Biomedical subjects

Michael Hörnquist

Publications and source records attributed to Michael Hörnquist.

3 recordsLinked to original sources

PubMed2003

Effective dimensionality for principal component analysis of time series expression data.

Large-scale expression data are today measured for thousands of genes simultaneously. This development has been followed by an exploration of theoretical tools to get as much information out of these data as possible. Several groups have used principal component analysis (PCA) for this task. However, since this approach is data-driven, care must be taken in order not to analyze the noise instead of the data. As a strong warning towards uncritical use of the output from a PCA, we employ a newly developed procedure to judge the effective dimensionality of a specific data set. Although this data set is obtained during the development of rat central nervous system, our finding is a general property of noisy time series data. Based on knowledge of the noise-level for the data, we find that the effective number of dimensions that are meaningful to use in a PCA is much lower than what could be expected from the number of measurements. We attribute this fact both to effects of noise and the lack of independence of the expression levels. Finally, we explore the possibility to increase the dimensionality by performing more measurements within one time series, and conclude that this is not a fruitful approach.

Algorithms↗

PubMed2001

Scale-free growing networks imply linear preferential attachment.

It has been recognized for some time that a network grown by the addition of nodes with linear preferential attachment will possess a scale-free distribution of connectivities. Here we prove by some analytical arguments that the linearity is a necessary component to obtain this kind of distribution. However, the preferential linking rate does not necessarily apply to single nodes, but to groups of nodes of the same connectivity. We also point out that for a time-varying mean connectivity the linking rate will deviate from a linear expression by an extra asymptotically logarithmic term.

Journal Article↗

PubMedDate not supplied

Effective dimensionality of large-scale expression data using principal component analysis.

Large-scale expression data are today measured for thousands of genes simultaneously. This development is followed by an exploration of theoretical tools to get as much information out of these data as possible. One line is to try to extract the underlying regulatory network. The models used thus far, however, contain many parameters, and a careful investigation is necessary in order not to over-fit the models. We employ principal component analysis to show how, in the context of linear additive models, one can get a rough estimate of the effective dimensionality (the number of information-carrying dimensions) of large-scale gene expression datasets. We treat both the lack of independence of different measurements in a time series and the fact that that measurements are subject to some level of noise, both of which reduce the effective dimensionality and thereby constrain the complexity of models which can be built from the data.

Gene Expression Profiling↗