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<h1 data-toc-skip>Linear Segmentation</h1>
<h4 class="author">John Mount</h4>
<h4 class="date">2020-12-15</h4>
<small class="dont-index">Source: <a href="https://github.com/WinVector/RcppDynProg/blob/master/vignettes/SegmentationL.Rmd"><code>vignettes/SegmentationL.Rmd</code></a></small>
<div class="hidden name"><code>SegmentationL.Rmd</code></div>
</div>
<p>In this example we fit a piecewise linear function to example data.<br>
Please see <a href="https://github.com/WinVector/RcppDynProg">here</a> for a discussion of the methodology.</p>
<div class="sourceCode" id="cb1"><pre class="downlit">
<span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="st"><a href="https://github.com/WinVector/RcppDynProg/">"RcppDynProg"</a></span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/r/base/Random.html">set.seed</a></span><span class="op">(</span><span class="fl">2018</span><span class="op">)</span>
<span class="va">g</span> <span class="op"><-</span> <span class="fl">100</span>
<span class="va">d</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html">data.frame</a></span><span class="op">(</span>
x <span class="op">=</span> <span class="fl">0.05</span><span class="op">*</span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="op">(</span><span class="fl">3</span><span class="op">*</span><span class="va">g</span><span class="op">)</span><span class="op">)</span><span class="op">)</span> <span class="co"># ordered in x</span>
<span class="va">d</span><span class="op">$</span><span class="va">y_ideal</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/Trig.html">sin</a></span><span class="op">(</span><span class="op">(</span><span class="fl">0.3</span><span class="op">*</span><span class="va">d</span><span class="op">$</span><span class="va">x</span><span class="op">)</span><span class="op">^</span><span class="fl">2</span><span class="op">)</span>
<span class="va">d</span><span class="op">$</span><span class="va">y_observed</span> <span class="op"><-</span> <span class="va">d</span><span class="op">$</span><span class="va">y_ideal</span> <span class="op">+</span> <span class="fl">0.25</span><span class="op">*</span><span class="fu"><a href="https://rdrr.io/r/stats/Normal.html">rnorm</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/length.html">length</a></span><span class="op">(</span><span class="va">d</span><span class="op">$</span><span class="va">y_ideal</span><span class="op">)</span><span class="op">)</span>
<span class="co"># plot</span>
<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">d</span><span class="op">$</span><span class="va">x</span>, <span class="va">d</span><span class="op">$</span><span class="va">y_observed</span>,
xlab <span class="op">=</span> <span class="st">"x"</span>, ylab <span class="op">=</span> <span class="st">"y"</span>,
main <span class="op">=</span> <span class="st">"raw data\ncircles: observed values, dashed line: unobserved true values"</span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/r/graphics/lines.html">lines</a></span><span class="op">(</span><span class="va">d</span><span class="op">$</span><span class="va">x</span>, <span class="va">d</span><span class="op">$</span><span class="va">y_ideal</span>,
type <span class="op">=</span> <span class="st">"l"</span>,
lty <span class="op">=</span> <span class="st">"dashed"</span><span class="op">)</span></pre></div>
<p><img src="SegmentationL_files/figure-html/r1-1.png" width="768" style="display: block; margin: auto;"></p>
<div class="sourceCode" id="cb2"><pre class="downlit">
<span class="va">x_cuts</span> <span class="op"><-</span> <span class="fu"><a href="../reference/solve_for_partition.html">solve_for_partition</a></span><span class="op">(</span><span class="va">d</span><span class="op">$</span><span class="va">x</span>, <span class="va">d</span><span class="op">$</span><span class="va">y_observed</span>, penalty <span class="op">=</span> <span class="fl">1</span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">x_cuts</span><span class="op">)</span></pre></div>
<pre><code>## x pred group what
## 1 0.05 -0.1570880 1 left
## 2 4.65 1.1593754 1 right
## 3 4.70 1.0653666 2 left
## 4 6.95 -0.9770792 2 right
## 5 7.00 -1.2254925 3 left
## 6 9.20 0.8971391 3 right
## 7 9.25 1.3792437 4 left
## 8 11.10 -1.1542021 4 right
## 9 11.15 -1.0418353 5 left
## 10 12.50 1.1519490 5 right
## 11 12.55 1.3964906 6 left
## 12 13.75 -1.2045219 6 right
## 13 13.80 -1.3791405 7 left
## 14 15.00 1.0195679 7 right</code></pre>
<div class="sourceCode" id="cb4"><pre class="downlit">
<span class="va">d</span><span class="op">$</span><span class="va">estimate</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/approxfun.html">approx</a></span><span class="op">(</span><span class="va">x_cuts</span><span class="op">$</span><span class="va">x</span>, <span class="va">x_cuts</span><span class="op">$</span><span class="va">pred</span>, xout <span class="op">=</span> <span class="va">d</span><span class="op">$</span><span class="va">x</span>, method <span class="op">=</span> <span class="st">"linear"</span>, rule <span class="op">=</span> <span class="fl">2</span><span class="op">)</span><span class="op">$</span><span class="va">y</span>
<span class="va">d</span><span class="op">$</span><span class="va">group</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/character.html">as.character</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/findInterval.html">findInterval</a></span><span class="op">(</span><span class="va">d</span><span class="op">$</span><span class="va">x</span>, <span class="va">x_cuts</span><span class="op">[</span><span class="va">x_cuts</span><span class="op">$</span><span class="va">what</span><span class="op">==</span><span class="st">"left"</span>, <span class="st">"x"</span><span class="op">]</span><span class="op">)</span><span class="op">)</span></pre></div>
