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How to find the actual cluster sizes in a k-means algorithm?
I’m new to clustering and I’m currently working with the k-means algorithm. When I started implementing this algorithm, I read the notion of cluster quality like this:
The quality of the clusters is approximately equal to the ratio of the
within-cluster sum of squares to the total sum of squares.
This was just an intuitive definition which I still don’t really understand.
So my question is: Why is the sum of squares in a cluster equal to the sum of the squares of that cluster (we would call these the mean squares or the expected cluster centers)? In other words, how can we calculate this quantity?
A:
When you use k-means, you are trying to minimize the following objective function:
$J_{k-means} = \sum_{i=1}^{n} \sum_{j=1}^{k} (x_{i} – \mu_{j})^2$
Where $x_i$ represents the centroid of the $i$-th cluster (the cluster means) and $\mu_j$ represents the clustering center of the $j$-th cluster (the cluster centers).
The actual cluster sizes are unknown to you, so you need to guess the cluster means and the cluster centers (i.e. the centers of the clusters in your data). Note that these are just estimates, so they may not be what you intend.
If you apply the k-means algorithm to this data $x$, where $x$ is a real data matrix, then you will find that clusters will be formed where each cluster center will be near the group of data which belong to that group of points.
In order to calculate the actual cluster sizes, you will need the sum of the squares of the actual cluster centers (the cluster means) or you will need to estimate the actual cluster centers (using the actual cluster sizes).
A:
Your question (with my emphasis):
How can we calculate this quantity?
This is nothing
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A:
EDIT: It was very imprecise, since I mixed up the locations that I had ransomed, while they are geographically disjoint (and, in fact, seem to have been based on OS X versions) I’m leaving this answer and will try to look for some sort of upstream answer.
So, I got into a situation where I needed to go after a couple of documents that I had put on DropBox (and moved to a new hard disk to which I then moved DropBox), despite the fact that I had not backed the files up. I did the following:
First I ran Dropbox to find the full Dropbox.log file that contained the logs of the Ransom transactions.
After opening it in a text editor I found what seemed to be a transaction id starting with QJJ….
I immediately ran the following commands:
$ curl -s “” | python -c ‘import mechanize; mechanize.Browser().open(“sek.ru” + mechanize.Browser().open(“”)’
That seems to be a way to determine a transaction ID from a file with one of the usually encoded gibberish characters.
A:
Don’t you mean this file?
download the archive file: recuva.archive.zip
extract it.
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