Factoring nonnegative matrices with linear programs

This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to express the remaining features. More precisely, given a data matrix X, the algorithm identifies a matrix C such that X approximately equals CX and some linear constraints. The constraints are chosen to ensure that the matrix C selects features; these features can then be used to find a low-rank NMF of X. A theoretical analysis demonstrates that this approach has guarantees similar to those of the recent NMF algorithm of Arora et al. (2012). In contrast with this earlier work, the proposed method extends to more general noise models and leads to efficient, scalable algorithms. Experiments with synthetic and real datasets provide evidence that the new approach is also superior in practice. An optimized C++ implementation can factor a multigigabyte matrix in a matter of minutes.Comment: 17 pages, 10 figures. Modified theorem statement for robust recovery conditions. Revised proof techniques to make arguments more elementary. Results on robustness when rows are duplicated have been superseded by arxiv.org/1211.668

Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NP-hard. In this paper, we show that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds with overwhelming probability. The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this pre-existing concept and outline a dictionary relating concepts from cardinality minimization to those of rank minimization

Radiation effects on silver and zinc battery electrodes, i interim report, apr. - jul. 1965

Radiation effects on silver and zinc battery electrode

Radiation effects on silver and zinc battery electrodes, II Interim report, Jul. - Oct. 1965

Radiation effects on silver and zinc electrodes in silver-zinc batter

Radiation effects on silver and zinc battery electrodes, III Interim report, Oct. 1965 - Jan. 1966

Radiation effects on silver-zinc battery electrode

The effects of radiation on nickel-cadmium battery electrodes, i final report, jun. 1963 - apr. 1965

Effect of radiation on nickel-cadmium battery electrode

Efficient Discrete Approximations of Quantum Gates

Quantum compiling addresses the problem of approximating an arbitrary quantum gate with a string of gates drawn from a particular finite set. It has been shown that this is possible for almost all choices of base sets and furthermore that the number of gates required for precision epsilon is only polynomial in log 1/epsilon. Here we prove that using certain sets of base gates quantum compiling requires a string length that is linear in log 1/epsilon, a result which matches the lower bound from counting volume up to constant factor.Comment: 7 pages, no figures, v3 revised to correct major error in previous version

The association between subjective assessment of menstrual bleeding and measures of iron deficiency anemia in premenopausal African-American women: a cross-sectional study

BACKGROUND: Both iron deficiency and iron deficiency anemia are common in the United States with a prevalence amongst women of 12 % and 4 % respectively. These numbers are even higher in African-American women (AAW) and are often a result of heavy menstrual bleeding (HMB). The primary objective of this study was to determine if perceived assessment of menstrual bleeding was associated with objective and subjective measures of anemia in AAW. METHODS: Quantitative cross-sectional pilot study with surveys and venipuncture. RESULTS: 44 premenopausal AAW (mean age 37.9 years ± 9. 4) participated in the study. Iron deficiency was present in 68.2 % of the participants and 18.2 % were anemic. Almost half of the participants reported that their menses were heavy or very heavy, and there was a relationship between perceived heaviness of menstrual flow and anemia (P = 0.021). Of the individuals who reported that their menses were heavy or very heavy, 35.0 % were anemic. AAW who reported heavy or very heavy menses had significantly lower hemoglobin (P = 0.015), hematocrit (P = 0.003), and ferritin (P = 0.012) levels, as well as more general (P = 0.006) and menses-associated symptoms of anemia (P = 0.015) than those who reported normal or light menses. CONCLUSIONS: This pilot study of premenopausal AAW found that a significant percentage of women who report HMB are not only iron deficient, but also anemic. AAW should be educated on the consequences of HMB and counseled to seek care with a women’s health provider when they perceive HMB. More importantly, providers should be aware that when AAW report HMB, evaluation for iron deficiency and anemia are essential. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12905-016-0329-z) contains supplementary material, which is available to authorized users