1. Unsupervised-learning Methods for Image Clustering
Tal Berger and Avishay Shamay
Advisors: Oren Freifeld (BGU CS) and Roy Resh (Trax Image Recognition)

2. Project Goal Unsupervised clustering of product images.
Determine the number of cluster automatically.

3. problem Bounding boxes are unavailable
High variability in image quality and viewing angle

4. solution Unsupervised clustering of covariance features
we implemented two algorithms for this propose:
K – means
GMM EM - Gaussian Mixture Model and Expectation – maximization algorithm

5. Data Representation ( 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 )∈ ℝ 𝑛(𝑛+1) 2
First lets talk about what features we chose for each image and how we extract them: y
{𝑥,𝑦,𝑟,𝑔,𝑏, 𝜕𝑟 𝜕𝑥 , 𝜕𝑔 𝜕𝑥 , 𝜕𝑏 𝜕𝑥 , 𝜕𝑟 𝜕𝑦 , 𝜕𝑔 𝜕𝑦 , 𝜕𝑏 𝜕𝑦 }
𝑝 11 ⋯ 𝑝 1𝑛 ⋮ ⋱ ⋮ 𝑝 𝑚1 ⋯ 𝑝_𝑚𝑛
Create covariance matrix
Using covariance matrix symmetry
⋯ ⋮ ⋱ ⋮ ⋯
( 𝑥 1 , 𝑥 2 ,…, 𝑥 𝑛 )∈ ℝ 𝑛(𝑛+1) 2 x

6. K - means argmin 𝑆 𝑖=1 𝑘 𝑥∈ 𝑆 𝑖 𝑥− 𝜇 𝑖 2
Given a set of observations (x1, x2, …, xn), where each observation is a d-dimensional real vector, k-means clustering aims to partition the n observations into k (≤ n) sets S = {S1, S2, …, Sk} so as to minimize the within-cluster sum of square.
argmin 𝑆 𝑖=1 𝑘 𝑥∈ 𝑆 𝑖 𝑥− 𝜇 𝑖 2

7. GMM - EM
expectation–maximization (EM) algorithm is an iterative method to find maximum likelihood estimate from incomplete data.
GMM - a probabilistic model for representing the presence of subpopulations within an overall population.
Model Selection to find K using BIC:
𝐵𝐼𝐶= ln 𝑛 𝐾−2 ln 𝐿
Bayesian information criterion
© C. M. Bishop's book.

8. Conclusion and results
GMM outperforms K-means.
40 < optimal K < 60
Giving higher weights to the color features improved results.

9. Positive results

10. Negative results

11. Q & A