Question

I have a dataset of n data, where each data is represented by a set of extracted features. Generally, the clustering algorithms need that all input data have the same dimensions (the same number of features), that is, the input data X is a n*d matrix of n data points each of which has d features.
In my case, I’ve previously extracted some features from my data but the number of extracted features for each data is most likely to be different (I mean, I have a dataset X where data points have not the same number of features).
Is there any way to adapt them, in order to cluster them using some common clustering algorithms requiring data to be of the same dimensions.

Thanks

Answer 1

Sounds like the problem you have is that it’s a ‘sparse’ data set. There are generally two options.

1. Reduce the dimensionality of the input data set using multi-dimensional scaling techniques. For example Sparse SVD (e.g. Lanczos algorithm) or sparse PCA. Then apply traditional clustering on the dense lower dimensional outputs.

2. Directly apply a sparse clustering algorithm, such as sparse k-mean. Note you can probably find a PDF of this paper if you look hard enough online (try scholar.google.com).

[Updated after problem clarification]

In the problem, a handwritten word is analyzed visually for connected components (lines). For each component, a fixed number of multi-dimensional features is extracted. We need to cluster the words, each of which may have one or more connected components.

Suggested solution:

Classify the connected components first, into 1000(*) unique component classifications. Then classify the words against the classified components they contain (a sparse problem described above).

*Note, the exact number of component classifications you choose doesn’t really matter as long as it’s high enough as the MDS analysis will reduce them to the essential ‘orthogonal’ classifications.