 629
31
votes
8
answers
36k
views
Perform K-means (or its close kin) clustering with only a distance matrix, not points-by-features data
I want to perform K-means clustering on objects I have, but the objects aren't described as points in space, i.e. by objects x features dataset. However, I am able ...
- 313
22
votes
9
answers
12k
views
Pairwise Mahalanobis distances
I need to calculate the sample Mahalanobis distance in R between every pair of observations in a $n \times p$ matrix of covariates. I need a solution that is efficient, i.e. only $n(n-1)/2$ distances ...
- 1,409
23
votes
4
answers
56k
views
Euclidean distance score and similarity
I'm just working with the book Collective Intelligence (by Toby Segaran) and came across the Euclidean distance score. In the book the author shows how to calculate the similarity between two ...
- 345
39
votes
2
answers
21k
views
Understanding distance correlation computations
As far as I understood, distance correlation is a robust and universal way to check if there is a relation between two numeric variables. For example, if we have a set of pairs of numbers:
...
- 724
30
votes
1
answer
25k
views
Converting similarity matrix to (euclidean) distance matrix
In Random forest algorithm, Breiman (author) constructs similarity matrix as follows:
Send all learning examples down each tree in the forest
If two examples land in the same leaf increment ...
- 487
19
votes
4
answers
9k
views
Is it ok to use Manhattan distance with Ward's inter-cluster linkage in hierarchical clustering?
I am using hierarchical clustering to analyze time series data. My code is implemented using the Mathematica function DirectAgglomerate[...], which generates ...
- 191
10
votes
2
answers
27k
views
K-means: Why minimizing WCSS is maximizing Distance between clusters?
From a conceptual and algorithmic standpoint, I understand how K-means works. However, from a mathematical standpoint, I don't understand why minimizing the WCSS (within-cluster sums of squares) will ...
- 504
7
votes
2
answers
19k
views
Gower's (dis)similarity index
I would like to ask a question about Gower similarity/dissimilarity index.
Is it ok to use the Gower dissimilarity measure with Ward linkage clustering?
I was reading that the Gower similarity index ...
- 71
9
votes
2
answers
2k
views
Does a distance have to be a "metric" for an hierarchical clustering to be valid on it?
Let us say that we define a distance, which is not a metric, between N items.
Based on this distance we then use an Agglomerative hierarchical clustering.
Can we use each of the known algorithm (...
- 21.9k
7
votes
4
answers
12k
views
Pairwise Mahalanobis distance in R [duplicate]
I'm trying to calculate a Mahalanobis-type pairwise distance matrix in R. I have 33 individuals, each with 10 variables. The idea is to get a distance matrix D, where
$$D_{i,j}=(\mathbf{X}_i-\mathbf{...
- 183
6
votes
2
answers
7k
views
Sums-of-Squares (total, between, within): how to compute them from a Distance Matrix?
I am having trouble understanding the concept of Sum of Squares in the context of distance matrices (Studer et al. 2010).
The Sum of Squares I am familiar with is the classical $SS$ from ANOVA, ...
- 911