All Questions
12 questions
2
votes
0
answers
370
views
How does this prove that the objective function in K-means clustering never increases?
I am reading the ISLR textbook (pg. 518-519, 12.4) and having trouble understanding why K-means clustering never increases. I can understand it conceptually but I don't understand the mathematical ...
- 21
2
votes
2
answers
72
views
How to make clusters (consisting of demands) equal to the load of a truck?
I am working on a routing problem where I have thousands of points (places) with individual demands (in Weight and Volume).
So far I have created 5 clusters based on their location. Now I need to ...
- 200
0
votes
1
answer
193
views
How can one compute the "average" of a dataset of histograms that minimizes the mean Earth Mover's Distance between all data points and average?
It is my understanding that when the distance metric is euclidean distance, the mean of a dataset minimizes the average distance between all data points and the computed "mean".
In the case ...
1
vote
1
answer
27
views
clustering with equal elements
Assume that we have a set of observations: $\mathbf{X} = \{x_{1}, \dots, x_{n}\}\subseteq \mathbb{R}^{d}$, containing $n$ observations for a fixed dimensionality $d$. Assume, we have some fixed ...
- 668
1
vote
0
answers
318
views
Deterministic Methods to Initialize K-Means and K-Medoids Clustering Methods
I am looking for effective and deterministic methods to initialize K-Means and K-Medoids algorithms.
There is a great answer in Methods of initializing K-Means Clustering yet most of them has some ...
- 1,155
0
votes
1
answer
413
views
How to find better solutions for the k-means problem than by using the k-means/k-means++ algorithm?
The $k$-means problem in its common form can be stated as follows:
Given a data set $\mathcal{X}=x_1, ..., x_n$ consisting of $d$-dimensional vectors find a set $C = c_1,...,c_k$ of $d$-dimensional ...
- 113
3
votes
1
answer
106
views
Is Marina Meila's work "The Uniqueness of a Good Optimum for K-Means" a general result applicable to other clustering algorithms as well?
In this paper, a bound on the “error subspace” projection is established, which is then used to show that any two clusterings with small distortion are close. Which immediately follows that, if a good ...
- 261
1
vote
1
answer
46
views
K mean clustering
I have coordinates data set (X.Y) with an additional attribute "Z". I want to cluster the data into 5 clusters based on X and Y but I want to add some constrains on how much the sum of "Z" can be at ...
5
votes
1
answer
4k
views
Why do we merge "close" clusters post-processing in k-means clustering?
My professor mentioned that we may merge "close" clusters (those with relatively low sum of squared errors) after k-means clustering. However, I don't see the benefit in doing this. If a cluster has ...
- 437
2
votes
1
answer
61
views
Covering 2D data by m squares (alternative to k-means)
Let us have some data $x_i\in\mathbb{R}^2$ for $i=1,\dots,n$. Let $m=1000$. Let a small number is given, e.g. $m=5$.
The goals is to cover $n$ data by $m$ squares of the same size. The size shall be ...
- 2,846
2
votes
1
answer
142
views
Unnatural clustering with known clusters shapes and optimization criteria
My question is similar to this question Clustering with shape prior, but with additional information.
The second answer suggests a mixture model approach to this problem, which is something like ...
- 75
4
votes
1
answer
3k
views
Why is k-medians typically used with Manhattan rather than Euclidean distance?
K-medians is typically used with Manhattan distance rather than Euclidean distance. Why is this?
- 193