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UCSF RBVI Cytoscape Plugins

clusterMaker2: Creating and Visualizing Cytoscape Clusters

UCSF clusterMaker2 is a Cytoscape app that unifies different clustering, filtering, ranking, dimensionality reduction algorithms along with appropriate visualizations into a single interface. Current clustering algorithms include hierarchical, k-medoid, AutoSOME, k-means, HOPACH, and PAM for clustering expression or genetic data; and MCL, transitivity clustering, affinity propagation, MCODE, community clustering (GLAY), SCPS, and AutoSOME for partitioning networks based on similarity or distance values. In addition to the latter group, remotely running algorithms have been implemented in the newest release including Leiden, Infomap, Fast Greedy, Leading Eigenvector, Label Propagation and Multilevel clustering. Furthermore, fuzzy C-Means and a new "fuzzyfier" algorithm have been added to provide support for fuzzy partitioning of networks. Network partitioning clusters may also be refined by post-cluster filtering algiorithms. clusterMaker2 provides the ability to create a correlation network based on creating a distance matrix from a list of attributes and creating a "clustering" by assigning the connected components of a network to a cluster. Hierarchical, k-medoid, AutoSOME, and k-means clusters may be displayed as hierarchical groups of nodes or as heat maps. All network partitioning cluster algorithms create collapsible groups to allow interactive exploration of the putative clusters within the Cytoscape network, and results may also be shown as a separate network containing only the intra-cluster edges, or with inter-cluster edges added back.

In addition to the classical clustering algorithms discussed above, clusterMaker2 provides five algoririthms to rank clusters based on potentially orthogonal data (e.g. ranking the results of an MCL cluster based on expression data results), and dimensionality reduction approaches including Principal Component Analysis (PCA), Principal Coordinate Analysis (PCoA) and t-Distributed Stochastic Neighbor Embedding (tSNE) (hardcoded and remote implementations). clusterMaker2 also provides a selection of remotely calculated dimensionality reduction techniques namely Uniform Manifold Approximation and Projection (UMAP), Isomap, Locally Linear Embedding (LLE), Multidimensional Scaling (MDS) and Spectral Embedding.

clusterMaker2 requires version 3.8.0 or newer of Cytoscape and is available in the Cytoscape App Store.

Contents

1. Installation
2. Starting ClusterMaker2
3. Attribute Cluster Algorithms
   1. AutoSOME Clustering
   2. Creating Correlation Networks
   3. Hierarchical Clustering
   4. K-Means Clustering
   5. K-Medoid Clustering
   6. HOPACH Clustering
   7. Partition Around Medoids (PAM) Clustering
4. Network Cluster Algorithms
   1. Affinity Propagation
   2. Cluster "Fuzzifier"
   3. Connected Components
   4. Community Clustering (GLay)
   5. Fuzzy C-Means Clustering
   6. MCODE
   7. MCL
   8. SCPS (Spectral Clustering of Protein Sequences)
   9. Transitivity Clustering
   10. Leiden Clustering (remote)
   11. Infomap (remote)
   12. Fast Greedy (remote)
   13. Leading Eigenvector (remote)
   14. Label Propagation (remote)
   15. Multilevel Clustering (remote)
5. Filtering Clusters
   1. Best Neighbor Filter
   2. Cutting Edge Filter
   3. Density Filter
   4. Haircut Filter
6. Ranking Clusters
   1. Multiple nodes and edges (Additive sum)
   2. Multiple nodes and edges (Multiply sum)
   3. PageRank
   4. PageRank with Priors
   5. Hyperlink Induced Topic Search
7. Dimensionality Reduction
   1. Principal Components Analysis
   2. Principal Coordinates Analysis
   3. t-Distributed Stochastic Neighbor Embedding
   4. t-Distributed Stochastic Neighbor Embedding (remote)
   5. Uniform Manifold Approximation and Projection (remote)
   6. Isometric Mapping (remote)
   7. Locally Linear Embedding (remote)
   8. Multidimensional Scaling (remote)
   9. Spectral Embedding (remote)
8. Visualizing Results
   1. Create New Network from Attribute
   2. Create New Network from Clusters
   3. JTree TreeView
   4. JTree KnnView
   5. JTree HeatMapView (unclustered)
9. Interaction
   1. Link network selection
10. Commands
    1. cluster commands
    2. clusterrank commands
    3. clusterdimreduce commands
    4. clusterviz commands
11. Acknowledgements
12. References

1. Installation

clusterMaker2 is available through the Cytoscape App Store or by downloading the source directly from the RBVI git repository. To download clusterMaker2 using the App Store, you must be running Cytoscape 3.8.0 or newer. To install it, either launch Cytoscape 3.8.0 and then go to the App Store in your internet browser and search for "clusterMaker2". If you select the "clusterMaker2" button, you should get to the clusterMaker2 App page and the Install button should be available. Click on it and it will automatically install into Cytoscape. Alternatively, you can use the Apps→App Manager and search for clusterMaker2 and install it.

2. Starting ClusterMaker2

Once clusterMaker2 is installed, it will install four menu hierarchies under the Apps main menu: clusterMaker Cluster Attributes (Figure 2), clusterMaker Dimensionality Reduction (Figure 4), clusterMaker Filter Clusters (Figure 5), clusterMaker Ranking (Figure 6) and clusterMaker Visualizations (Figure 7).

Each of the supported clustering algorithm appears as a separate menu item underneath the clusterMaker menu. To cluster your data, simply select Apps→clusterMaker→algorithm, where algorithm is the clustering algorithm you wish to use. This will bring up the settings dialog for the selected algorithm.

There are three different types of clustering algorithms supported by clusterMaker2:

• Attribute Cluster Algorithms: a list of node attributes or a single edge attribute is chosen to perform the clustering. The normal visualization is some kind of heat map where the rows correspond to the nodes in the network. Selection of a row selects the corresponding node in the network. If an edge attribute is chosen, the columns also correspond to the nodes in the network and selection of cell in the heat map selects an edge in the network.
• Network Cluster Algorithms: an edge attribute is chosen to partition the network. Fuzzy cluster algorithms also partition the network but nodes are allowed to be in more than one cluster. The normal visualization is to create a new network from the clusters.
• Network Filter Algorithms: these are designed to be executed after a Network Cluster Algorithm has been run to refine the resulting partitioning.

