<html>
-<head><title>Principal Component Analysis</title></head>
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+<head>
+<title>Principal Component Analysis</title>
+</head>
<body>
<p><strong>Principal Component Analysis</strong></p>
<p>This calculation creates a spatial representation of the
-similarities within a selected group, or all of the sequences in
-an alignment. After the calculation finishes, a 3D viewer displays the
-set of sequences as points in 'similarity space', and similar
-sequences tend to lie near each other in the space.</p>
-<p>Note: The calculation is computationally expensive, and may fail for very large sets of sequences -
- usually because the JVM has run out of memory. A future release of
- Jalview will be able to avoid this by executing the calculation via a web service.</p>
+similarities within a selected group, or all of the sequences in an
+alignment. After the calculation finishes, a 3D viewer displays the set
+of sequences as points in 'similarity space', and similar sequences tend
+to lie near each other in the space.</p>
+<p><em>Caveats</em><br/>The calculation is computationally expensive, and may fail
+for very large sets of sequences - usually because the JVM has run out
+of memory. A future release of Jalview will be able to avoid this by
+executing the calculation via a web service.</p>
+
+<p><strong>About PCA</strong></p>
<p>Principal components analysis is a technique for examining the
structure of complex data sets. The components are a set of dimensions
-formed from the measured values in the data set, and the principle
-component is the one with the greatest magnitude, or length. The
-sets of measurements that differ the most should lie at either end of
-this principle axis, and the other axes correspond to less extreme
-patterns of variation in the data set.
-</p>
-
-<p>In this case, the components are generated by an eigenvector
-decomposition of the matrix formed from the sum of BLOSUM scores at
-each aligned position between each pair of sequences. The basic method
-is described in the paper by G. Casari, C. Sander and
-A. Valencia. Structural Biology volume 2, no. 2, February 1995 (<a
-href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=7749921">pubmed</a>)
- and implemented at the SeqSpace server at the EBI.
-</p>
+formed from the measured values in the data set, and the principal
+component is the one with the greatest magnitude, or length. The sets of
+measurements that differ the most should lie at either end of this
+principal axis, and the other axes correspond to less extreme patterns
+of variation in the data set.</p>
-<p><strong>The PCA Viewer</strong></p>
+ <p>
+ <em>Calculating PCAs for aligned sequences</em><br />Jalview can
+ perform PCA analysis on both proteins and nucleotide sequence
+ alignments. In both cases, components are generated by an eigenvector
+ decomposition of the matrix formed from the sum of substitution matrix
+ scores at each aligned position between each pair of sequences -
+ computed with one of the available score matrices, such as
+ <a href="scorematrices.html#blosum62">BLOSUM62</a>, <a
+ href="scorematrices.html#pam250">PAM250</a>, or the <a
+ href="scorematrices.html#simplenucleotide">simple single
+ nucleotide substitution matrix</a>. The options available for
+ calculation are given in the
+ <strong><em>Change Parameters</em></strong> menu.</p>
+ <p>
+ <em>PCA Calculation modes</em><br/>
+ The default Jalview calculation mode
+ (indicated when <em><strong>Jalview PCA Calculation</strong></em> is
+ ticked in the <strong><em>Change Parameters</em></strong> menu) is to
+ perform a PCA on a matrix where elements in the upper diagonal give
+ the sum of scores for mutating in one direction, and the lower
+ diagonal is the sum of scores for mutating in the other. For protein
+ substitution models like BLOSUM62, this gives an asymmetric matrix,
+ and a different PCA to a matrix produced with the method described in the
+ paper by G. Casari, C. Sander and A. Valencia. Structural Biology
+ volume 2, no. 2, February 1995 (<a
+ href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=7749921">pubmed</a>)
+ and implemented at the SeqSpace server at the EBI. This method
+ preconditions the matrix by multiplying it with its transpose, and can be employed in the PCA viewer by unchecking the <strong><em>Jalview
+ PCA Calculation</em></strong> option in the <strong><em>Change
+ Parameters</em></strong> menu.
