[Paper Review] Invariant Information Clustering for Unsupervised Image Classification and Segmentation(2018)

Invariant Information Clustering for Unsupervised Image Classification and Segmentation

Xu Ji, Joao F.Henriques, Andrea Vedaldi, arXiv 2018

 

PDF, Clustering By SeonghoonYu July 30th, 2021

 

Summary

 

 This paper presents IIC model which acieves SOTA performance on Image clustering and Image segmentation by maximizing the mutual information between the original image and the transformed image from original image.

 

 

 Optional overclustering is to learn useful representations from the noisy unlabelled subset.

 

(1) Image Clustering

 maximizing the mutual information between encoded variables.

 

 

 Calculate the joint probability distributions matrix P, where each element at row c and column c' constitutes $P_{cc'} = P(z=c,z'=c')$

 

 

 symetrize

 

 

 

 

(2) Image Segmentation  

 

 They maximize the mutual information between image patches on image segmentation task.

 

(3) Degenerate solutions are avoided

 Avoid degenerate solutions that other clustering methods are susceptible to by using the mutual information.

 

 

 

 Maximizing I(z,z') trade-off minimizing the conditional cluster assignment entropy H(zlz') and maximising individual cluster assignments entropy H(z). The smallest value of H(zlz') is 0, obtained when the cluster assignments are exactly predictable from each other. The largest value of H(z) is lnC, obtained when all clusters are equally likely to be picked. This occurs when the data is assigned evenly between the clusters, equalizing their mass.

 

 simese 기반 모델인데 contrastive loss라는게 기본적으로 P(y=i l x', x_i) 형태로 나온다. 어떤 말이냐면 negative set에서 affine transform된 자신을 찾을 수 있어야 로스값이 내려가는 구조. 이게 H(z;z')가 최소값.

 

 H(z)이 최대값이 되려면 모든 cluster가 균일하게 pick되는 경우인데, 이는 p(z)가 uniform 하다는 것을 의미함. p(z)이 유니폼할때 H(z) = 평균(log(p(z)))에서 최대값이 되나?

 

Experiment

 

What I like about the paper

• avoid degenerate problems that other clustering methods are susceptible to by using the mutual information
• interesting solving unsupervised image segmentation task using clustering

 

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my github about what i read

Seonghoon-Yu/Paper_Review_and_Implementation_in_PyTorch