---
# System prepended metadata

title: Validation update

---

# Validation update

## Experiments setting
- dataset: celeb_A (male, straight hair)
- dataset size: 256
- generative size: 512
- loss function: $MSE(1, \ K_{valid, train} K_{train, train}^{-1}(I-e^{- \eta t K_{train, train}}))$
## Algorithm
Let $x_{train}$ be the training data
1. Random split generative data into $x_{noise}^{valid}$ and $x_{noise}^{train}$
2. Get kernel matrix:
    - training set: [$x_{train}, x_{noise}^{train}$]
    - validating set: $x_{noise}^{valid}$
    - $K_{train, train}$: kernel matrix of training set
    - $K_{valid, train}$: kernel matrix of validating set and training set
4. Update validation set with loss function for $k$ steps.
5. Repeat 1. 2. 3.

## 只 random split 一次，update 直到 converge
- k = 100, iteration = 100
![](https://i.imgur.com/SQ3CeyO.png)
- k = 200, iteration = 200
![](https://i.imgur.com/4oD9U25.png)
- k = 400, iteration = 400
![](https://i.imgur.com/QyYRRl8.png)
- k = 800, iteration = 800
![](https://i.imgur.com/edXS5Ux.png)
- k = 1600, iteration = 1600
![](https://i.imgur.com/43cocYZ.png)
- k = 3200, iteration = 3200
![](https://i.imgur.com/ThlPxfv.png)
- 圖像確實會隨著 iteration 越多越往人臉靠近。目前看來，僅 random split 一次，就算是提高 iteration也不能獲得完整的 pattern。

## 固定 random split 次數, 改動 k-step
- random split 次數皆為 500 次
- k = 100, iteration = 50000
![](https://i.imgur.com/OCI1pxy.png)

- k = 200, iteration = 100000
![](https://i.imgur.com/hsRO9KS.png)

- k = 400, iteration = 200000
![](https://i.imgur.com/jE9fnGk.png)

- k = 800, iteration = 400000
![](https://i.imgur.com/OCc2TMR.png)

- 有人臉的形狀，但是是模糊的。目前觀察不出 k 對圖片的影響性。
- 經過測試之後少部分圖像不太有 creativity。但其他圖片太過模糊，很難比較相似性。
    - 以 k = 800 為例，左上角圖為生成的人臉，下圖(左上一)與(左上二)重複
![](https://i.imgur.com/GWc69PW.png)

