A Gradient Descent Algorithm on the Grassman Manifold for Matrix Completion

We consider the problem of reconstructing a low-rank matrix from a small subset of its entries. In this paper, we describe the implementation of an efficient algorithm called OptSpace, based on singular value decomposition followed by local manifold optimization, for solving the low-rank matrix completion problem. It has been shown that if the number of revealed entries is large enough, the output of singular value decomposition gives a good estimate for the original matrix, so that local optimization reconstructs the correct matrix with high probability. We present numerical results which show that this algorithm can reconstruct the low rank matrix exactly from a very small subset of its entries. We further study the robustness of the algorithm with respect to noise, and its performance on actual collaborative filtering datasets.Comment: 26 pages, 15 figure

Regularization for Matrix Completion

We consider the problem of reconstructing a low rank matrix from noisy observations of a subset of its entries. This task has applications in statistical learning, computer vision, and signal processing. In these contexts, "noise" generically refers to any contribution to the data that is not captured by the low-rank model. In most applications, the noise level is large compared to the underlying signal and it is important to avoid overfitting. In order to tackle this problem, we define a regularized cost function well suited for spectral reconstruction methods. Within a random noise model, and in the large system limit, we prove that the resulting accuracy undergoes a phase transition depending on the noise level and on the fraction of observed entries. The cost function can be minimized using OPTSPACE (a manifold gradient descent algorithm). Numerical simulations show that this approach is competitive with state-of-the-art alternatives.Comment: 5 pages, 3 figures, Conference Versio

Synthesis and fungicidal studies of niobium(V) complexes with N-alkylphenothiazines

Department of Studies in Chemistry, University of Mysore, Mysore-570 006 Manuscript received 31 January 1996, revised 19 August 1996, accepted 18 November 1996 Synthesis and Fungicidal Studies of Niobium(V) Complexes with N-Alkylphenothiazines

Synthesis and antibacterial studies of lanthanide (III) complexes with aminopromazine

New complexes of lanthanide(III) nitrates with aminopromazine, having the general formula Ln(AP)(2)(NO3)(2)]NO3 (Ln = La, Cc, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu and AP = aminopromazine) have been synthesised. The complexes have been screened far antibacterial activities

Enzyme assisted extraction of chitin from shrimp shells (Litopenaeus vannamei)

BACKGROUND: Chemical chitin extraction generates large amounts of wastes and increases partial deacetylation of the product. Therefore, the use of biological methods for chitin extraction is an interesting alternative. The effects of process conditions on enzyme assisted extraction of chitin from the shrimp shells in a systematic way were the focal points of this study. RESULTS: Demineralisation conditions of 25C, 20 min, shells-lactic acid ratio of 1:1.1 w/w; and shells-acetic acid ratio of 1:1.2 w/w, the maximum demineralisation values were 98.64 and 97.57% for lactic and acetic acids, respectively. A total protein removal efficiency of 91.10% by protease from Streptomyces griseus with enzyme-substrate ratio 55 U/g, pH 7.0 and incubation time 3 h is obtained when the particle size range is 50-25 μm, which was identified as the most critical factor. The X-ray diffraction and 13C NMR spectroscopy analysis showed that the lower percent crystallinity and higher degree of acetylation of chitin from enzyme assisted extraction may exhibit better solubility properties and less depolymerisation in comparison with chitin from the chemical extraction. CONCLUSION: The present work investigates the effects of individual factors on process yields, and it has shown that, if the particle size is properly controlled a reaction time of 3 h is more than enough for deproteination by protease. Physicochemical analysis indicated that the enzyme assisted production of chitin seems appropriate to extract chitin, possibly retaining its native structure

Enhancing the recovery of tiger nut (Cyperus esculentus) oil by mechanical pressing: moisture content, particle size, high pressure and enzymatic pre-treatment effects

Tiger nut (Cyperus esculentus) tuber contains oil that is high in monounsaturated fatty acids, and this oil makes up about 23% of the tuber. The study aimed at evaluating the impact of several factors and enzymatic pre-treatment on the recovery of pressed tiger nut oil. Smaller particles were more favourable for pressing. High pressure pre-treatment did not increase oil recovery but enzymatic treatment did. The highest yield obtained by enzymatic treatment prior to mechanical extraction was 33 % on a dry defatted basis, which represents a recovery of 90 % of the oil. Tiger nut oil consists mainly of oleic acid; its acid and peroxide values reflect the high stability of the oil