Skip to content

M
musicinformationretrieval-com
Commit b4bef024 authored by Steve Tjoa's avatar Steve Tjoa
Browse files
Options

dtw initializtion

parent 324a76d1
Hide whitespace changes
Inline Side-by-side
Showing with 7110 additions and 8499 deletions
dtw.html
View file @ b4bef024
......@@ -11820,7 +11820,7 @@ div#notebook {
<div class="text_cell_render border-box-sizing rendered_html">
<p><strong>Dynamic time warping (DTW)</strong> (<a href="https://en.wikipedia.org/wiki/Dynamic_time_warping">Wikipedia</a>; FMP, p. 131) is an algorithm used to align two sequences of similar content but possibly different lengths.</p>
<p>Given two sequences, $x[n], n \in \{0, ..., N_x - 1\}$, and $y[n], n \in \{0, ..., N_y - 1\}$, DTW produces a set of index coordinate pairs $\{ (i, j) ... \}$ such that $x[i]$ and $y[j]$ are similar.</p>
<p>We will use the same approach described in the notebooks <a href="dp.html">Dynamic Programming</a> and <a href="lcs.html">Longest Common Subsequence</a>.</p>
<p>We will use the same dynamic programming approach described in the notebooks <a href="dp.html">Dynamic Programming</a> and <a href="lcs.html">Longest Common Subsequence</a>.</p>
</div>
</div>
......@@ -11884,7 +11884,7 @@ div#notebook {
<div class="output_text output_subarea output_execute_result">
<pre>&lt;matplotlib.legend.Legend at 0x1175965d0&gt;</pre>
<pre>&lt;matplotlib.legend.Legend at 0x108828210&gt;</pre>
</div>
</div>
......@@ -12518,6 +12518,15 @@ ERGRrKfBRUREREREsp4GFxERERERyXr/ALLpGQK5/Mj/AAAAAElFTkSuQmCC
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
<div class="inner_cell">
<div class="text_cell_render border-box-sizing rendered_html">
<p>For more distance metrics, see <a href="https://docs.scipy.org/doc/scipy/reference/spatial.distance.html"><code>scipy.spatial.distance</code></a>.</p>
</div>
</div>
</div>
<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
</div>
......@@ -12580,23 +12589,19 @@ $$ \mathrm{argmin} \ \{ d(x[i-1], y[j]), d(x[i], y[j-1]), d(x[i-1], j-1]) \} $$
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">dtw_table</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="n">nx</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">ny</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
<span class="n">table</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">ny</span><span class="o">+</span><span class="mi">1</span><span class="p">)]</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">nx</span><span class="o">+</span><span class="mi">1</span><span class="p">)]</span>
<span class="n">table</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">nx</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">ny</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span>
<span class="c1"># Compute left column separately, i.e. j=0.</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">nx</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">spatial</span><span class="o">.</span><span class="n">distance</span><span class="o">.</span><span class="n">euclidean</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="mi">0</span><span class="p">)</span>
<span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">d</span> <span class="o">+</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
<span class="n">table</span><span class="p">[</span><span class="mi">1</span><span class="p">:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">inf</span>
<span class="c1"># Compute top row separately, i.e. i=0.</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">ny</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">spatial</span><span class="o">.</span><span class="n">distance</span><span class="o">.</span><span class="n">euclidean</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">y</span><span class="p">[</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">table</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">d</span> <span class="o">+</span> <span class="n">table</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">table</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">:]</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">inf</span>
<span class="c1"># Fill in the rest.</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">nx</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">ny</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">spatial</span><span class="o">.</span><span class="n">distance</span><span class="o">.</span><span class="n">euclidean</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">y</span><span class="p">[</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">d</span> <span class="o">+</span> <span class="nb">min</span><span class="p">(</span><span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">],</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">d</span> <span class="o">+</span> <span class="nb">min</span><span class="p">(</span><span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">],</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="k">return</span> <span class="n">table</span>
</pre></div>
......@@ -12639,7 +12644,7 @@ $$ \mathrm{argmin} \ \{ d(x[i-1], y[j]), d(x[i], y[j-1]), d(x[i-1], j-1]) \} $$