<div class="sourceCode" id="cb5"><pre class="downlit">
<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/sum.html">sum</a></span><span class="op">(</span><span class="op">(</span><span class="va">d</span><span class="op">$</span><span class="va">y_observed</span> <span class="op">-</span> <span class="va">d</span><span class="op">$</span><span class="va">y_ideal</span><span class="op">)</span><span class="op">^</span><span class="fl">2</span><span class="op">)</span><span class="op">)</span></pre></div>
<pre><code>## [1] 20.42462</code></pre>
<div class="sourceCode" id="cb7"><pre class="downlit">
<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/sum.html">sum</a></span><span class="op">(</span><span class="op">(</span><span class="va">d</span><span class="op">$</span><span class="va">estimate</span> <span class="op">-</span> <span class="va">d</span><span class="op">$</span><span class="va">y_ideal</span><span class="op">)</span><span class="op">^</span><span class="fl">2</span><span class="op">)</span><span class="op">)</span></pre></div>
<pre><code>## [1] 3.536541</code></pre>
<div class="sourceCode" id="cb9"><pre class="downlit">
<span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/sum.html">sum</a></span><span class="op">(</span><span class="op">(</span><span class="va">d</span><span class="op">$</span><span class="va">estimate</span> <span class="op">-</span> <span class="va">d</span><span class="op">$</span><span class="va">y_observed</span><span class="op">)</span><span class="op">^</span><span class="fl">2</span><span class="op">)</span><span class="op">)</span></pre></div>
<pre><code>## [1] 20.53796</code></pre>
<div class="sourceCode" id="cb11"><pre class="downlit">
<span class="co"># plot</span>
<span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">d</span><span class="op">$</span><span class="va">x</span>, <span class="va">d</span><span class="op">$</span><span class="va">y_observed</span>,
xlab <span class="op">=</span> <span class="st">"x"</span>, ylab <span class="op">=</span> <span class="st">"y"</span>,
main <span class="op">=</span> <span class="st">"RcppDynProg piecewise linear estimate\ndots: observed values, segments: estimated shape"</span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/r/graphics/points.html">points</a></span><span class="op">(</span><span class="va">d</span><span class="op">$</span><span class="va">x</span>, <span class="va">d</span><span class="op">$</span><span class="va">y_ideal</span>,
type <span class="op">=</span> <span class="st">"l"</span>,
lty <span class="op">=</span> <span class="st">"dashed"</span><span class="op">)</span>
<span class="va">cmap</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="st">"#a6cee3"</span>,
<span class="st">"#1f78b4"</span>,
<span class="st">"#b2df8a"</span>,
<span class="st">"#33a02c"</span>,
<span class="st">"#fb9a99"</span>,
<span class="st">"#e31a1c"</span>,
<span class="st">"#fdbf6f"</span>,
<span class="st">"#ff7f00"</span>,
<span class="st">"#cab2d6"</span>,
<span class="st">"#6a3d9a"</span>,
<span class="st">"#ffff99"</span>,
<span class="st">"#b15928"</span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/r/base/names.html">names</a></span><span class="op">(</span><span class="va">cmap</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/character.html">as.character</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/seq.html">seq_len</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/length.html">length</a></span><span class="op">(</span><span class="va">cmap</span><span class="op">)</span><span class="op">)</span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/r/graphics/points.html">points</a></span><span class="op">(</span><span class="va">d</span><span class="op">$</span><span class="va">x</span>, <span class="va">d</span><span class="op">$</span><span class="va">y_observed</span>, col <span class="op">=</span> <span class="va">cmap</span><span class="op">[</span><span class="va">d</span><span class="op">$</span><span class="va">group</span><span class="op">]</span>, pch<span class="op">=</span><span class="fl">19</span><span class="op">)</span>
<span class="va">groups</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/sort.html">sort</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/unique.html">unique</a></span><span class="op">(</span><span class="va">d</span><span class="op">$</span><span class="va">group</span><span class="op">)</span><span class="op">)</span>
<span class="kw">for</span><span class="op">(</span><span class="va">gi</span> <span class="kw">in</span> <span class="va">groups</span><span class="op">)</span> <span class="op">{</span>
<span class="va">di</span> <span class="op"><-</span> <span class="va">d</span><span class="op">[</span><span class="va">d</span><span class="op">$</span><span class="va">group</span><span class="op">==</span><span class="va">gi</span>, , drop <span class="op">=</span> <span class="cn">FALSE</span><span class="op">]</span>
<span class="fu"><a href="https://rdrr.io/r/graphics/lines.html">lines</a></span><span class="op">(</span><span class="va">di</span><span class="op">$</span><span class="va">x</span>, <span class="va">di</span><span class="op">$</span><span class="va">estimate</span>, col <span class="op">=</span> <span class="va">cmap</span><span class="op">[</span><span class="va">di</span><span class="op">$</span><span class="va">group</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span><span class="op">]</span>, lwd<span class="op">=</span><span class="fl">2</span><span class="op">)</span>
<span class="op">}</span></pre></div>
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