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
3.1 KiB
3.1 KiB
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
- 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}
- 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}
- Finalise, the cumulative distance up to the final point gives the total cost of the match:
D(T,N)
- Euclidean distances
Distortion Penalty
- 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}
- 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
andd_H
are costs associated with vertical and horizontal transitions respectively
- 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
- 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}
- 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}
- Final point gives the total alignment cost D(T,N) and the end coordinates of the best path
z_K=[T,N]
, whereK
is the number of nodes on the optimal path - 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