<span class="n">z0</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">z0</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="k">print</span> <span class="p">(</span><span class="s1">&#39;</span><span class="si">%4s</span><span class="s1"> |&#39;</span> <span class="o">%</span> <span class="n">z0</span><span class="p">)</span> <span class="o">+</span> <span class="s1">&#39;&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="s1">&#39;</span><span class="si">%4d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">z</span> <span class="k">for</span> <span class="n">z</span> <span class="ow">in</span> <span class="n">row</span><span class="p">)</span>
<span class="k">print</span> <span class="p">(</span><span class="s1">&#39;</span><span class="si">%4s</span><span class="s1"> |&#39;</span> <span class="o">%</span> <span class="n">z0</span><span class="p">)</span> <span class="o">+</span> <span class="s1">&#39;&#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="s1">&#39;</span><span class="si">%4.0f</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">z</span> <span class="k">for</span> <span class="n">z</span> <span class="ow">in</span> <span class="n">row</span><span class="p">)</span>
</pre></div>
</div>
......@@ -12658,14 +12663,14 @@ $$ \mathrm{argmin} \ \{ d(x[i-1], y[j]), d(x[i], y[j-1]), d(x[i-1], j-1]) \} $$
<div class="output_subarea output_stream output_stdout output_text">
<pre> 1 3 4 3 1 -1 -2 -1 0
+----------------------------------------
| 0 1 4 8 11 12 13 15 16 16
0 | 0 1 4 8 11 12 13 15 16 16
4 | 4 3 2 2 3 6 11 17 20 20
4 | 8 6 3 2 3 6 11 17 22 24
0 | 8 7 6 6 5 4 5 7 8 8
-4 | 12 12 13 14 12 9 7 7 10 12
-4 | 16 17 19 21 19 14 10 9 10 14
0 | 16 17 20 23 22 15 11 11 10 10
| 0 inf inf inf inf inf inf inf inf inf
0 | inf 1 4 8 11 12 13 15 16 16
4 | inf 4 2 2 3 6 11 17 20 20
4 | inf 7 3 2 3 6 11 17 22 24
0 | inf 8 6 6 5 4 5 7 8 8
-4 | inf 13 13 14 12 9 7 7 10 12
-4 | inf 18 20 21 19 14 10 9 10 14
0 | inf 19 21 24 22 15 11 11 10 10
</pre>
</div>
</div>
......@@ -12720,14 +12725,14 @@ $$ \mathrm{argmin} \ \{ d(x[i-1], y[j]), d(x[i], y[j-1]), d(x[i-1], j-1]) \} $$
<span class="n">path</span> <span class="o">=</span> <span class="p">[(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)]</span>
<span class="k">while</span> <span class="n">i</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">minval</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">inf</span>
<span class="k">if</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">minval</span><span class="p">:</span>
<span class="n">minval</span> <span class="o">=</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
<span class="k">if</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">minval</span><span class="p">:</span>
<span class="n">minval</span> <span class="o">=</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span>
<span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
<span class="k">if</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">minval</span><span class="p">:</span>
<span class="n">minval</span> <span class="o">=</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">minval</span> <span class="o">=</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">if</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">minval</span><span class="p">:</span>
<span class="n">minval</span> <span class="o">=</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">minval</span> <span class="o">=</span> <span class="n">table</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">step</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">path</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">step</span><span class="p">)</span>
<span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">step</span>
......@@ -12765,7 +12770,6 @@ $$ \mathrm{argmin} \ \{ d(x[i-1], y[j]), d(x[i], y[j-1]), d(x[i-1], j-1]) \} $$
<div class="output_text output_subarea output_execute_result">
<pre>[(0, 0),
(1, 0),
(1, 1),
(2, 2),
(2, 3),
......@@ -12850,7 +12854,7 @@ $$ \mathrm{argmin} \ \{ d(x[i-1], y[j]), d(x[i], y[j-1]), d(x[i-1], j-1]) \} $$
<div class="prompt input_prompt">In&nbsp;[17]:</div>
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">table</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">table</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span>
</pre></div>
</div>
......
dtw.ipynb
View file @ b4bef024
......@@ -45,7 +45,7 @@
"\n",
"Given two sequences, $x[n], n \\in \\{0, ..., N_x - 1\\}$, and $y[n], n \\in \\{0, ..., N_y - 1\\}$, DTW produces a set of index coordinate pairs $\\{ (i, j) ... \\}$ such that $x[i]$ and $y[j]$ are similar.\n",
"\n",
"We will use the same approach described in the notebooks [Dynamic Programming](dp.html) and [Longest Common Subsequence](lcs.html)."
"We will use the same dynamic programming approach described in the notebooks [Dynamic Programming](dp.html) and [Longest Common Subsequence](lcs.html)."
]
},
{
......@@ -84,7 +84,7 @@
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1175965d0>"
"<matplotlib.legend.Legend at 0x108828210>"
]
},
"execution_count": 3,
......@@ -95,7 +95,7 @@
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAy4AAADBCAYAAAApSeRhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1174f4210>"
"<matplotlib.figure.Figure at 0x10edab390>"
]
},
"metadata": {},
......@@ -283,6 +283,13 @@
"scipy.spatial.distance.cosine([1, 0], [-1, 0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For more distance metrics, see [`scipy.spatial.distance`](https://docs.scipy.org/doc/scipy/reference/spatial.distance.html)."
