andy
b24f551589
Affected files: .obsidian/backlink.json .obsidian/graph.json .obsidian/workspace-mobile.json .obsidian/workspace.json Events/🪣🪣🪣.md Health/ADHD.md STEM/AI/Classification/Gradient Boosting Machine.md STEM/AI/Neural Networks/CV/Visual Search/Visual Search.md STEM/AI/Neural Networks/Learning/Tasks.md STEM/AI/Pattern Matching/Dynamic Time Warping.md STEM/AI/Problem Solving.md STEM/CS/Regex.md STEM/img/dtw-graph-unit.png STEM/img/dtw-graph.png STEM/img/dtw-gross-partitioning.png STEM/img/dtw-heatmap-distortion.png STEM/img/dtw-heatmap.png STEM/img/dtw-possible-movements.png STEM/img/dtw-score-pruning.png STEM/img/nn-tasks-function-approx-inverse.png STEM/img/nn-tasks-function-approx.png STEM/img/nn-tasks-pattern.png STEM/img/problem-solving-arch.png STEM/img/problem-solving-goal-based.png STEM/img/problem-solving-reflex.png STEM/img/visual-search-arch.png STEM/img/visual-search-crude.png
73 lines
3.1 KiB
Markdown
73 lines
3.1 KiB
Markdown
***Deterministic
|
|
Pattern Recogniser***
|
|
Allows timescale variations in sequences for same class
|
|
|
|
|
|
|
|
$$D(T,N)=\min_{t,i}\sum_{\substack{t\in1..T \\ i\in1..N}}d(t,i)$$
|
|
- $d(t,i)$ is distance between features from $t$-th frame of test to $i$-th frame of template
|
|
|
|
$$D(t,i)=\min[D(t,i-1),D(t-1, i-1),D(t-1,i)]+d(t,i)$$
|
|
- Allowing transition from current and previous frame only
|
|
- Recursive
|
|
|
|
|
|
|
|
# Problems
|
|
- How much flexibility to allow?
|
|
- How to penalise warping?
|
|
- How to determine a fair distance metric?
|
|
- How many templates to register?
|
|
- How to select best ones?
|
|
|
|
# Basic Algorithm
|
|
1. Initialise the cumulative distances for $t=1$
|
|
$$D(1,i)=\begin{cases}d(1,i) & \text{for }i=1, \\ D(1, i-1)+d(1,i) & \text{for }i=2,...,N\end{cases}$$
|
|
2. Recur for $t=2,...,T$
|
|
$$D(t,i)=\begin{cases}D(t-1,i) + d(t,i) & \text{for }i=1, \\ \min[D(t, i-1), D(t-1, i-1),D(t-1,i)] + d(t,i) & \text{for }i=2,...,N\end{cases}$$
|
|
3. Finalise, the cumulative distance up to the final point gives the total cost of the match: $D(T,N)$
|
|
|
|
|
|
- Euclidean distances
|
|
|
|
# Distortion Penalty
|
|
1. Initialise the cumulative distances for $t=1$
|
|
$$D(1,i)=\begin{cases}d(1,i) & \text{for }i=1, \\ d(1,i)+D(1, i-1)+d_V & \text{for }i=2,...,N\end{cases}$$
|
|
2. Recur for $t=2,...,T$
|
|
$$D(t,i)=\begin{cases}d(t,i)+D(t-1,i1)+d_H & \text{for }i=1, \\ \min[d(t,i)+D(t,i-1)+d_V,2d(t,i)+D(t-1,i-1),d(t,i)+D(t-1,i)+d_H] & \text{for }i=2,...,N\end{cases}$$
|
|
- Where $d_V$ and $d_H$ are costs associated with vertical and horizontal transitions respectively
|
|
3. Finalise, the cumulative distance up to the final point gives the total cost of the match: $D(T,N)$
|
|
|
|
- Allows weighting for dynamic penalties when moving horizontally or vertically
|
|
- As opposed to diagonally
|
|
|
|
|
|
|
|
# Store Best Path
|
|
1. Initialise distances and traceback indicator for $t=1$
|
|
$$D(1,i)=\begin{cases}d(1,i) & \text{for } i=1,\\ d(1,i)+D(1,i-1) & \text{for }i = 2,...,N\end{cases}$$
|
|
$$\phi(1,i)=\begin{cases}[0,0] & \text{for } i=1,\\ [1,i-1] & \text{for }i = 2,...,N\end{cases}$$
|
|
2. Recur for cumulative distances at $t=2,...,T$
|
|
$$D(1,i)=\begin{cases}d(t,i)+D(t-1,i) & \text{for } i=1,\\ d(t,i)+\min[D(t,i-1),D(t-1,i-1),D(t-1,i)] & \text{for }i = 2,...,N\end{cases}$$
|
|
$$\phi(1,i)=\begin{cases}[t-1,i] & \text{for } i=1,\\ \arg\min[D(t,i-1),D(t-1,i-1),D(t-1,i)] & \text{for }i = 2,...,N\end{cases}$$
|
|
3. Final point gives the total alignment cost D(T,N) and the end coordinates of the best path $z_K=[T,N]$, where $K$ is the number of nodes on the optimal path
|
|
4. Trace the path back for $k=K-1,...,1,z_k=\phi(z_{k+1}), \text{ and }Z=\{z_1,...,z_K\}$
|
|
- Stores best path
|
|
|
|
|
|
- Vary allowable movements through grid
|
|
- Second row for blocking multiple of the same movements in succession
|
|
|
|
# Search Pruning
|
|
- Speed up algorithm for real-time
|
|
- Kill bad options
|
|
|
|
## Gross Partitioning
|
|
|
|
- Too far from diagonal
|
|
- Probably wrong or bad
|
|
|
|
## Score Pruning
|
|
|
|
- Examine existing branches
|
|
- See which scores are really bad |