The clusterMaker Dimensionality Reduction menu contains the dimensionality reduction algorithms available in clusterMaker2. When the dimensionality reduction algorithm is selected, a settings dialog for it opens.

The clusterMaker Ranking lists all the ranking options implemented in clusterMaker2. Each menu item is a different ranking algorithm that when selected will open a settings dialog.

The clusterMaker Visualization menu contains the visualization options, including showing a heat map of the data (without clustering), and options appropriate for displaying Hierarchical or k-Means clusters if either of those methods had been performed on the current network. Because information about clusters is saved in Cytoscape attributes, the JTree TreeView and JTree KnnView options will be available in a session that was saved after clustering.

Some of the network cluster algorithms as well as majority of the dimensionality reduction techniques have been implemented using an RESTful API. It allows sending the network data to a remote server to be calculated and receiving the results back to the clusterMaker2 client. If the server does not respond in maximum of 20 seconds, the job moves to be executed asynchronously in the background. clusterMaker2 uses the algorithms on scikit-learn (https://scikit-learn.org/stable/modules/classes.html) API and classes in cytoscape.jobs package (http://code.cytoscape.org/javadoc/3.8.0/org/cytoscape/jobs/package-summary.html).

3. Attribute Cluster Algorithms

3.3 Hierarchical Clustering

Hierarchical clustering builds a dendrogram (binary tree) such that more similar nodes are likely to connect more closely into the tree. Hierarchical clustering is useful for organizing the data to get a sense of the pairwise relationships between data values and between clusters. The clusterMaker2 hierarchical clustering dialog is shown in Figure 10. There are several options for tuning hierarchical clustering:

Linkage:

In agglomerative clustering techniques such as hierarchical clustering, at each step in the algorithm, the two closest groups are chosen to be merged. In hierarchical clustering, this is how the dendrogram (tree) is constructed. The measure of "closeness" is called the linkage between the two groups. Four linkage types are available:

• pairwise average-linkage: the mean distance between all pairs of elements in the two groups
• pairwise single-linkage: the smallest distance between all pairs of elements in the two groups
• pairwise maximum-linkage: the largest distance between all pairs of elements in the two groups
• pairwise centroid-linkage: the distance between the centroids of all pairs of elements in the two groups

Distance Metric:

There are several ways to calculate the distance matrix that is used to build the cluster. In clusterMaker2 these distances represent the distances between two rows (usually representing nodes) in the matrix. clusterMaker2 currently supports eight different metrics:

• Euclidean distance: this is the simple two-dimensional Euclidean distance between two rows calculated as the square root of the sum of the squares of the differences between the values.
• City-block distance: the sum of the absolute value of the differences between the values in the two rows.
• Pearson correlation: the Pearson product-moment coefficient of the values in the two rows being compared. This value is calculated by dividing the covariance of the two rows by the product of their standard deviations.
• Pearson correlation, absolute value: similar to the value above, but using the absolute value of the covariance of the two rows.
• Uncentered correlation: the standard Pearson correlation includes terms to center the sum of squares around zero. This metric makes no attempt to center the sum of squares.
• Uncentered correlation, absolute value: similar to the value above, but using the absolute value of the covariance of the two rows.
• Spearman's rank correlation: Spearman's rank correlation (ρ) is a non-parametric measure of the correlation between the two rows. This metric is useful in that it makes no assumptions about the frequency distribution of the values in the rows, but it is relatively expensive (i.e., time-consuming) to calculate.
• Kendall's tau: Kendall tau rank correlation coefficient (τ) between the two rows. As with Spearman's rank correlation, this metric is non-parametric and computationally much more expensive than the parametric statistics.
• None -- attributes are correlations: No distance calculations are performed. This assumes that the attributes are already correlations (probably only useful for edge attributes). Note that the attributes are also not normalized, so the correlations must be between 0 and 1.

Array sources

Node attributes for cluster:

This area contains the list of all numeric node columns that can be used for calculating the distances between the nodes. One or more node attributes must be selected to perform the clustering.

Edge column for cluster:

An alternative to using multiple node columns for the clustering is to select a single edge column. In this case, the resulting clustering will be across the diagonal.

Clustering Parameters

Only use selected nodes/edges for cluster:

Under certain circumstances, it may be desirable to cluster only a subset of the nodes in the network. Checking this box limits all of the clustering calculations and results to the currently selected nodes or edges.

Cluster attributes as well as nodes:

If this box is checked, the clustering algorithm will be run twice, first with the rows in the matrix representing the nodes and the columns representing the attributes. The resulting dendrogram provides a hierarchical clustering of the nodes given the values of the attributes. In the second pass, the matrix is transposed and the rows represent the attribute values. This provides a dendrogram clustering the attributes. Both the node-based and the attribute-base dendrograms can be viewed, although Cytoscape groups are only formed for the node-based clusters.

Ignore nodes/edges with no data:

A common use of clusterMaker2 is to map expression data onto a pathway or protein-protein interaction network. Often the expression data will not cover all of the nodes in the network, so the resulting dendrogram will have a number of "holes" that might make interpretation more difficult. If this box is checked, only nodes (or edges, if using an edge column) that have values in at least one of the columns will be included in the matrix.

Advanced Parameters

Set missing data to zero:

In some circumstances (e.g. hierarchical clustering of edges) it is desirable to set all missing edges to zero rather than leave them as missing. This is not a common requirement.

Adjust loops

In some circumstances (e.g. hierarchical clustering of edges) it's useful to set the value of the edge between and node and itself to a large value. This is not a common requirement.

Visualization Options

Create groups from clusters:

If this button is checked, hierarchical Cytoscape groups will be created from the clusters. Hierarchical groups can be very useful for exploring the clustering in the context of the network. However, if you intend to perform multiple runs to try different parameters, be aware that repeatedly removing and recreating the groups can be very slow.

Show TreeView when complete:

If this option is selected, a JTree TreeView is displayed after the clustering is complete.

