Singular value decomposition separation

Secondly, although stable solutions covering the entire temporal range of interest are attainable, the spectra may not be well resolved that is, for a given dataset and noise, a limit exists on the smallest resolvable structure (or separation of structures) in the Laplace inversion spectrum [54]. Estimates can be made on this resolution parameter based on a singular-value decomposition analysis of K and the signal-to-noise ratio of the data [56], It is important to keep in mind the concept of the spectral resolution in order to interpret the LI results, such as DDIF, properly. 

This is acceptable provided that the assumption is stated up front. The melt curves in the lower part of Fig. 17.3 were fit this way. Alternatively, the full model can be used, with additional steps taken to ensure the validity of the results. An example is shown in the upper part of Fig. 17.3. Here, the experiments were repeated multiple times (minimizing the measurement error), the data were fit simultaneously (using a global fitting algorithm), and the results were corroborated using a separate singular value decomposition analysis. 

Wu and Shivakumar (1994) developed a neural network system for classification of ribosomal RNAs according to phylogenetic classes. Two separate networks were trained, one for 220 small subunit classes, and the other for 15 large subunit classes. The input sequences were encoded using various n-gram encoding schemes, followed by a singular value decomposition compression to different number of reduced dimensions. It was... 

To improve reproducibility in MRSI in human brain, simultaneous acquisition of the internal water reference and metabolite signals was evaluated. Use of singular value decomposition techniques and finite impulse response filters proved effective in separating water and metabolite signals and providing estimations of the metabolite concentrations. 

By far, singular value decomposition (SVD) is the most popular algorithm to estimate the rank of the data matrix D. As a drawback of SVD, the threshold that separates significant contributions from noise is difficult to settle. Other eigenvalue-based and error functions can be utilized in a similar way, but the arbitrariness in the selection of the significant factors still persists. For this reason, additional assays may be required, especially in the case of complex data sets. 

The linear equations are usually solved with the singular value decomposition method [9,13]. After the calculation of the weighing matrix A, clear representations of the separated fluorophores can be created (Figs. 2 and 3). 

The conditions that the pseudo-inverse must satisfy are not very helpful for computing A+. Computation is most easily accomplished by using the singular value decomposition (SVD) of A. The SVD can be visualized as a factoring of A into three separate matrices as follows ... 

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