549 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 ...
94k 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? ...
117k 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 ...
19k 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 ...
40k 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 ...
9k 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 ...
28k 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 ...
8k 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: ...
6k 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 ...
12k 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 ...
15k 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 ...
1k 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 (...
9k 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{...
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, ...
I have an expression for a covariance matrix $C$ in terms of the indices $i$ and $j$. In this way I can analytically calculate the elements of my covariance matrix, however when I try to invert $C$ ...