3.5 K-Medoid Clustering

K-Medoid clustering is essentially the same as K-Means clustering except that the medoid of the cluster is used rather than the means to determine the goodness of fit. All other options are the same.

3.6 HOPACH Clustering

HOPACH (Hierarchical Ordered Partitioning and Collapsing Hybrid) is a clustering algorithm that builds a hierarchical tree by recursively partitioning a data set with PAM -- sort of like an upside-down hierarchical cluster, but with a twist. At each level of the tree clusters are ordered and potentially collapsed. The Mean/Median Split Silhouette (MSS) criteria is used to identify the level of the tree with maximally homogeneous clusters.

Basic HOPACH Tuning Parameters

Distance Metric

Split cost type:

This setting determines the method used to determine the cost of splitting a cluster. The options are:

Average split silhouette:

Calculate the average split silhouette for the clusters

Average silhouette:

Calculate the average silhouette for the clusters

Value summary method:

This setting determines the method used to calculate the summary of the values for evalutating the cluster. It can either be Mean or Median.

Maximum number of levels:

The maximum number of levels in the tree. This value should be less than 16 for performance reasons.

Maximum number of clusters at each level:

A value between 1 and 9 secifying the maximum number of children at each node in the tree.

Maximum number of subclusters at each level:

A value between 1 and 9 secifying the maximum number of children at each node in the tree when calculating MSS. This is typically the same as the value above.

Force splitting at initial level:

If true, force the initial cluster to be split.

Minimum cost reduction for collapse:

A number between 0 and 1 speciying the margin of improvement in MSS to accept a collapse step.

Array Sources

HOPACH Parameters

Use only selected nodes/edges for cluster

Cluster attributes as well as nodes

Visualization Options

Create groups from clusters:

If this button is checked, Cytoscape groups will be created from the clusters. Groups can be very useful for exploring the clustering in the context of the network. However, if you intend to perform multiple runs to try different parameters, be aware that repeatedly removing and recreating the groups can be very slow.

Show HeatMap when complete:

If this option is selected, a JTree KnnView is displayed after the clustering is complete.

3.7 Partition Around Medoids (PAM) Clustering

PAM is a common clustering algorithm similar to k-Means and k-Medoid that uses a greedy search to partition the network.

K-Cluster parameters

Distance Metric

Array sources

PAM Parameters

Use only selected nodes/edges for cluster

Cluster attributes as well as nodes

Visualization Options

Create groups from clusters:

If this button is checked, Cytoscape groups will be created from the clusters. Groups can be very useful for exploring the clustering in the context of the network. However, if you intend to perform multiple runs to try different parameters, be aware that repeatedly removing and recreating the groups can be very slow.

Show HeatMap when complete:

If this option is selected, a JTree KnnView is displayed after the clustering is complete.

4. Network Cluster Algorithms

The primary function of the network cluster algorithms is to detect natural groupings of nodes within the network. These groups are generally defined by a numeric edge attribute that contains some similarity or distance metric between two nodes, although some algorithms function purely on the existance of an edge (i.e. the connectivity). Nodes that are more similar (or closer together) are more likely to be grouped together.

5. Filtering Clusters

Filters are a tool to "fine tune" clusters after a clustering algorithm has completed. In general, the idea behing the filters are to examine the results of a clustering algorithm and, based on some metric, trim the edges (drop nodes) or add edges to improve the clustering. The goal is to reduce noise and increase the cluster quality.

6. Ranking Clusters

These algorithms were developed and added to clusterMaker2 by Henning Lund-Hanssen as part of his Master's work at the University of Oslo. For background on the motivation and details on the implementation, see his Thesis entitled: Ranklust: An extension of the Cytoscape clusterMaker2 plugin and its application to prioritize network biomarkers in prostate cancer, 2016. The general idea behind the inclusion of these algorithms into clusterMaker2 is the desire to attempt to rank the results of a clustering result based on potentially orthogonal information. For example, a user could use MCL clustering to partition a network based on an edge weight, then use node attribute information (e.g. expression data) to rank those clusters. In order to use any of the techniques below, the network should first be clustered using one of the network partitioning cluster algorithms (e.g. MCL) and a new network should be created without adding back the inter-cluster edges. Then select that network to use the following algorithms. The text below is taken from the above cited thesis. Results from cluster ranking may be displayed in the

6.1 Multiple nodes and edges (Additive sum)

The multiple attribute additive (MMA) panel provides the user the option of choosing an unlimited amount of attributes from nodes and edges.

MMA goes through all of the nodes in each cluster and sums up the number- attributes the user chose. Each cluster is then ranked based on the average sum in each cluster and ranked descending, with the highest ranking cluster as the most likely prostate cancer biomarker cluster.

There is a question as to how to rank the edges in the cluster. We chose to rank each edge as it is listed to the user in Cytoscape. So if it is listed only once time in the edge table, it will only be scored additively once. This decision was based on simplicity. To not represent the edge as something the user did not define it as, or is unable to understand. Some clustering algorithms might assign the same node or edge to several clusters, though this is not the case with the algorithms I use in this thesis. Support for this is only implemented by MAA and MAM, as they were implemented before a final decision on which clustering algorithms should be used. If MAA/MAM discovers this special case of several scores for a single node or edge, it will assign it the highest value. The reason for leaving this feature in Ranklust is to have an example on how it can be done, should it be a problem in the future.

6.2 Multiple nodes and edges (Multiply sum)

Multiple attribute multiplication (MAM) method is to some degree redundant, considering what exists from before in clusterMaker2 cluster ranking. The only difference from MAA is the scale the scores will be in. MAA adds the scores from each node and edge in the cluster through addition, MAM does it with multiplication.

A problem that occurs with multiplication is calculating scores for clusters that contain nodes with a score between 0 and 1, since the score would decrease to such a degree that it would be difficult to work with when normalizing the scores. The solution I have chosen for this problem is to make a new score from the score that is to be added to the cluster average, and add 1.0 to it. This way, when the existing average score in the cluster is multiplied with the new score, it will always increase, unless the old value was 0.0, or both the old and the new value was 1.0. In the case of values above 1, they will also be given an increase by 1.0 in order to keep it consistent if the scores vary between 0 to n. Normalizing every value before running the algorithm contributes to keep all of the values between 0 and 1, and in that way prevent scaling problems when adding 1.0 to a score over 1.0. The whole reason to add 1.0 was to counteract the problem with the score decreasing when it should be increasing.