+ </p>
+ <img src="pcaviewer.gif">
+ <p><strong>The PCA Viewer</strong></p>
<p>This is an interactive display of the sequences positioned within
- the similarity space. The colour of each sequence point is the same
- as the sequence group colours, white if no colour has been
- defined for the sequence, and green if the sequence is part of a
- the currently selected group.
-</p>
- <p>The 3d view can be rotated by dragging the mouse with the
- <strong>left mouse button</strong> pressed. The view can also be
- zoomed in and out with the up and down <strong>arrow
- keys</strong> (and the roll bar of the mouse if present). Labels
- will be shown for each sequence if the entry in the View menu is
- checked, and the plot background colour changed from the
- View→Background Colour.. dialog box. The File menu allows the
- view to be saved (File→Save submenu) as an EPS or PNG image or
- printed, and the original alignment data and matrix resulting from
- its PCA analysis to be retrieved.
-</p>
- </p>
+the similarity space, as points in a rotateable 3D scatterplot. The
+colour of each sequence point is the same as the sequence group colours,
+white if no colour has been defined for the sequence, and green if the
+sequence is part of a the currently selected group.</p>
+<p>The 3d view can be rotated by dragging the mouse with the <strong>left
+mouse button</strong> pressed. The view can also be zoomed in and out with the up
+and down <strong>arrow keys</strong> (and the roll bar of the mouse if
+present). Labels will be shown for each sequence if the entry in the
+View menu is checked, and the plot background colour changed from the
+View→Background Colour.. dialog box. The File menu allows the view
+to be saved (<strong>File→Save</strong> submenu) as an EPS or PNG
+image or printed, and the original alignment data and matrix resulting
+from its PCA analysis to be retrieved. The coordinates for the whole PCA
+space, or just the current view may also be exported as CSV files for
+visualization in another program or further analysis.<p>
+<p>Options for coordinates export are:</p>
+<ul>
+<li>Output Values - complete dump of analysis (TxT* matrix computed from sum of scores for all pairs of aligned residues from from i->j and j->i, conditioned matrix to be diagonalised, tridiagonal form, major eigenvalues found)</li>
+<li>Output Points - The eigenvector matrix - rows correspond to sequences, columns correspond to each dimension in the PCA</li>
+<li>Transformed Points - The 3D coordinates for each sequence as shown in the PCA plot</li></ul>
+
<p>A tool tip gives the sequence ID corresponding to a point in the
- space, and clicking a point toggles the selection of the
- corresponding sequence in the alignment window. Rectangular region
- based selection is also possible, by holding the 'S' key whilst
- left-clicking and dragging the mouse over the display.
-</p>
+space, and clicking a point toggles the selection of the corresponding
+sequence in the associated alignment window views.<!-- Rectangular region
+based selection is also possible, by holding the 'S' key whilst
+left-clicking and dragging the mouse over the display. --> By default,
+points are only associated with the alignment view from which the PCA
+was calculated, but this may be changed via the <strong>View→Associate
+Nodes</strong> sub-menu.</p>
<p>Initially, the display shows the first three components of the
- similarity space, but any eigenvector can be used by changing the selected
- dimension for the x, y, or z axis through each ones menu located
- below the 3d display.
-</p>
+similarity space, but any eigenvector can be used by changing the
+selected dimension for the x, y, or z axis through each ones menu
+located below the 3d display. The <strong><em>Reset</em></strong> button will reset axis and rotation settings to their defaults.</p>
<p>
-
+<p>
+<em>The output of points and transformed point coordinates was added to the Jalview desktop in v2.7.</em>
+<em>The Reset button and Change Parameters menu were added in Jalview 2.8.</em>
+<em>Support for PAM250 based PCA was added in Jalview 2.8.1.</em>
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