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Advanced Preprocessing: Simple Mathematical Operations - Revision history
2024-03-29T15:04:52Z
Revision history for this page on the wiki
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imported>Donal: /* Log10 */
2015-11-09T07:47:59Z
<p><span dir="auto"><span class="autocomment">Log10</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Log10===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Log10===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>A base 10 logarithm (that is, <math>\mathbf{X}_p = log_{10}(\mathbf{X})</math> ) can be used whenever the response of the data is linear to the function 10<sup>X</sup>. <del style="font-weight: bold; text-decoration: none;">Note that </del>negative values will become undefined values (NaN = Not a Number)<del style="font-weight: bold; text-decoration: none;">. Most modeling algorithms will attempt </del>to <del style="font-weight: bold; text-decoration: none;">replace these values with their least-biasing value</del>. <del style="font-weight: bold; text-decoration: none;">As such, the </del>use of an absolute value preprocessing step prior to a Log10 step <del style="font-weight: bold; text-decoration: none;">may be necessary </del>to <del style="font-weight: bold; text-decoration: none;">avoid problems </del>during <del style="font-weight: bold; text-decoration: none;">modeling</del>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>A base 10 logarithm (that is, <math>\mathbf{X}_p = log_{10}(\mathbf{X})</math> ) can be used whenever the response of the data is linear to the function 10<sup>X</sup>. <ins style="font-weight: bold; text-decoration: none;">Since log of </ins>negative values will become undefined values (NaN = Not a Number) <ins style="font-weight: bold; text-decoration: none;">this operation first sets negative data values </ins>to <ins style="font-weight: bold; text-decoration: none;">zero</ins>. <ins style="font-weight: bold; text-decoration: none;">This effect can be avoided by </ins>use of an absolute value preprocessing step prior to a Log10 step<ins style="font-weight: bold; text-decoration: none;">. A minimum value filter is also used to prevent huge negative log values when x is very small. This is achieved by adding a constant, c, </ins>to <ins style="font-weight: bold; text-decoration: none;">x before applying log. This constant is removed </ins>during <ins style="font-weight: bold; text-decoration: none;">the "undo" step. c = 10<sup>-5</sup> by default</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>There are no settings associated with this preprocessing method. The command line function to perform this operation is the MATLAB command log10.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>There are no settings associated with this preprocessing method. The command line function to perform this operation is the MATLAB command log10 <ins style="font-weight: bold; text-decoration: none;">(however this does not set negative values to zero before taking log, and does not use a minimum value filter)</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Transmission to Absorbance (log(1/T))===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Transmission to Absorbance (log(1/T))===</div></td></tr>
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imported>Donal
https://www.wiki.eigenvector.com/index.php?title=Advanced_Preprocessing:_Simple_Mathematical_Operations&diff=6184&oldid=prev
imported>Scott at 19:53, 17 April 2013
2013-04-17T19:53:04Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:53, 17 April 2013</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There are no settings associated with this preprocessing method. The command line function to perform this operation is the MATLAB command log10(1./X).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There are no settings associated with this preprocessing method. The command line function to perform this operation is the MATLAB command log10(1./X).</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===Arithmetic===</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Apply simple arithmetic operations to all or part of dataset. See [[arithmetic]].</ins></div></td></tr>
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imported>Scott
https://www.wiki.eigenvector.com/index.php?title=Advanced_Preprocessing:_Simple_Mathematical_Operations&diff=6183&oldid=prev
imported>Jeremy: /* Transmission to Absorbance (log(1/T)) */
2011-07-26T23:29:05Z
<p><span dir="auto"><span class="autocomment">Transmission to Absorbance (log(1/T))</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:29, 26 July 2011</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Transmission to Absorbance (log(1/T))===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Transmission to Absorbance (log(1/T))===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The spectroscopic transformation <math>\mathbf{X}_p = log_{10}(1/\mathbf<del style="font-weight: bold; text-decoration: none;">(</del>X<del style="font-weight: bold; text-decoration: none;">)</del>)</math> is often used when data has been collected as transmission (ratio of measured signal relative to incident signal). The transformation converts the signal to "absorbance" but, in general, transforms data which follows the inverse log relationship.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The spectroscopic transformation <math>\mathbf{X}_p = log_{10}(1/\mathbf<ins style="font-weight: bold; text-decoration: none;">{</ins>X<ins style="font-weight: bold; text-decoration: none;">}</ins>)</math> is often used when data has been collected as transmission (ratio of measured signal relative to incident signal). The transformation converts the signal to "absorbance" but, in general, transforms data which follows the inverse log relationship.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There are no settings associated with this preprocessing method. The command line function to perform this operation is the MATLAB command log10(1./X).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There are no settings associated with this preprocessing method. The command line function to perform this operation is the MATLAB command log10(1./X).</div></td></tr>