6.3 PageRank

Discussed below as part of PRWP.

6.4 PageRank with Priors

A Random Walks algorithm which used priors, called seed-weighted random walks ranking, proved to be effective at prioritizing biomarker candidates. PageRank (PR) is an algorithm based on the Random Walks principle, and was previously used by Google to rank webpages. PageRank with Priors (PRWP) is a modified version of PR, where nodes and edges can be assigned a score prior to the PR’s traversal of the network. PR can have values assigned to the edges, but it does not require any scores in order to rank clusters, which PRWP does.

The difference between MAA and MAM compared to PR and PRWP is how the network is scored. MAA and MAM calculates the score for each cluster by summing up the attributes in edges and nodes according to the cluster attribute. PRWP scores the current network regardless of the clustering attribute.

MCL gives the option of creating a clustered network, which opens up the possibility of working with two types of the same network, non-clustered and clustered. They both have the clustering attribute in the network, edge and node table, so that the ranking algorithms are able to score the clusters. PRWP scores the currently selected network in Cytoscape, resulting in the option of scoring the non-clustered network or clustered network. The last option gives the clustering algorithm a bigger impact on the score, because the clustered network has perturbated edges between nodes that is not in the same cluster. MCL in Cytoscape can show the "inter-cluster" connecting edges, which is the egdes that was perturbed during clustering. This last option is a combination of the two others. It will be visually close to the clustered network, but algorithms that run on the network with inter- cluster edges will have the same result as the network only containing the cluster attribute.

Implementation wise, there is also a difference in how the scores are stored in the network after the algorithm is finished executing. All the scores are stored in the nodes. To give information to the user about the scores the edges received, each edge will display the total score for the cluster it is a member of, just like the nodes. Only PRWP and PR will also display the single node score.

6.5 Hyperlink Induced Topic Search

Hyperlink-Induced Topic Search, HITS, an algorithm that is similar to PageRank, was developed around the same time. HITS will not be used to calculate cluster scores and ranks, due to the fact that it does not require any form of weighting in nodes or edges. Though, it can be used in combination with other ranking algorithms through the use of MAM or MAA.

An example of this could be running PRWP with a score attribute, then HITS on the same network. The next step would be to combine the two scores from PRWP and HITS with MAA.

7. Dimensionality Reduction

New in clusterMaker2 version 1.1 and later is the addition of algorithms for performing dimensionality reduction. A reasonable discussion of dimensionality reduction analysis is available in Wikipedia.

7.1 Principal Components Analysis

The main linear technique for dimensionality reduction, principal component analysis, performs a linear mapping of the data to a lower-dimensional space in such a way that the variance of the data in the low-dimensional representation is maximized. In practice, the covariance (and sometimes the correlation) matrix of the data is constructed and the eigen vectors on this matrix are computed. The eigen vectors that correspond to the largest eigenvalues (the principal components) can now be used to reconstruct a large fraction of the variance of the original data. The clusterMaker2 implementation of PCA provides the ability to choose covariance or correlation.

Array Sources

Node attributes for PCA:

Choose the list of attributes to use for the analysis

Only use selected nodes for PCA:

Restricts the calculation to a subset of the network

Ignore nodes with no data:

If none of the attributes has a value for a node, that node is excluded

PCA Parameters

Type of matrix to use for PCA:

The type of matrix to use for the principal components:

covariance:

Compute the covariance matrix

correlation:

Compute the correlation matrix

Standardize data?:

If this is checked, the input data is standardized by adjusting each column by subtracting the mean of the column from each data item and dividing by the standard deviation.

Result Options

Create PCA Result Panel:

Adds a new tab to the results panel with each principal component. Selecting the component will select all of the nodes in the network that are part of that component

Create PCA scatter plot:

If checked, after the PCA calculation is complete, a scatter plot is displayed (see Figure 28). The scatter plot includes the loading vectors for each node attribute as well as options to color the loading vectors, select the components to use for the X and Y axes.

Minimum variance for components (%):

This sets the minimum explained variance for a component to be considered for display in the scatter plot.

7.2 Principal Coordinates Analysis

Principal coordinates analysis (PCoA; also known as metric multidimensional scaling) summarises and attempts to represent inter-object (dis)similarity in a low-dimensional, Euclidean space. PCoA is similar to PCA except that it takes a dissimilarity matrix rather than a matrix, which makes it better suited to performing dimensionality reduction on the variance in edge attributes. Note that you must make sure that you convert your edge attribute values to distances (e.g. smaller is better) rather than weights (larger is better).

Source for Array Data

Edge weight cutoff

Array data adjustments

PCoA Parameters

Negative eigenvalue handling:

Changes how the algorithm deals with negative eigenvalues:

Discard:

The default -- just discard the values

Keep:

Keep the negative eigenvalues

Correct:

Attempt to correct the negative eigenvalues

Result Options

Create PCoA scatter plot:

If checked, after the PCoA calculation is complete, a scatter plot is displayed (see Figure 29). The scatter plot only includes the first 2 components, organized as X and Y. Buttons allow the user to map node colors from the network view to the scatter plot and to map the X and Y positions on the scatter plot to the network. In this way, PCoA can be used as a layout algorithm that emphasizes the positions that account for the most variance in the network.

7.3 t-Distributed Stochastic Neighbor Embedding

t-Distributed Stochastic Neighbor Embeding (tSNE) is a technique or dimensionality reduction that is particularly well suited for the visualization of high-dimensional datasets. The technique can be implemented via Barnes-Hut approximations, allowing it to be applied on large real-world datasets.

Array Sources

t-SNE Parameters

Use only selected nodes/edges for cluster

Ignore nodes with no data:

If none of the attributes has a value for a node, that node is excluded

Initial Dimensions

This provides an opportunity to reduce the number of dimensions of the data set before even attempting to run t-SNE. If this is -1 no initial reduction is attempted. For larger values, the data is first passed through PCA and only the data corresponding to the first Initial Dimensions components is used.

