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@@ -15,7 +15,7 @@ The number of clusters or the number of centroids determine the vocabulary size
## Bag-of-words histogram quantisation of descriptor vectors
-An example histogram for training image shown on figure \ref{fig:histo_tr}, computed with a vocubulary size of 100. A corresponding testing image of the same class is shown in figure \ref{fig:histo_te}. The histograms appear to have similar counts for the same words, demonstrating they had a descriptors which matched the *keywowrds* in similar proportions. We later look at the effect of the vocubalary size (as determined by the number of K-mean centroids) on the classificaiton accuracy in figure \ref{fig:km_vocsize}.
+An example histogram for training image shown on figure \ref{fig:histo_tr}, computed with a vocubulary size of 100. A corresponding testing image of the same class is shown in figure \ref{fig:histo_te}. The histograms appear to have similar counts for the same words, demonstrating they had a descriptors which matched the *keywowrds* in similar proportions. We later look at the effect of the vocubalary size (as determined by the number of centroids) on the classificaiton accuracy in figure \ref{fig:km_vocsize}.
The time complexity of quantisation with a K-means codebooks is $O(n^{dk+1})$ , where n is the number of entities to be clustered, d is the dimension and k is the cluster count [@km-complexity]. As the computation time is high, the tests we use a subsample of descriptors to compute the centroids. An alternative method is NUNZIO PUCCI WRITE HERE