Gene expression experiments from developing barley seeds between day 0 after fertilization (daf) and 26 daf are under investigation.
Macroarray technology is used to study gene expression intensities. The above images refer to laser scans of radioactive spots of hybridization membranes. Further processing, such as described in another project of the group, yield two basic data views:

1. Inter-experiment view focusing on the problem, how the single experiments, containing several thousand gene expression values, are related to each other. The visual grouping of the experiments helps to identify driving-forces ('axes') of interest, such as developmental stages, tissues, or stress.

2. Inter-gene perspective trying to find functional clusters of gene profiles, such as co-expressed genes, or temporally delayed expression dynamic. The correlation of gene expression profiles is of interest.

Tools developed in this project in order to facilitate analysis comprise two types of models:

1. Supervised data models make use of labeled data, such as the classes of early vs. late developmental stage, which are connected to expression data. These classes can be used to construct classifiers that allow to classify, i.e. to predict the class of unknown data. Common methods are C4.5 classification trees or k-nearest neighbor. Here, supervised relevance neural gas (SNG) is used.

2. Unsupervised data models are used to cluster high-dimensional data or to reduce the data dimensionality. Principal component analysis (PCA) or self-organizing maps (SOM) are standard tools for visualization and clustering respectively. Here, an efficient variant of multidimensional scaling for high throughput application (HiT-MDS) is presented.

The methods found at project page site use paradigms of soft-computing (artificial neural networks).

and Generalized Relevance Learning Vector Quantization (GRLVQ)

Supervised Neural Gas is a well-established prototype-based classifier that combines learning vector quantization (LVQ) with neural gas (NG). It implements a gradient descent on a misclassification cost function into which a custom similarity measure can be integrated. See this draft article for a detailed description of generalized relevance LVQ (GRLVQ) which is a specific realization of SNG.

The available package is distributed under General GNU Public License.

snggm package:  Implementation of supervised neural gas with general metrics, source code.

Sources require ANSI compatible C compiler (gcc preferred).
Cygwin and linux environments with gnu utilities are recommended for full functionality.

Download:  gzipped tar archive snggm-11-oct-2005.tar.gz (267 755 bytes)/ zip archive snggm-11-oct-2005.zip (272 815 bytes). See README.txt.

On relationships between gene expression experiments and
the quest for clusters of coexpressed genes.


Marc Strickert (Pattern Recognition Group) / April 2005

Scaling (MDS) is a powerful dimension reduction technique for embedding high-dimensional data into a low-dimensional target space. Thereby, similarities or distance relationships between the source data are reconstructed in the target space as best as possible. High-Throughput MDS (HiT-MDS) has been designed for dealing with large data sets such as multi-parallel gene expression probes. Particularly for the task of detecting clusters of coexpressed genes, the combination of HiT-MDS with correlation-based gene profile comparison proves to be very suitable for visual data inspection.

Multidimensional Scaling (MDS) is a powerful dimension reduction technique for embedding high-dimensional data into a low-dimensional target space. Thereby, similarities or distance relationships between the source data are reconstructed in the target space as best as possible. High-Throughput MDS (HiT-MDS) has been designed for dealing with large data sets such as multi-parallel gene expression probes. Particularly for the task of detecting clusters of coexpressed genes, the combination of HiT-MDS with correlation-based gene profile comparison proves to be very suitable for visual data inspection.

The preliminary c-sources can be downloaded:    hit-mds.tar.gz  (205794 bytes).

A presentation from the PlantMetaNet Meeting is available:    strickert-HitMDS.pdf   (1,469,179 bytes).

The paper M. Strickert, S. Teichmann, N. Sreenivasulu, and U. Seiffert, 'High-Throughput Multi-Dimensional Scaling (HiT-MDS) for cDNA-Array Expression Data' submitted to the International Conference of Artificial Neural Networks (ICANN05) can still be obtained:     hit-mds_submitted2icann05.pdf  (231402 bytes).

Two studies are presented that show the suitability of HiT-MDS for the analysis of high-throughput expression data. In the experimental design several 11786 gene expression patterns were analyzed during barley seed development, 0–26 days after flowering in steps of 2 days, in three distinct tissues: pericarp (p), endosperm (end), and embryo (e). With 2 independent experiments per configuration, a total of 62 experiments has been made available.

