An Objective Approach to Identify Spectral Distinctiveness for Hearing Impairment

Algorithm 1

The dynamic time warping algorithm.

Step 1. Initialization

  DTW(1, 1) = 𝑑₁₁

  Path(1, 1) = (0, 0)

  For 𝑎=2 to 𝑛_𝑖

    DTW(𝑎, 1) = 𝑑_𝑎1 + DTW(𝑎−1, 1)

    Path(𝑎, 1) = (𝑎−1, 1)

  End For

  For 𝑏=2 to 𝑛_𝑗

    DTW(1, 𝑏) = 𝑑_1𝑏 + DTW(1, 𝑏−1)

    Path(1, 𝑏) = (1, 𝑏−1)

  End For

Step 2. Iteration

  For 𝑎=2 to 𝑛_𝑖

    For 𝑏=2 to 𝑛_𝑗

      DTW(𝑎,𝑏)=𝑑_𝑎𝑏+min_{)),((,),(𝑣∈{((𝑎−1,𝑏𝑎,𝑏−1))((𝑎−1𝑏−1))}}𝑑_𝑣

      Path(𝑎,𝑏)=argmin_{)),((,),(𝑣∈{((𝑎−1,𝑏𝑎,𝑏−1))((𝑎−1𝑏−1))}}𝑑_𝑣

    End For

  End For

Step 3. Backtracking and Termination

  The optimal (minimum) distance is DTW(𝑛_𝑖, 𝑛_𝑗).

  The optimal matching path H is found by simple backtracking from Path(𝑛_𝑖, 𝑛_𝑗).

  𝐻=Ø

  𝑙𝑝 = (𝑛_𝑖, 𝑛_𝑗)

  While 𝑙𝑝≠(0,0) Do

    𝐻=𝐻∪𝑙𝑝

    𝑙𝑝 = Path(𝑙𝑝)

  End While