diff --git a/docs/2_method/2_dtw.md b/docs/2_method/2_dtw.md index 4e3ff64..74b147e 100644 --- a/docs/2_method/2_dtw.md +++ b/docs/2_method/2_dtw.md @@ -27,7 +27,7 @@ The DTW distance is the sum of the Euclidean distance between each point and its $y_1$ (monotonicity). 3. Each point is mapped to at least one other point, i.e., there are no jumps in time (continuity). -Finding the optimal warping arrangement is an optimisation problem that can be solved using dynamic programming, which splits the problem into easier sub-problems and solves them recursively, storing intermediate solutions until the final solution is reached. To understand the memory-efficient method used in ''DTW-C++``, it is useful to first examine the full-cost matrix solution, as follows. For each pairwise comparison, an ($n$) by ($m$) matrix $C^{n\times m}$ is calculated, where each element represents the cumulative cost between series up to the points $x_i$ and $y_j$: +Finding the optimal warping arrangement is an optimisation problem that can be solved using dynamic programming, which splits the problem into easier sub-problems and solves them recursively, storing intermediate solutions until the final solution is reached. To understand the memory-efficient method used in *DTW-C++*, it is useful to first examine the full-cost matrix solution, as follows. For each pairwise comparison, an ($n$) by ($m$) matrix $C^{n\times m}$ is calculated, where each element represents the cumulative cost between series up to the points $x_i$ and $y_j$: $$ c_{i,j} = (x_i-y_j)^2+\min \begin{cases}