منابع مشابه
Bilinear Control: Rank-one Inputs
indeed has $D=b¥cdot c^{*}$ for $b^{*}=(0,¥ldots,0,1)$ and $c^{*}$ with entries $¥frac{1}{2}(¥beta_{k}-a_{k})$ . (As Jan Willems once pointed out, all the entries are constants; however, the zeros and ones are stiff structure constants, while only the last row has “soft” parameters, to be encompassed by a rank-one control matrix.) Section 1 presents a canonic decomposition of the state space of...
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In many real-world applications, data are represented by matrices or high-order tensors. Despite the promising performance, the existing 2-D discriminant analysis algorithms employ a single projection model to exploit the discriminant information for projection, making the model less flexible. In this paper, we propose a novel compound rank- k projection (CRP) algorithm for bilinear analysis. T...
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متن کاملSupplemental Material for:Finding Dense Subgraphs via Low-Rank Bilinear Optimization
We can use the above derivations to rewrite the set Sd that contains all top k coordinates in the span of Vd as: Sd = {topk(c1 · v1 + . . .+ cd · vd) : c1, . . . , cd ∈ R} = {topk ± (v(φ)) : φ ∈ Φd−1} = {topk ± ((sinφ1) · v1 + (cosφ1 sinφ2) · v2 + . . .+ (cosφ1 cosφ2 . . . cosφd−1) · vd), φ ∈ Φd−1} Observe again that each element of v(φ) is a continuous spectral curve in the d− 1 auxiliary vari...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1988
ISSN: 0304-3975
DOI: 10.1016/0304-3975(88)90130-2