Perplexity

Sets the balance between local and global aspects of the data. The value roughly represents the average number of neighbors for each node.

Number of iterations

The number of iteractions to

Use Barnes-Hut approximation

If selected, use the Barnes-Hut approximation.

Theta value for Barnes-Hut

The theta value determines how exact the Barnes-Hut approximation is. A value of 0 is an exact calculation (actually it isn't really supported by the underlying implementation), and a value of 1 is the loosest approximation.

Result Options

Show scatter plot with results:

If checked, after the calculation is complete, a scatter plot is displayed (see Figure 30). Buttons allow the user to map node colors from the network view to the scatter plot and to map the X and Y positions on the scatter plot to the network. In this way, t-SNE can be used as a layout algorithm that emphasizes the positions that account for the most variance in the network.

Figure 30. The t-SNE settings dialog.

7.4 t-Distributed Stochastic Neighbor Embedding (remote)

t-SNE is a tool to visualize high-dimensional data. It converts similarities between data points to joint probabilities and tries to minimize the Kullback-Leibler divergence between the joint probabilities of the low-dimensional embedding and the high-dimensional data. t-SNE has a cost function that is not convex, i.e. with different initializations we can get different results. It is highly recommended to use another dimensionality reduction method (e.g. PCA for dense data or TruncatedSVD for sparse data) to reduce the number of dimensions to a reasonable amount (e.g. 50) if the number of features is very high. This will suppress some noise and speed up the computation of pairwise distances between samples.

Array Sources

t-SNE (remote) Parameters

Perplexity

The perplexity is related to the number of nearest neighbors that is used in other manifold learning algorithms. Larger datasets usually require a larger perplexity. Consider selecting a value between 5 and 50. Different values can result in significantly different results.

Number of iterations

The number of iterations of the algorithm to perform

Early Exaggeration

Controls how tight natural clusters in the original space are in the embedded space and how much space will be between them. For larger values, the space between natural clusters will be larger in the embedded space. Again, the choice of this parameter is not very critical. If the cost function increases during initial optimization, the early exaggeration factor or the learning rate might be too high.

Metric

The metric to use when calculating distance between instances in a feature array. The default is "euclidean" which is interpreted as squared euclidean distance.

• Minkowski style metrics
• Euclidean
• Manhattan
• Chebyshev
• Minkowski
• Miscellaneous spatial metrics
• Canberra
• Braycurtis
• Haversine
• Normalized spatial metrics
• Mahalanobis
• Wminkowski
• Seuclidean
• Angular and correlation metrics
• Cosine
• Correlation
• Metrics for binary data
• Hamming
• Jaccard
• Dice
• Russellrao
• Kulsinski
• Rogerstanimoto
• Sokalmichener
• Sokalsneath
• Yule

Learning rate

The learning rate for t-SNE is usually in the range [10.0, 1000.0]. If the learning rate is too high, the data may look like a ‘ball’ with any point approximately equidistant from its nearest neighbours. If the learning rate is too low, most points may look compressed in a dense cloud with few outliers. If the cost function gets stuck in a bad local minimum increasing the learning rate may help.

Init

Initialization of embedding. Possible options are ‘random’, ‘pca’, and a numpy array of shape (n_samples, n_components). PCA initialization cannot be used with precomputed distances and is usually more globally stable than random initialization.

Result Options

Show scatter plot with results:

If checked, after the calculation is complete, a scatter plot is displayed. Buttons allow the user to map node colors from the network view to the scatter plot and to map the X and Y positions on the scatter plot to the network. In this way, t-SNE can be used as a layout algorithm that emphasizes the positions that account for the most variance in the network.

Figure 31. The UMAP settings dialog.

7.5 Uniform Manifold Approximation and Projection (remote)

Uniform Manifold Approximation and Projection (UMAP) is a dimension reduction technique that can be used for visualisation similarly to t-SNE, but also for general non-linear dimension reduction.

Array Sources

UMAP Parameters

Number of Neighbors

This parameter controls how UMAP balances local versus global structure in the data. It does this by constraining the size of the local neighborhood UMAP will look at when attempting to learn the manifold structure of the data. This means that low values of number of neighbors will force UMAP to concentrate on very local structure (potentially to the detriment of the big picture), while large values will push UMAP to look at larger neighborhoods of each point when estimating the manifold structure of the data, losing fine detail structure for the sake of getting the broader of the data.

Minimum Distance

The minimum distance parameter controls how tightly UMAP is allowed to pack points together. It, quite literally, provides the minimum distance apart that points are allowed to be in the low dimensional representation. This means that low values of minimum distance will result in clumpier embeddings. This can be useful if you are interested in clustering, or in finer topological structure. Larger values of minimum distance will prevent UMAP from packing points together and will focus on the preservation of the broad topological structure instead.

Metric

This controls how distance is computed in the ambient space of the input data. By default UMAP supports a wide variety of metrics.

• Minkowski style metrics
• Euclidean
• Manhattan
• Chebyshev
• Minkowski
• Miscellaneous spatial metrics
• Canberra
• Braycurtis
• Haversine
• Normalized spatial metrics
• Mahalanobis
• Wminkowski
• Seuclidean
• Angular and correlation metrics
• Cosine
• Correlation
• Metrics for binary data
• Hamming
• Jaccard
• Dice
• Russellrao
• Kulsinski
• Rogerstanimoto
• Sokalmichener
• Sokalsneath
• Yule

Scale

true/false. If true, preprocess the data to scale the matrix.

Result Options

Show scatter plot with results:

If checked, after the calculation is complete, a scatter plot is displayed. Buttons allow the user to map node colors from the network view to the scatter plot and to map the X and Y positions on the scatter plot to the network.

7.6 Isometric Mapping (remote)

Non-linear dimensionality reduction through Isometric Mapping. One of the earliest approaches to manifold learning is the Isomap algorithm, short for Isometric Mapping. Isomap can be viewed as an extension of Multi-dimensional Scaling (MDS) or Kernel PCA. Isomap seeks a lower-dimensional embedding which maintains geodesic distances between all points.

