Sentence examples for matrix approximation and from inspiring English sources

The proposed algorithms are based on penalized rank-1 matrix approximation and differ from the existing ones in the matrices they use for their derivation.

Fig. 1 Example of two syllables: a syllable A; b syllable B. The corresponding MT spectrograms with window length 6.9 ms, frequency resolution 1770 Hz and K=8;:c syllable A; d syllable B. The filtered ambiguity spectra: e syllable A; f syllable B. The singular value decomposition is a low-rank matrix approximation and a popular noise-reduction technique for a data matrix.

These proposed algorithms differ from the existing ones in their derivation which is based on penalized rank-1 matrix approximation and the orthogonal projectors onto the space spanned by the two sets of multidimensional variables instead of the simple cross-matrix product [7, 10 12].

These algorithms differ from the existing ones in their derivation which is based on penalized rank-1 matrix approximation and the orthogonal projectors onto the space spanned by the two sets of multidimensional variables instead of the simple cross-matrix product.

Second, our method is based on well established theories of matrix approximation and regularization which have sound mathematical principles.

This novel matching of Bills of Materials uses linear time algorithms, compared to state-of- the-art algorithms which use integer programming and matrix approximation, hence, leading to more computational efficiency.

To improve the predictive power of the individual quantitative datasets, we further developed our computational matrix approximation strategy [ 34], and showed that it could transform the original fitness matrices so that these allow for better discrimination of not only negative but also the positive end of interaction spectrum from the background variability [ 31].

ROL and VPE developed and implemented the matrix approximation method.

Suppose that A is a low-rank matrix approximation of D, where D and A are (m times n) matrices.

From (18),we can observe that the optimization problem (10) that involves the two constraints (Vert boldsymbol {w}^{T}_{x}boldsymbol {X}Vert _{2}=1) and (Vert boldsymbol {w}^{T}_{y}boldsymbol {Y}Vert _{2}=1) has now been transformed into a rank-1 matrix approximation problem free of constraints and which can be solved with an SVD.

More generally, the computational approach based on the sequential matrix approximation can provide a principled framework for exploring and classifying genetic networks and interactions using a wide spectrum of global data sources, including the localization, mRNA or protein expression, physical interaction and functional annotation of the proteins encoded by the genes [19].