Sentence examples for matrix approximation of from inspiring English sources

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

In this paper, we adopt an alternative formulation of the CCA problem which is based on rank-1 matrix approximation of the orthogonal projectors of data sets [13].

In Section 3, we present a formulation of CCA using a rank-1 matrix approximation of the orthogonal projectors of data sets and derive the smoothed solution.

In order to estimate the canonical projectors, we define the nearest rank-1 matrix approximation of K xy by: boldsymbol{K}_{1} = d_{1},boldsymbol{u}_{1}boldsymbol{v}_{1}^{T}~, where the nearest means that the squared Frobenius norm between K xy and K 1, defined by (big Vert boldsymbol {K}_{xy}-boldsymbol {K}_{1} big Vert _{F}^{2}), is minimal.

Therefore, the rank-1 matrix approximation of K xy can be formulated as solving the following optimization from: underset{boldsymbol{w}_{x}, boldsymbol{w}_{y}}{text{arg},text{min}}~bigVert boldsymbol{K}_{xy}-boldsymbol{X}^{T}boldsymbol{w}_{x}boldsymbol{w}_{y}^{T}boldsymbol{ Y bigVert_{F}^{2}~.

For a given subset of mutation pairs, we calculated the matrix approximation of Eq. 2 using the decomposition algorithm by De Leeuw [16].

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.

The complexity of CFO compensation in[26] can be lowered by a banded matrix approximation at the cost of performance degradation.

We have previously shown, using a high-resolution screen of genetic interactions among a small number of genes, that a rank-one matrix approximation can provide accurate estimates of the single-mutant fitness effects and improved prediction of functional relationships among the genes [46].

The underlying idea of the matrix approximation it to decompose the original fitness matrix into separate components, W = x ⊗ y, where the m and n-dimensional vectors x and y model the variability across the array and query mutants, respectively [ 31, 34].

We then proceed to study the expected error of matrix approximation.