Array Sources

Isomap Parameters

Number of Neighbors

Number of neighbors to consider for each point.

Eigen Solver

• ‘auto’ : Attempt to choose the most efficient solver for the given problem.
• ‘arpack’ : Use Arnoldi decomposition to find the eigenvalues and eigenvectors.
• ‘dense’ : Use a direct solver (i.e. LAPACK) for the eigenvalue decomposition.

Convergence Tolerance

Convergence tolerance passed to arpack or lobpcg. Not used if Eigen Solver is set to ‘dense’.

Path Method

Method to use in finding shortest path.

• ‘auto’ : attempt to choose the best algorithm automatically.
• ‘FW’ : Floyd-Warshall algorithm.
• ‘D’ : Dijkstra’s algorithm.

Neighbors Algorithm

Algorithm to use for nearest neighbors search, passed to neighbors. Nearest Neighbors instance.

Maximum Iterations

Maximum number of iterations for the arpack solver. Not used if Eigen Solver is set to ‘dense’.

Result Options

Show scatter plot with results:

If checked, after the calculation is complete, a scatter plot is displayed. Buttons allow the user to map node colors from the network view to the scatter plot and to map the X and Y positions on the scatter plot to the network.

7.7 Locally Linear Embedding (remote)

Locally linear embedding (LLE) seeks a lower-dimensional projection of the data which preserves distances within local neighborhoods. It can be thought of as a series of local Principal Component Analyses which are globally compared to find the best non-linear embedding.

Array Sources

LLE Parameters

Number of Neighbors

Number of neighbors to consider for each point.

Regularization Constant

Regularization constant, multiplies the trace of the local covariance matrix of the distances

Eigen Solver

• 'auto' : algorithm will attempt to choose the best method for input data
• 'arpack': use arnoldi iteration in shift-invert mode. For this method, M may be a dense matrix, sparse matrix, or general linear operator. Warning: ARPACK can be unstable for some problems. It is best to try several random seeds in order to check results.
• 'dense': use standard dense matrix operations for the eigenvalue decomposition. For this method, M must be an array or matrix type.

Tolerance

Tolerance for ‘arpack’ method. Not used if Eigen Solver is set to ’dense’.

Maximum Iterations

Maximum number of iterations for the arpack solver. Not used if Eigen Solver is set to ’dense’.

Method

standard: use the standard locally linear embedding algorithm. hessian: use the Hessian eigenmap method. This method requires n_neighbors> n_components * (1 + (n_components + 1) / 2. modified: use the modified locally linear embedding algorithm. ltsa: use local tangent space alignment algorithm.

Hessian Tolerance

Tolerance for Hessian eigenmapping method. Only used if Method is set to 'hessian'

Modified Tolerance

Tolerance for modified LLE method. Only used if Method is set to 'modified'

Neighbors Algorithm

Algorithm to use for nearest neighbors search, passed to neighbors. Nearest Neighbors instance.

Result Options

Show scatter plot with results:

If checked, after the calculation is complete, a scatter plot is displayed. Buttons allow the user to map node colors from the network view to the scatter plot and to map the X and Y positions on the scatter plot to the network.

7.8 Multidimensional Scaling (remote)

Multidimensional scaling (MDS) seeks a low-dimensional representation of the data in which the distances respect well the distances in the original high-dimensional space. In general, MDS is a technique used for analyzing similarity or dissimilarity data. It attempts to model similarity or dissimilarity data as distances in a geometric spaces. The data can be ratings of similarity between objects, interaction frequencies of molecules, or trade indices between countries. There exists two types of MDS algorithm: metric and non metric. In Metric MDS, the input similarity matrix arises from a metric (and thus respects the triangular inequality), the distances between output two points are then set to be as close as possible to the similarity or dissimilarity data. In the non-metric version, the algorithms will try to preserve the order of the distances, and hence seek for a monotonic relationship between the distances in the embedded space and the similarities/dissimilarities.

Array Sources

MDS Parameters

Metric

If checked, perform metric MDS; otherwise, perform nonmetric MDS.

Number of Initializations

Number of times the SMACOF algorithm will be run with different initializations. The final results will be the best output of the runs, determined by the run with the smallest final stress.

Maximum Iterations

Maximum number of iterations of the SMACOF algorithm for a single run.

Eps

Relative tolerance with respect to stress at which to declare convergence.

Dissimilarity

Dissimilarity measure to use:

• ‘euclidean’: Pairwise Euclidean distances between points in the dataset.
• ‘precomputed’: Pre-computed dissimilarities are passed directly to fit and fit_transform.

Result Options

Show scatter plot with results:

If checked, after the calculation is complete, a scatter plot is displayed. Buttons allow the user to map node colors from the network view to the scatter plot and to map the X and Y positions on the scatter plot to the network.

7.9 Spectral Embedding (remote)

Spectral Embedding is an approach to calculating a non-linear embedding. It finds a low dimensional representation of the data using a spectral decomposition of the graph Laplacian. The graph generated can be considered as a discrete approximation of the low dimensional manifold in the high dimensional space. Minimization of a cost function based on the graph ensures that points close to each other on the manifold are mapped close to each other in the low dimensional space, preserving local distances.

Array Sources

Spectral Parameters

Affinity

• ‘nearest_neighbors’ : construct the affinity matrix by computing a graph of nearest neighbors.
• ‘rbf’ : construct the affinity matrix by computing a radial basis function (RBF) kernel.
• ‘precomputed’ : interpret X as a precomputed affinity matrix.
• ‘precomputed_nearest_neighbors’ : interpret X as a sparse graph of precomputed nearest neighbors, and constructs the affinity matrix by selecting the n_neighbors nearest neighbors.
• callable : use passed in function as affinity the function takes in data matrix (n_samples, n_features) and return affinity matrix (n_samples, n_samples).

Gamma

Kernel coefficient for rbf kernel. If None, gamma will be set to 1/n_features.

Eigen Solver

The eigenvalue decomposition strategy to use. AMG requires pyamg to be installed. It can be faster on very large, sparse problems. If None, then 'arpack' is used.

