Model selection for cluster data analysis
View Patent ↗A model selection method is provided for choosing the number of clusters, or more generally the parameters of a clustering algorithm. The algorithm is based on comparing the similarity between pairs of clustering runs on sub-samples or other perturbations of the data. High pairwise similarities show that the clustering represents a stable pattern in the data. The method is applicable to any clustering algorithm, and can also detect lack of structure. We show results on artificial and real data using a hierarchical clustering algorithm.
1. A computer implemented method for clustering data comprising a plurality of letters within text or speech, the method comprising:
(a) inputting the data into a computer system having a memory and a processor for executing a clustering algorithm;
(b) selecting a clustering algorithm based on a dissimilarity measure between pairs of the letters' principal components;
(c) randomly assigning class labels to the letters;
(d) defining a plurality of clusters of letters within each labeled class;
(e) measuring dissimilarity between each cluster of letters by measuring a residual of a fit of one cluster onto another cluster, wherein the residual fit comprises using a fit that is invariant with respect to affine transformations, wherein the affine transformations comprise a combination of translation, scaling and rotation;
(f) reassigning letters to the labeled class with the most similar cluster;
(g) repeating steps (d) through (f) until assignment of letters to the labeled classes remains constant; and
(h) displaying a graph showing the letters clustered into the labeled classes.
2. The method of claim 1 wherein the clustering algorithm is a k-means algorithm.
3. A computer implemented method for clustering patterns in a dataset comprising letters in text or speech, the method comprising:
inputting the dataset into a computer system having a memory and a processor for executing a clustering algorithm;
selecting a plurality of granularity levels k, and for each granularity level k:
(a) inducing perturbations in the dataset to generate a modified dataset;
(b) applying the clustering algorithm to the at least one modified dataset to produce k clusters under each of the perturbations;
(c) creating a data subset comprising the clusters identified in step (b);
(d) applying the clustering algorithm to the data subset using the same value of k clusters;
(e) determining the stability of the clusterings at each granularity level k by measuring dissimilarity between data in the data subset and the cluster center for the cluster into which the data was assigned;
measuring fit of the data to the cluster centers for all k granularity levels, wherein the fit comprises using a fit that is invariant with respect to affine transformations, wherein the affine transformations comprise a combination of translation, scaling and rotation;
selecting from among the plurality of granularity levels an optimum granularity level k corresponding to the best fit;
generating an output comprising the dataset clustered into a plurality of subsets corresponding to the optimal granularity level k; and
displaying a graph showing the letters of the text or speech clustered into the plurality of subsets.
4. The method of claim 3 , wherein the perturbations comprise a combination of one or more of sub-sampling the dataset, changing initialization of the clustering algorithm, and adding noise to the dataset.
5. A computer implemented method for clustering patterns in a dataset comprising letters in text or speech, the method comprising:
inputting the dataset into a computer system having a memory and a processor for executing a clustering algorithm;
randomly assigning labels to the letters in the dataset by partitioning the dataset into k subsets, wherein k has a minimum number and a maximum number;
for each value of k, beginning with the minimum value, for each pair of subsets,
computing a correlation score on the intersection between the pair of subsets, wherein the correlation score comprises a similarity measure between the pair of subsets and the greatest similarity has the highest score; and displaying a histogram comprising a distribution of the correlation scores for each value of k, wherein the distribution comprising the highest value of k that remains concentrated near the highest correlation score corresponds to a clustering of the letters according to their actual labels.
6. The method of claim 5 , wherein the step of computing the correlation score comprises selecting a fraction of the letters in each subset for comparison with other subsets.
7. The method of claim 5 , wherein the fraction is greater than 0.5.