This document summarizes a research paper on multi-scale fusion subspace clustering using similarity constraints. The paper proposes a new network that uses multiple self-expressive layers at different scales. It introduces a multi-scale fusion module to combine the self-expression coefficient matrices from different layers. Additionally, it includes a similarity constraint module to guide the training of the fused coefficient matrix. The network is tested on object and face clustering datasets and compared to other subspace clustering methods. Experimental results analyze the impact of different loss functions, fusion methods, and kernel initialization approaches.

1. Multi-Scale Fusion Subspace
Clustering Using Similarity
Constraint
2020.08.24
국민대 HCI 연구실
백상원

2. Outline
• Abstract
• Subspace clustering
• Keyword
• Multi Scale Clustering

3. Subspace clustering
• Classical subspace clustering methods often assume that the raw form data lie in
a union of the low-dimension linear subspace.
• 차원의 저주
• 차원이 늘어남에 따라 학습에 필요한 데이터의 양이 기하급수적으로 증가

4. Subspace clustering
• Deep Subspace clustering Network (2017, Nips)
• Deep auto-encoder
• Non-linear map raw data
• Self-expressive layer

5. Spectral clustering
• Clustering of graph theory
• Non-linear Clustering

6. Spectral clustering
1. Affinity matrix A (adjacency/similarity matrix) construction
• Affinity: Use of Gaussian kernel
2. Feature vector extraction using Laplacian matrix L
I. L=D-A (D: Degree matrix)
II. Eigen-decomposition of L

7. Keyword
• Multi-Scale layers Feature
• Multi-Scale Fusion Module for self-expression coefficient
matrix
• Similarity module to guide the fused self-expression
coefficient matrix in training

8. Network 구조 비교
Deep Subspace clustering network(2017, Nips) Multi-Scale Fusion Subspace Clustering Using Similarity Constraint(2020, CVPR)
• Encoder
• Decoder
• Self-expressive layer
• Encoder
• Decoder
• Self-expressive layers
• Multi-scale module
• Similarity Constraint Module
• Channel Fusion layer

9. Multi-Scale Fusion Module & Similarity Module
• Multi-Scale Fusion Module
• Stacked each Coefficient Matrix
• Using NxN kernel 1 layer
• Channel Fusion
• Similarity Module
• 겹쳐진 Coef Matrix를 합
• Denoise, 0~1 사이의 값은 모두 0
• Similarity Matrix

10. Loss Function 비교(DSC)
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£4
£1
£3
£2
DSC SC-MSFSC
Recon Loss
1
2
𝑋 − ෠
𝑋 𝐹
2 1
2
෍
𝑙
𝐿
𝑋𝑙 − ෠
𝑋𝑙 𝐹
2
+
1
2
𝑋𝐿 − ෠
𝑋𝐹 𝐹
2
𝐿: 𝑙𝑎𝑠𝑡 𝑙𝑎𝑦𝑒𝑟
෠
𝑋𝐹: fusion recon
𝐶 𝐹
2
෍
𝑙
𝐿
𝐶𝑙 𝐹
2
+ 𝐶𝐹 𝐹
2
෠
𝑋𝑙: L layer recon
1
2
𝑍 − 𝑍𝐶 𝐹
2
1
2
෍
𝑙
𝐿
𝑍𝑙 − 𝑍𝑙𝐶𝑙 𝐹
2
1
2
𝑍 − 𝑍𝐶𝐹 𝐹
2
𝐶𝐹: Fusion Coef
l ∶ l layer
𝐶𝑙: layer Coef
𝐶𝐷𝑒 − 𝐶𝐹 𝐹
2
Reg loss
self-expression
loss
Fuse Self loss
Similarity
constraint loss
𝐶𝐷𝑒: Denoise Coef

11. 실험
• Coil 20 , Coil100 Object Clustering
• ORL, EyaleB Face Clustering

12. 실험
• Loss 별 분석

13. 실험
Layer 별 Loss 비교
Fusion Method Loss 비교
Kernel 초기화 방법 Loss 비교