Number of Neighbors

Number of nearest neighbors for graph building. If None, Number of Neighbors will be set to max(n_samples/10, 1).

Result Options

Show scatter plot with results:

If checked, after the calculation is complete, a scatter plot is displayed. Buttons allow the user to map node colors from the network view to the scatter plot and to map the X and Y positions on the scatter plot to the network.

8. Visualizing Results

clusterMaker2 provides two basic approaches for visualizations: Heat Maps and Networks. clusterMaker2 provides three options for network display: Create New Network from Attribute, Create New Network from Clusters, and three types of heat map display: HeatMapView (unclustered), JTree KnnView. JTree TreeView, and

Figure 32. The network created by clusterMaker2's MCL clustering algorithm for MS/TAP protein-protein interaction data from yeast. The network was created by using Create New Network from Attribute and selecting the option to add inter-cluster edges back.

6.1 Create New Network from Attribute

This menu item can be used to create a network from any numerical attribute, where only the nodes with the same values of the attribute are connected. Note that there is no binning of these values, so using continues values would result in clusters that make little sense. There are two options on the dialog:

Display only selected nodes (or edges)

Self-explanatory, the new network will contain only the nodes selected in the current network

Restore inter-cluster edges after layout

If this option is selected, the resulting network will be created with only the intra-cluster edges. Then, after the network is laid out (and partitioned as a result) the inter-cluster edges will be added back in.

6.2 Create New Network from Clusters

This menu item will be selectable if a network cluster algorithm has completed and stored the cluster numbers in a node attribute. When selected, this menu will create a new network that contains only the intra-cluster edges, then layout that network using the unweighted force-directed layout algorithm. All inter-cluster edges will be dropped. If there is value in visualizing the network with the inter-cluster edges also, see the Create New Network from Attribute menu item above. The user interfaces for the heat map displays are very similar. The most complicated is the JTree TreeView, which will be discussed in detail first. The JTree KnnView and HeatMapView (unclustered) will then be discussed briefly, with an emphasis on how they differ from the JTree TreeView.

Figure 33. clusterMaker2's JTree TreeView. The larger image shows the results of hierarchically clustering the nodes and five node attributes (expression data from a heat shock experiment). The inset shows the results of hierarchical clustering using an edge attribute. The resulting network is symmetrical across the diagonal, and the dendrograms at the left and top are the same.

6.4 JTree TreeView

Hierarchical clustering results are usually displayed with the JTree TreeView (see Figure 33). This view provides a color-coded "Heat Map" of the data values and the dendrogram from clustering. The JTree TreeView can be created by clicking on the Visualize Clusters button in the Hierarchical cluster dialog (Figure 10) or by selecting Apps→clusterMaker Visualizations→JTree TreeView from the Cytoscape tool bar. Note that both of these methods will be "grayed out" unless hierarchical clustering has been performed on the current network. The information necessary to create the TreeView is retained across sessions (stored in network attributes), so these options should be available when you reload a session that had been saved after hierarchical clustering.

The basic TreeView window has four main vertical windows: Node Dendrogram, Global HeatMap, Zoom HeatMap, and the Node List. These windows may be resized to emphasize different portions of the TreeView. Each of the windows is discussed in detail below. Note that selection of a row in TreeView will select the corresponding node in the current network view in Cytoscape (if that node exists). The reverse is also true -- selection in Cytoscape will select the corresponding nodes in TreeView. This is an important feature of clusterMaker2: multiple views (current network, multiple heat maps if present) respond simultaneously to a selection in any one view.

Node Dendrogram

The leftmost pane displays the node dendrogram for the heat map. At the top of the pane is a Status window that changes depending on the location of the pointer. With the pointer over the node dendrogram, the Status window will display the ID and correlation for the currently selected branch of the dendrogram (if any). If the cursor is over the Global HeatMap window the Status window displays the number of genes (nodes) and arrays (attributes) selected and the range of the selections. Finally, if the cursor is over the Zoom HeatMap window, the Status window displays the node and attribute name as well as the value of the spot under the pointer.

Mouse and keyboard actions in node dendrogram pane

Action	Target	Result
click	Dendrogram branch	Select that branch of the dendrogram and all children
up arrow	If there is a currently selected branch, select its parent and all subsequent children
down arrow	If there is a currently selected branch, move to the top branch and deselect the bottom branch
left arrow	If there is a currently selected branch, move to the top branch and deselect the bottom branch
right arrow	If there is a currently selected branch, move to the bottom branch and deselect the top branch

Global HeatMap

The Global HeatMap is the next pane over, divided into two parts. The upper part contains the dendrogram for the attributes (if they were clustered) and the lower part contains the entire heat map in a scrolling window. Horizontal and vertical scroll bars will be provided as needed. Selection of branches in the dendrogram in the upper window is similar to that in the node dendrogram (see above). Selections in the Global HeatMap pane are shown with a thin yellow outline. The area corresponding to the Zoom HeatMap view is shown with a thin blue outline.

Mouse and keyboard actions in global heatmap pane

Action	Target	Result
+	Heat map	Zoom the global view by 2X
-	Heat map	Zoom the global view by 1/2 (but not smaller than 1 pixel in width or height for each cell)
click	Heat map	Select that row of the heat map
shift-click	Heat map	Select that cell of the heat map
drag	Heat map	Select the rows encompassed by the dragged-out region
shift-drag	Heat map	Select the region encompassed by the dragged-out area
up arrow	If there is a current selection, move that selection up one row
down arrow	If there is a current selection, move that selection down one row
left arrow	If there is a current selection, move that selection left one column
right arrow	If there is a current selection, move that selection right one column
control-up arrow	If there is a current selection, expand that selection by two rows (one on the top and one on the bottom)
control-down arrow	If there is a current selection, contract that selection by two rows (one on the top and one on the bottom)
control-left arrow	If there is a current selection, expand that selection by two columns (one on the left and one on the right)
control-right arrow	If there is a current selection, contract that selection by two columns (one on the left and one on the right)

Zoom HeatMap

The Zoom HeatMap view shows the nodes and attributes selected in the Global HeatMap window. It has three sections: the top section lists the names of the attributes that correspond to the columns in the heat map, the next section down contains the dendrogram for the columns (if one was calculated), and the bottom section contains the heat map itself. There are no mouse or keyboard actions in the top or bottom windows, but if a dendrogram is present, it will respond to mouse and keyboard actions in the same way as the Global HeatMap dendrogram.

Node List

Finally, the right-most pane lists each node shown in the Zoom HeatMap pane. The list is sized to correspond exactly to the rows in the Zoom HeatMap pane and scrolls along with it so that the names stay aligned with the rows.

In addition to the various windows, each heat map dialog provides a series of buttons:

• Settings...
• Save Data...
• Export Graphics...
• Flip Tree Nodes (in the JTree TreeView dialog only)
• Map Colors Onto Network...
• Close

Figure 34. Pixel Settings Dialog.

Settings...

The Settings... button brings up the Pixel Settings dialog, which allows users to customize the dimensions of heat map cells in the Global and Zoom panes. The dimensions can be specified as pixel values (Fixed scale) for X (width) and Y (height), or to automatically fill the available space (Fill).

Users can specify which color scheme should be used: a red-green (RedGreen) continuum or the default yellow-blue (YellowBlue). Color schemes may also be customized by setting the Positive, Zero, Negative, and Missing values. Once these values have been assigned, they can be saved as presets (Make Preset). The Load... and Save.. buttons are used to load and save color sets, respectively.

The Pixel Settings dialog also provides a Contrast slider to adjust the contrast of the colors. This is useful to emphasize more subtle differences in heat map values. Finally, LogScale rather than a linear mapping of values to colors can be used, and the center point set to improve the display of single-tailed data.

Save Data...

In order to facilitate data exchange and analysis by other software, the Save Data... button will export the current data in Cluster format, including the .cdt, .gtr, and .atr files, as appropriate.

Figure 35. Export Graphics Dialog.

Export Graphics...

The Export Graphics... button brings up the Export Graphics Dialog (see Figure 35), which provides an interface to export the heat map to a variety of different graphics formats:

Graphics Formats Supported by clusterMaker2

Format Type Quality

png Bitmap highest bitmap quality

jpg Bitmap reasonable bitmap quality, but aberrations visible at high scales

bmp Bitmap very good bitmap quality

pdf Vector excellent quality

svg Vector excellent quality, but not widely supported

eps Vector excellent quality, but will need to be processed by a separate program

Figure 36. Example export of a portion of a TreeView heat map showing both the Node and Attribute dendrograms (click on the image to see a larger version).

Generally, vector formats yield a higher-quality appearance, as they can be scaled. Particularly for use in a graphics package such as Adobe Illustrator or Adobe Photoshop, vector formats are much preferred. For inclusion in a web page or presentation, png is a reasonable choice if you are not planning on doing any significant zooming and cropping (see Figure 36).

Options for what is included in the output depend on the type of display. For TreeView heat maps that are symmetric (i.e., created using an edge attribute), the Left Node Tree and the Top Node Tree may be included in the output, and you will almost always want to include the Heat Map itself. For TreeView heat maps with both nodes and attributes clustered, you will be able to include the Node Tree, Attribute Tree, and the Heat Map. If the attributes were not clustered, the Attribute Tree will not be available.

If only part of the heat map is desired, you can choose to save just the selected portion (Selection Only). Note that to include dendrograms in the output, you will need to select a full subtree.

Flip Tree Nodes

The Flip Tree Nodes button will flip the order of the trees in the top dendrogram, if it exists. At this time, there is no corresponding way to flip the left dendrogram.

Map Colors Onto Network...

The Map Colors Onto Network... button provides a method for mapping the colors from the heat map back onto Cytoscape nodes (and edges for symmetric heat maps). If a single column (attribute) is selected, a new VizMap will be created and the colors corresponding to that attribute will be assigned to the nodes in the network view. If multiple columns are selected, the Map Colors to Network dialog (shown in Figure 37 below) will be displayed. From this dialog, you will be able to select a single attribute and create the VizMap for that attribute, or select multiple attributes to create a VizMap for each attribute and animate through them. An Animation Speed slider allows the user to select the speed of the animation. The initial pass will take slightly longer as the VizMap for each attribute needs to be created, but after that, the animation speed should correspond closely to the slider. If the nodeCharts plugin is loaded, you will also be able to create "HeatStrips", which are small bar-charts that represent the heat map values, that will appear under the corresponding nodes in the network view.

NOTE: At this time, there is no way to save the animation as a movie, although this is a much-requested feature and will be implemented in the future.

Figure 37. The Map Colors to Network Dialog

Close

The Close button closes the dialog.

Figure 38. The JTree KnnView dialog showing the results of visualizing a k-Means cluster with k=30.

6.5 JTree KnnView

The results of k-Means clustering can be shown with the JTree KnnView (Figure 38). This is much the same as the JTree TreeView discussed above, except that the dendrogram areas are empty and the clusters are separated by a blank space the width of one cell. All of the features discussed as part of the JTree TreeView are available in the JTree KnnView except the Flip Tree Nodes button, and the Node Tree and Attribute Tree options are not available in the Export Graphics dialog.

6.6 HeatMapView (unclustered)

Any attribute or group of attributes may be shown as a heat map using the clusterMaker2 HeatMapView (unclustered). The dialog is identical to the JTree KnnView except that since there are no clusters, there are no blank spaces separating the clusters.

7. Interaction

7.1 Link network selection

This capability is planned, but not yet implemented in clusterMaker2

8. Acknowledgements

The Hierarchical and k-Means implementations of clusterMaker2 are based on the Cluster 3.0 C implementation (from Michiel de Hoon while at the Laboratory of DNA Information Analysis at the University of Tokyo), which was based on the original Cluster program written by Michael Eisen. The heatmap/dendrogram visualization is based on Java TreeView implemented by Alok Saldanha while at Stanford University. The MCL cluster algorithm was written based on the original thesis by Stejn van Dongen, with reference to the Java implementation by Gregor Heinrichi (see http://www.arbylon.net/projects/knowceans-mcl/doc/).

9. References

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