The two major questions of interest are:

1. How are the experiments, representing the tissues at a particular developmental stage, characterized with respect to their transcriptome similarity of specifically expressed genes?
2. Can inter-experimental clusters of coexpressed genes be identified for which, afterwards, regulatory functions can be assigned?

HiT-MDS is used to embed the 62 available gene expression experiments obtained from cDNA-Arrays with 11786 probed genes into 2D-plots.

A standard computation is shown in the first figure: This is a plot of the genes projected to the first two eigenvectors. The squared correlation of the given inter-point distances with the distances in the original 11786-D gene space is r² = 0.9305. A good grouping of the experiments (e₁,e₂), the tissues (e,p,end), and the temporal order (numbers) becomes visible.

Higher confidence can be put in the second visualization for which the squared correlation between the displayed point distances and the original distances is r² = 0.9430. The embedding method spreads the data points more faithfully, without being constrained by a linear mapping function: any point can be moved freely in order to maximize the inter-distance correlations.

Particularly interesting results can be obtained if the experiments are compared according to the (1-correlation)–measure. Then the log-transformed cDNA gray-level images are compared invariantly to scaling (histogram stretches) and shifting (light vs. dark). Again a clear grouping is obtained. Long-term saturation (>=16 DAF) is well emphasized in clusters and the intermediate transient developmental stages (6,8,10,12 DAF) are given space. The inter-point distance correlation is r² =.935 which seems low, but which results from the fact that the (1-experiment correlation)–measure is converted into the plottable Euclidean distances.

Since the minimum dissimilarity is 0 (perfect correlation) and the maximum dissimilarity is 2 (not infinity as in Euclidean terms) potentially circular shapes will be the result of such a space conversion with many anticorrelated features.

Gene clustering is a much more demanding task because up to 11786 data points, the gene in their 31 dimensions of experimental expression levels, are processed. As usual in expression analysis, the expression intensity levels are subject to standard logarithmic transform.

If all genes from one series of experiments are embedded with Euclidean distances, donut shaped regions of high density are obtained, where more details are to be found. The squared correlation of the visualized reconstruction with the original data matrix is r² = 0.958.

At first glance, the PCA projection looks similar. However, the central region with its many data points is distorted from donut shape to a two-dot structure. The squared correlation is only r² =0.878, thus HiT-MDS yields clearly more faithful representations, i.e. the donut-shape with its 31-dimensional equivalent can be more trusted.

In order to see how more details are revealed when large groups of anti-correlated genes are separated and further processed (“zoomed in”), a plot of individual genes is used to find groups of interest. If the high-density cluster of green points is omitted, then the relaxed embedding constraints yield finer notions of anti-correlatedness for the group of genes related to the red points.

After reembedding these points, much more details and clusters of coexpressed genes become apparent. The spatial differentiation is very good: clusters of high density denote similar gene profiles.

The HiT-MDS is a useful tool in order to obtain good visual representations of multi-parallel cDNA-Array data. Particularly space conversions from correlatedness into Euclidean proximity help to identify clusters of coexpressed genes and to get more independent of data shifts and scaling that do often occur in the measuring practice. Therefore, HiT-MDS has many more applications than the presented one for gene expression analysis.

MDSLocalize is a SVD-based reconstruction method for converting a given squared NxN distance matrix into a set of d-dimensional points. Follow the link for the original paper of Drineas et al. Usually, a number of d=1,2,or 3 output dimensions is chosen for visualization. The technique made available here, replaces SVD by PCA which is efficiently approximated by its neural formulation based on Sanger's rule. As pointed out in the draft, Note that the provided implementation does not yet allow incomplete distance information.

• PDF draft of paper submitted to ESANN conference before review changes (670.616 bytes).
• ZIP archive of MDSLocalize C-Code (9.688 bytes).

Multidimensional scaling:

• http://www.research.att.com/areas/stat/xgobi/


• Y-h. Taguchi's MDS-Page, including fast non-metric nMDS by Y-h. Taguchi and Y. Oono.

• http://pgrc-16.ipk-gatersleben.de/~stricker/