]
},
{
"cell_type": "markdown",
"metadata": {},
......@@ -340,23 +347,19 @@
"def dtw_table(x, y):\n",
" nx = len(x)\n",
" ny = len(y)\n",
" table = [[0 for _ in range(ny+1)] for _ in range(nx+1)]\n",
" table = numpy.zeros((nx+1, ny+1))\n",
" \n",
" # Compute left column separately, i.e. j=0.\n",
" for i in range(1, nx+1):\n",
" d = scipy.spatial.distance.euclidean(x[i-1], 0)\n",
" table[i][0] = d + table[i-1][0]\n",
" table[1:, 0] = numpy.inf\n",
" \n",
" # Compute top row separately, i.e. i=0.\n",
" for j in range(1, ny+1):\n",
" d = scipy.spatial.distance.euclidean(0, y[j-1])\n",
" table[0][j] = d + table[0][j-1]\n",
" table[0, 1:] = numpy.inf\n",
" \n",
" # Fill in the rest.\n",
" for i in range(1, nx+1):\n",
" for j in range(1, ny+1):\n",
" d = scipy.spatial.distance.euclidean(x[i-1], y[j-1])\n",
" table[i][j] = d + min(table[i-1][j], table[i][j-1], table[i-1][j-1])\n",
" table[i, j] = d + min(table[i-1, j], table[i, j-1], table[i-1, j-1])\n",
" return table"
]
},
......@@ -389,14 +392,14 @@
"text": [
" 1 3 4 3 1 -1 -2 -1 0\n",
" +----------------------------------------\n",
" | 0 1 4 8 11 12 13 15 16 16\n",
" 0 | 0 1 4 8 11 12 13 15 16 16\n",
" 4 | 4 3 2 2 3 6 11 17 20 20\n",
" 4 | 8 6 3 2 3 6 11 17 22 24\n",
" 0 | 8 7 6 6 5 4 5 7 8 8\n",
" -4 | 12 12 13 14 12 9 7 7 10 12\n",
" -4 | 16 17 19 21 19 14 10 9 10 14\n",
" 0 | 16 17 20 23 22 15 11 11 10 10\n"
" | 0 inf inf inf inf inf inf inf inf inf\n",
" 0 | inf 1 4 8 11 12 13 15 16 16\n",
" 4 | inf 4 2 2 3 6 11 17 20 20\n",
" 4 | inf 7 3 2 3 6 11 17 22 24\n",
" 0 | inf 8 6 6 5 4 5 7 8 8\n",
" -4 | inf 13 13 14 12 9 7 7 10 12\n",
" -4 | inf 18 20 21 19 14 10 9 10 14\n",
" 0 | inf 19 21 24 22 15 11 11 10 10\n"
]
}
],
......@@ -408,7 +411,7 @@
" z0 = ''\n",
" else:\n",
" z0 = x[i-1]\n",
" print ('%4s |' % z0) + ''.join('%4d' % z for z in row)"
" print ('%4s |' % z0) + ''.join('%4.0f' % z for z in row)"
]
},
{
......@@ -453,14 +456,14 @@
" path = [(i, j)]\n",
" while i > 0 or j > 0:\n",
" minval = numpy.inf\n",
" if table[i-1][j] < minval:\n",
" minval = table[i-1][j]\n",
" if table[i-1, j] < minval:\n",
" minval = table[i-1, j]\n",
" step = (i-1, j)\n",
" if table[i][j-1] < minval:\n",
" minval = table[i][j-1]\n",
" minval = table[i, j-1]\n",
" step = (i, j-1)\n",
" if table[i-1][j-1] < minval:\n",
" minval = table[i-1][j-1]\n",
" minval = table[i-1, j-1]\n",
" step = (i-1, j-1)\n",
" path.insert(0, step)\n",
" i, j = step\n",
......@@ -476,7 +479,6 @@
"data": {
"text/plain": [
"[(0, 0),\n",
" (1, 0),\n",
" (1, 1),\n",
" (2, 2),\n",
" (2, 3),\n",
......@@ -558,7 +560,7 @@
}
],
"source": [
"table[-1][-1]"
"table[-1, -1]"
]
},
{
......
dtw_example.html
View file @ b4bef024
This source diff could not be displayed because it is too large. You can view the blob instead.
dtw_example.ipynb
View file @ b4bef024
This source diff could not be displayed because it is too large. You can view the blob instead.
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment