What is the highest dimensional visualization you can think of? Now imagine it being interactive. The following details a Frankenstein visualization packing a smorgasbord of multivariate goodness.
Enter first, self-organizing maps (SOM). I first fell into a love dream with SOMs after using the kohonen package. The wines data set example is a beautiful display of information.
Eloquently, making the visualization above is relatively easy. SOM is used to organize the data into related groups on a grid. Hierarchical cluster analysis (HCA) is used to classify the SOM codes into three groups.
HCA cluster information is mapped to the SOM grid using hexagon background colors. The radial bar plots show the variable (wine compounds’) patterns for samples (wines).
The goal for this project was to reproduce the kohonen.plot using ggplot2 and make it interactive using shiny.
The main idea was to use SOM to calculated the grid coordinates, geom_hexagon for the grid packing and any ggplot for the hexagon-inset sub plots. Some basic inset plots could be bar or line plots.
Part of the beauty is the organization of any ggplot you can think of (optionally grouping the input data or SOM codes) based on the SOM unit classification.
A Pavlovian response might be; does it network?
Yes we can (network). Above is an example of different correlation patterns between wine components in related groups of wines. For example the green grid points identify wines showing a correlation between phenols and flavanoids (probably reds?). Their distance from each other could be explained (?) by the small grid size (see below).
The next question might be, does it scale?
There is potential. The 4 x 4 grid shows radial bar plot patterns for 16 sub groups among the 3 larger sample groups. The next next 6 x 6 plot shows wine compound profiles for 36 ~related subsets of wines.
A useful side effect is that we can use SOM quality metrics to give us an extra-dimensional view into tuning the visualization. For example we can visualize the number of samples per grid point or distances between grid points (dissimilarity in patterns).
This is useful to identify parts of the somClustPlot showing the number of mapped samples and greatest differences.
One problem I experienced was getting the hexagon packing just right. I ended making controls to move the hexagons ~up/down and zoom in/out on the plot. It is not perfect but shows potential (?) for scaffolding highly multivariate visualizations? Some of my other concerns include the stochastic nature of SOM and the need for som random initialization for the embedding. Make sure to use it with set.seed() to make it reproducible, and might want to try a few seeds. Maybe someone out there knows how to make this aspect of SOM more robust?
R users: networkly: network visualization in R using Plotly
In addition to their more common uses, networks can be used as powerful multivariate data visualizations and exploration tools. Networks not only provide mathematical representations of data but are also one of the few data visualization methods capable of easily displaying multivariate variable relationships. The process of network mapping involves using the network manifold to display a variety of other information e.g. statistical, machine learning or functional analysis results (see more mapped network examples).
The combination of Plotly and Shiny is awesome for creating your very own network mapping tools. Networkly is an R package which can be used to create 2-D and 3-D interactive networks which are rendered with plotly and can be easily integrated into shiny apps or markdown documents. All you need to get started is an edge list and node attributes which can then be used to generate interactive 2-D and 3-D networks with customizable edge (color, width, hover, etc) and node (color, size, hover, label, etc) properties.
2-Dimensional Network (interactive version)
3-Dimensional Network (interactive version)
Recently I had the pleasure of teaching data analysis at the 2014 UC Davis Proteomics Workshop. This included a hands on lab for making gene ontology enrichment networks. You can check out my lecture and tutorial below or download all the material.
2014 UC Davis Proteomics Workshop Dmitry Grapov is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Fig. 1 Immune cell infiltration and beta-cell destruction in prediabetic NOD mice. A Visualization of spatial islet distribution in the context of the vascular network in the intact pancreas. A prediabetic NOD mouse at 27-week. B The body region of the NOD mouse shown in A. Note that substantial beta-cell destruction is observed in the NOD pancreas (i.e. a loss of GFP-expressing beta-cells). C Intraislet capillary network in the body region of a wild-type mouse at 21-week. D Immunohistochemical staining. Insulin (green), glucagon (red), somatostatin (white) and nuclei (blue). E Hypertrophic islet with massive infiltration of T-lymphocytes. (a) Hematoxylin-Eosin (HE) staining of the islet showing peripheral- and intra-islet infiltrating lymphocytes and remaining endocrine islet cells. (b) A serial section stained for CD4-positive lymphocytes by ABC-staining (brown). c A serial section stained for CD8-positive lymphocytes. F Ultrastructural analysis of hypertrophic islets in non-diabetic and diabetic littermates. (a) Non-diabetic male NOD mouse (41-week old, 4-h fasting BG: 136 mg/dL) showing a hyperactive beta-cell with lymphocyte infiltration and vesicles without dense core granules. (b) Beta-cells in diabetic female NOD mouse (40-week old, 4-h fasting BG: 559 mg/dL) appears to be intact despite the presence of ongoing insulitis. G Progressive degradation of endoplasmic reticulum (ER). (a) Well-developed ER (ER) in a beta-cell undergoing insulitis. (b) ER degradation. Ribosomes are detached (shed) from the ER membrane and are aggregated (ER). Nuclear damage is seen with the formation of foam-like structures (N). Immature granules with less dense cores (G) as well as cytoplasmic liquefaction (CL) are observed. (c) ER membrane breakdown. ER membrane breakdown resulted in aggregation of shed ribosomes (ER). An adjacent PP-cell (PP) appears to be intact (identified by characteristic moderately dense cores of pancreatic polypeptide-containing secretory granules). (d) Beta-cell degradation. ER swelling (ER), ribosome shedding, amorphous cytoplasmic material (R) and cytoplasmic, liquefaction (L) are observed in the same beta-cell
Fig. 2 Progression of autoimmune diabetes in NOD mice. A (a) Virtual slice capture of a whole mouse pancreas from mouse insulin promoter I (MIP)-GFP mice on NOD background. (b) Measured beta-cell/islet distribution. (c) Corresponding 3D scatter plot of islet parameters depicts distribution of islets with various sizes and shapes. Each dot represents a single islet. B (a) Representative data showing islet growth in wild-type mice at 20- and 28-week of age. (b) Examples of beta-cell loss at 20-week (non-diabetic) and 28-week (diabetic) in NOD mice. C Heterogeneous beta-cell loss in NOD mice. Frequency is plotted against islet size. D Three distinct groups in the development of T1D in NOD mice. 3D scatter plot showing the relationship among blood glucose levels (BG), total beta-cell area and age. Three groups of mice are color-coded as diabetic mice (red), young mice with normoglycemia (<25 week; green) and old mice with normoglycemia (25–40 week; blue)
Fig. 3 Biochemical network displaying metabolic differences between diabetic and non-diabetic NOD mice. Metabolites are connected based on biochemical relationships (blue, KEGG RPAIRS) or structural similarity (violet, Tanimoto coefficient ≥0.7). Metabolite size and color represent the importance (O-PLS-DA model loadings, LV 1) and relative change (gray p adj > 0.05; green increase; red decrease) in diabetic compared non-diabetic NOD mice. Shapes display metabolites’ molecular classes or biochemical sub-domains and top descriptors of T1D-associated metabolic perturbations (Table 1) are highlighted with thick black borders
Fig. 4 Partial correlation network displaying associations between all type 1 diabetes-dependent metabolomic perturbations. All significantly altered metabolites (p adj ≤ 0.05, Supplemental Table S3) are connected based on partial correlations (p adj ≤ 0.05). Edge width displays the absolute magnitude and color the direction (orange positive; blue negative) of the partial-coefficient of correlation. Metabolite size and color represent the importance (O-PLS-DA model loadings, LV 1) and relative change (gray p adj > 0.05; green increase; red decrease) in diabetic compared non-diabetic NOD mice. Shapes display metabolites’ molecular classes or biochemical sub-domains (see Fig. 3 legend), and top descriptors of T1D-associated metabolic perturbations (Table 1) are highlighted with thick black borders
In conclusion, we identified marked differences in the rates of progression of NOD mice to T1D. Metabolomic analysis was used to identify age and sex independent metabolic markers, which may explain this heterogeneity. Future studies combining metabolic end points (as they correlate with beta-cell mass) and genetic risk profiles will ultimately lead to a more complete understanding of disease onset and progression.