If the SOI is highly correlated with an important biological or clinical attribute of the samples, then ζ explains and helps to interpret the sample attribute of interest in terms of the selected variables. The set of s variables associated with the selected rows define a Multi-Modal SIGnature (MMSIG) of D denoted by ζ where s = dim( ζ). Then the joint analysis of 𝔇 involves the identification of s > 0 rows of the super-matrix D that models a univariate SOI in the row-space of D as a linear combination of the selected rows. We assume that D is appropriately scaled by its Frobenius norm to account for differences in the number of rows and dynamic range of the different D k’s. Following Friedland and others, let D = D(𝔇) be the p × n super-matrix that vertically “stacks” each of the pre-processed p k × n matrices D k ∈ 𝔇 along their columns where p = ∑ k = 1 K p k. For example, pre-processing of mRNA data would likely involve log2-transformation, quantile normalization, and row-centering, while a methylation data matrix would be transformed from Beta-values to M-values prior to normalization and row-centering. We assume that each D k has been appropriately pre-processed as function of its data type. This growing inventory of multi-modal data presents a major analytical bottleneck in the translation of big, genomic data sets into clinically actionable knowledge.įormally, the measurements for K > 1 different data types collected from a common set of n biospecimens, S n = , can be represented by a collection of K data matrices, D = D k k = 1 K, where: i) D k is the p k × n data matrix representing measurements for the kth data type and ii) at least one of the D k is big, i.e., p k > > n. Falling data acquisition costs have resulted in MMDS accumulating at an exponential rate in academic research laboratories, private industry, and public data repositories such as The Cancer Genome Atlas (TCGA) and the International Cancer Genome Consortium (ICGC). Unfortunately, the lack of analytical tools for the joint analysis of multiple data types has slowed the discovery of novel predictive biomarkers and therapeutic targets that account for interactions between networks of diverse molecular species across space and time. As before, the goal is to detect sparse signatures for each data type that individually, or in combination, explain a SOI that characterizes an important biological and/or clinical attribute of the samples. MMDSs pose even greater analytical challenges since the goal is to jointly analyze two or more data matrices in an integrated manner, which exacerbates problems related to data dimensionality and SNR ‘. We call this subset of variables a signature in D, and if D is big, then we assume that the signature is “sparse” in D, i.e., s ≪ p.
In this context, we are interested in selecting s > 0 rows of D that best approximate a dominant SOI in the row-space of D that may represent a clinically and/or biologically significant attribute of the samples. The low SNR is due in large part to the relatively small number of variables (out of many thousands measured) that truly represent a Signal of Interest (SOI) in the data that is associated with an important biological and/or clinical attribute of the samples.
For big data types we have p ≫ n, making such “tall and thin” matrices difficult to analyze using standard statistical techniques due to a severe multiple comparisons problem and low Signal-to-Noise Ratio (SNR). The measurement of p > 1 variables of a given data type obtained from a collection of n > 1 samples can be organized into a p × n data matrix D with rows representing variables and columns representing measurements of the p variables in each of the n samples. Such “big” data types include genome-wide measurements of messenger RNA (mRNA) and microRNA expression, DNA methylation, single nucleotide polymorphisms (SNPs), next-generation sequence data, and quantitative features extracted from Positron Emission Tomography (PET) images. Advances in array technology, high-throughput sequencing, and clinical imaging platforms enable the measurement of ten’s of thousands of variables of a specific data type in a fixed set of tissue samples.
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