Joint Unsupervised Learning of Deep Representations and Image Clusters Supplementary materials
نویسندگان
چکیده
This supplementary materials explain some implementation details and present additional experiments that are complementary to our main paper ”Joint Unsupervised Learning of Deep Representations and Image Clusters”. The source code for this work can be downloaded from https://github.com/jwyang/ joint-unsupervised-learning. 1. Affinity Measure for Clusters In this paper, we employ the affinity measure in [13] A(Ci, Cj) = A(Cj → Ci) +A(Ci → Cj) = 1 |Ci| 1T|Ci|WCi,CjWCj ,Ci1|Ci| + 1 |Cj |2 1T|Cj |WCj ,CiWCi,Cj1|Cj | (1) where W is the affinity matrix for samples, and WCi,Cj ∈ R|Ci|×|Cj | is the submatrix in W pointing from samples in Ci to samples in Cj , and WCj ,Ci ∈ R|Cj |×|Ci| is the one pointing from Cj to Ci. 1|Ci| and 1|Cj | are two vectors with all |Ci| and |Cj | elements be 1, respectively. Therefore, we have A(Ci, Cj) = A(Cj , Ci). According to (1), we can derive A((Cm ∪ Cn)→ Ci) = A(Cm → Ci) +A(Cn → Ci) (2) which has also been shown in [13]. Meanwhile, A(Ci → (Cm ∪ Cn)) = β1T|Cm|+|Cn|WCm∪Cn,CiWCi,Cm∪Cn1|Cm|+|Cn| = β1T|Cm|WCm,CiWCi,Cm1|Cm| + β1 T |Cn|WCn,CiWCi,Cn1|Cn| + β1T|Cm|WCm,CiWCi,Cn1|Cn| + β1 T |Cn|WCn,CiWCi,Cm1|Cm| (3) where β = 1/(|Cm|+ |Cn|). 2. Approximated Affinity Measure During agglomerative clustering, we need to re-compute the affinity between the merged cluster to all other clusters based on 2 and 3 repeatedly. It is simple to compute 2. However, to get A(Ci → (Cm∪Cn)), we need a lot of computations. These time costs become dominant and remarkable when we have a large-scale dataset. To accelerate the computations, we introduce an approximation method. At the right side of (3), we assume samples in Cm and Cn have similar affinities to Ci. This assumption is mild because the condition to merge Cm and Cn is that they are similar to each other. In this case, the ratio betweenWCi,Cm1|Cm| and WCi,Cn1|Cn| is analogy to the ratio between the number of samples in two set, i.e., WCi,Cm1|Cm| = |Cm| |Cn| WCi,Cn1|Cn| (4) Based on (4), we can re-formulate (3) to
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