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imported>Jeremy
https://www.wiki.eigenvector.com/index.php?title=Advanced_Preprocessing:_Simple_Mathematical_Operations&diff=6182&oldid=prev
imported>Jeremy at 23:28, 26 July 2011
2011-07-26T23:28:42Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:28, 26 July 2011</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Log10===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Log10===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>A base 10 logarithm (that is, <math><del style="font-weight: bold; text-decoration: none;">X_p </del>= log_{10}(\mathbf{X})</math> ) can be used whenever the response of the data is linear to the function 10<sup>X</sup>. Note that negative values will become undefined values (NaN = Not a Number). Most modeling algorithms will attempt to replace these values with their least-biasing value. As such, the use of an absolute value preprocessing step prior to a Log10 step may be necessary to avoid problems during modeling.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>A base 10 logarithm (that is, <math><ins style="font-weight: bold; text-decoration: none;">\mathbf{X}_p </ins>= log_{10}(\mathbf{X})</math> ) can be used whenever the response of the data is linear to the function 10<sup>X</sup>. Note that negative values will become undefined values (NaN = Not a Number). Most modeling algorithms will attempt to replace these values with their least-biasing value. As such, the use of an absolute value preprocessing step prior to a Log10 step may be necessary to avoid problems during modeling.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There are no settings associated with this preprocessing method. The command line function to perform this operation is the MATLAB command log10.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There are no settings associated with this preprocessing method. The command line function to perform this operation is the MATLAB command log10.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===Transmission to Absorbance (log(1/T))===</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The spectroscopic transformation <math>\mathbf{X}_p = log_{10}(1/\mathbf(X))</math> is often used when data has been collected as transmission (ratio of measured signal relative to incident signal). The transformation converts the signal to "absorbance" but, in general, transforms data which follows the inverse log relationship.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">There are no settings associated with this preprocessing method. The command line function to perform this operation is the MATLAB command log10(1./X).</ins></div></td></tr>
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imported>Jeremy
https://www.wiki.eigenvector.com/index.php?title=Advanced_Preprocessing:_Simple_Mathematical_Operations&diff=6181&oldid=prev
imported>Jeremy: moved Advanced Preprocessing: Mathematical Operations to Advanced Preprocessing: Simple Mathematical Operations
2010-07-07T23:13:57Z
<p>moved <a href="/index.php?title=Advanced_Preprocessing:_Mathematical_Operations&action=edit&redlink=1" class="new" title="Advanced Preprocessing: Mathematical Operations (page does not exist)">Advanced Preprocessing: Mathematical Operations</a> to <a href="/index.php?title=Advanced_Preprocessing:_Simple_Mathematical_Operations" title="Advanced Preprocessing: Simple Mathematical Operations">Advanced Preprocessing: Simple Mathematical Operations</a></p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:13, 7 July 2010</td>
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imported>Jeremy
https://www.wiki.eigenvector.com/index.php?title=Advanced_Preprocessing:_Simple_Mathematical_Operations&diff=6180&oldid=prev
imported>Jeremy: Created page with 'Two preprocessing methods involve simple mathematical operations which are used to linearize or otherwise modify certain kinds of data. ===Absolute Value=== The absolute value …'
2010-07-07T23:13:45Z
<p>Created page with 'Two preprocessing methods involve simple mathematical operations which are used to linearize or otherwise modify certain kinds of data. ===Absolute Value=== The absolute value …'</p>
<p><b>New page</b></p><div>Two preprocessing methods involve simple mathematical operations which are used to linearize or otherwise modify certain kinds of data.<br />
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===Absolute Value===<br />
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The absolute value method is used to remove any sign information from the data. Although unusual, this method may be useful following a derivative or other method which creates negative values. Such correction can allow the use of non-negativity constraints, or simply improve interpretability of derivatized spectra. It should be noted, however, that an absolute value following any method which centers data (such as mean- or median-centering) may create a non-linear response and complicate modeling.<br />
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There are no settings associated with this preprocessing method. The command line function to perform this operation is the MATLAB command abs.<br />
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===Log10===<br />
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A base 10 logarithm (that is, <math>X_p = log_{10}(\mathbf{X})</math> ) can be used whenever the response of the data is linear to the function 10<sup>X</sup>. Note that negative values will become undefined values (NaN = Not a Number). Most modeling algorithms will attempt to replace these values with their least-biasing value. As such, the use of an absolute value preprocessing step prior to a Log10 step may be necessary to avoid problems during modeling.<br />
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There are no settings associated with this preprocessing method. The command line function to perform this operation is the MATLAB command log10.</div>
imported>Jeremy