Singular Value Decomposition and R-component CP model.

<p>Singular Value Decomposition and R-component CP model.</p

In vitro tissue samples remain structurally different from histology samples (blue) over time.

<p>We identified no time point in the development of the in vitro samples that is mathematically similar to histology data. (a) Brain cancer cultures vary considerably over time getting very close to the histology samples, demonstrating they best resemble the histology samples. In vitro bone cancer (b) and breast cancer (c) samples remain clustered over all time points and exhibit no mixing of data points with histology data.</p

In vitro vs. histology samples of cancerous tissue (10a Brain, 10b Bone, and 10c Breast samples).

<p>The first two components of SVD analysis explain 72.4%, 65.9%, 66.5% of the variance for each tissue type, respectively. SVD yields a linear separation between in vitro and histology cancerous tissue samples. Two clusters (red and green) are very well separated, with few outliers. This defines and quantifies a structural difference between engineered tissues and the native tissues.</p

Analysis of histology and in vitro data sets using coupled matrix and tensor factorization (CMTF).

<p>Time mode is slotted as 0, 1, 2, 4, 6, 10, 16, 24, 72, 120, 168 in hours. Features mode contains the cell graph features: average degree, clustering coefficient C, clustering coefficient D, clustering coefficient E, average eccentricity, diameter, radius, average eccentricity 90, diameter 90, radius 90, average path length, effective hop diameter, hop plot exponent, giant connected component ratio, # connected components, average connected component size, % isolated points, % end points, # central points, % central points, mean, std, skewness, kurtosis, # nodes, # edges. These features are defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032227#pone.0032227.s001" target="_blank">Table S1</a>.</p

Three-way and two-way analysis of in vitro breast tissue data.

<p>(a) CP factorization of the tensor with modes: <i>features</i>, <i>samples</i> and <i>time</i>. Only the 2nd component can separate the two different functional states: cancer (red-triangle sign) from normal (green-plus sign) tissue samples; (b) SVD of matrix of type: <i>features</i> by <i>samples (across all times)</i>; (c) features projected over the 2nd CP component. Cell-graph features such as <i>% of end points, number of connected components, average connected component size, average path length, average eccentricity</i> are identified as influential in the analysis.</p

Coupled factorization of in vitro bone samples represented by tensor

<p><b>and histology samples represented by matrix Y.</b> (a) Both the 1st and the 2nd column of matrix <b>B</b> extracted by a CMTF model separate cancer (blue-square sign) from normal (light blue-plus sign) samples; (b) Matrix <b>D</b> corresponding to the histology samples mode extracted using a CMTF model is useful to narrow the coupled analysis since only the 1st component can separate cancer (red-triangle sign) from healthy (green-star sign) samples; (c) features captured by the 1st CMTF component.</p

Three-way and two-way analysis of in vitro bone tissue data.

<p>(a) CP factorization of the tensor with modes: <i>features</i>, <i>samples</i> and <i>time</i>. Both the 1st and the 2nd components separate the two different functional states: cancer (red-triangle sign) from normal (green-plus sign) tissue samples; (b) SVD of matrix of type: <i>features</i> by <i>samples (across all times)</i>; (c) features projected over the 1st component of CP model. Cell-graph features such as <i>% of end points</i>, <i>number of connected components</i>, <i>giant connected component ratio, average path length, average eccentricity</i> are identified as influential in the analysis since their coefficients diverge the most from zero; (d) since the 2nd component can also distinguish between two functional states we also show the 2nd CP component in features mode. Note that the influential features are different in the 2nd component, e.g., while the <i>number of connected components</i> has a high coefficient in the 1st component, its coefficient in the 2nd component is close to 0.</p

Coupled matrix and tensor factorization on in vitro breast samples represented by tensor

<p><b>and histology samples represented by matrix Y (</b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032227#pone-0032227-g002" target="_blank"><b>Figure 2</b></a><b>).</b> (a) The 1st column of matrix <b>B</b> corresponding to the in vitro samples mode extracted by a CMTF model can separate cancer (blue-square sign) from normal (light blue-plus sign) tissue samples; (b) Unlike for brain and bone tissues, matrix <b>D</b> corresponding to the histology samples mode extracted using a CMTF model cannot separate cancer samples (red-triangle sign) from healthy (green-star sign) samples; (c) features captured by the common component extracted by CMTF. Cell-graph features identified as influential in the coupled analysis are similar to the features in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032227#pone-0032227-g005" target="_blank">Figure 5c</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032227#pone-0032227-g007" target="_blank">7c</a> with some minor differences.</p

Scatter plot of the category names projected on the 1'st vector of the category component matrix of Tucker3 analysis

<p><b>Copyright information:</b></p><p>Taken from "Multiway modeling and analysis in stem cell systems biology"</p><p>http://www.biomedcentral.com/1752-0509/2/63</p><p>BMC Systems Biology 2008;2():63-63.</p><p>Published online 14 Jul 2008</p><p>PMCID:PMC2527292.</p><p></p

We projected the data over the first component vector (with explained variance of 85

64%) of the second mode (populations and time) obtained for Tucker3 analysis. At one end we have undifferentiated hMSC (Tissue Culture Plastic, or TCP) and at the other end we have the target state (fully differentiated hOST). In between we plot the data for each stimulus and time point (e.g., NSD2 = no stretch, day 2; SD5 = stretch, day 5). Because the "SD" points lie closer to the target (hOST) than their corresponding "NSD" conditions on days 2 and 5, we conclude that the stimulus "stretch" accelerates osteogenic differentiation when compared to the same stimulus without stretch.<p><b>Copyright information:</b></p><p>Taken from "Multiway modeling and analysis in stem cell systems biology"</p><p>http://www.biomedcentral.com/1752-0509/2/63</p><p>BMC Systems Biology 2008;2():63-63.</p><p>Published online 14 Jul 2008</p><p>PMCID:PMC2527292.</p><p></p