Mosses from the Mascarenes - 6

Sixty taxa of mosses, mainly pleurocarps, are reported from the Mascarenes. Two are new to Afr.3 sensu Index Muscorum, i.e., Brachythecium plumosum (Hedwig) Schimper in BSG and Palamocladium sericeum (Jaeger) C.Müller. Nine are new to the Mascarenes, i.e., Brachythecium decurrens Cardot, Callicostella parvocellulata Demaret & P.Varde, Helicodontium lanceolatum (Hampe & C.Müller) Jaeger, Lepidopilum carrougeauanum Thér. & P.Varde, Mittenothamnium microthamnioides (Geh.) Wijk & Marg., Orthostichopsis longinervis (Ren. & Cardot) Broth., Plagiothecium nitens Dixon, Rhynchostegium comorae (C.Müller) Jaeger and Trachypus bicolor var. hispidulus (C.Müller) Cardot. One is new to Mauritius and Réunion, but known from Rodrigues, i.e., Meiothecium madagascariense (Bridel) Broth. Five taxa are new to Mauritius, i.e., Callicostella salaziae (Besch.) Broth., Lopidium struthiopteris (Bridel) Fleischer, Macrohymenium acidodon (Mont.) Dozy & Molk., Orthostichella pentasticha (Bridel) Buck and Vesicularia lepervanchei (Besch.) Broth

Mosses from the Mascarenes : 3

37 species of mosses are reported from the Mascarenes. Of these 19 belong to the genus Campylopus and 8 to Leucoloma. Three are new to the Mascarenes i.e. Campylopus leucochlorus (C.Müll.) Par., C. paludicola Broth. and C. subperichaetialis Biz. & Kilb., two are new to Mauritius i.e. Bryum truncorum (Brid.) Brid. and Leucoloma cinclidotioides Besch. and four are new to Réunion i.e. Campylopus incacorralis Herz. C. praetermissus J.-P. Frahm, C. trachyblepharon (C. Müll.) Mitt. ssp. comatus (Ren. & Card.) J.- P. Frahm and Leucoloma rutenbergii (Geh.) Wright var. elatum Ren. The variety is new to the Mascarenes

Sparse and Unique Nonnegative Matrix Factorization Through Data Preprocessing

Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being highly ill-posed, that is, there typically exist many different but equivalent factorizations. In this paper, we introduce a completely new way to obtaining more well-posed NMF problems whose solutions are sparser. Our technique is based on the preprocessing of the nonnegative input data matrix, and relies on the theory of M-matrices and the geometric interpretation of NMF. This approach provably leads to optimal and sparse solutions under the separability assumption of Donoho and Stodden (NIPS, 2003), and, for rank-three matrices, makes the number of exact factorizations finite. We illustrate the effectiveness of our technique on several image datasets.Comment: 34 pages, 11 figure

Robustness Analysis of Hottopixx, a Linear Programming Model for Factoring Nonnegative Matrices

Although nonnegative matrix factorization (NMF) is NP-hard in general, it has been shown very recently that it is tractable under the assumption that the input nonnegative data matrix is close to being separable (separability requires that all columns of the input matrix belongs to the cone spanned by a small subset of these columns). Since then, several algorithms have been designed to handle this subclass of NMF problems. In particular, Bittorf, Recht, R\'e and Tropp (`Factoring nonnegative matrices with linear programs', NIPS 2012) proposed a linear programming model, referred to as Hottopixx. In this paper, we provide a new and more general robustness analysis of their method. In particular, we design a provably more robust variant using a post-processing strategy which allows us to deal with duplicates and near duplicates in the dataset.Comment: 23 pages; new numerical results; Comparison with Arora et al.; Accepted in SIAM J. Mat. Anal. App

Generalized Separable Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and hyperspectral unmixing. Given a data matrix $M$ and a factorization rank $r$, NMF looks for a nonnegative matrix $W$ with $r$ columns and a nonnegative matrix $H$ with $r$ rows such that $M \approx WH$. NMF is NP-hard to solve in general. However, it can be computed efficiently under the separability assumption which requires that the basis vectors appear as data points, that is, that there exists an index set $\mathcal{K}$ such that $W = M(:,\mathcal{K})$. In this paper, we generalize the separability assumption: We only require that for each rank-one factor $W(:,k)H(k,:)$ for $k=1,2,\dots,r$, either $W(:,k) = M(:,j)$ for some $j$ or $H(k,:) = M(i,:)$ for some $i$. We refer to the corresponding problem as generalized separable NMF (GS-NMF). We discuss some properties of GS-NMF and propose a convex optimization model which we solve using a fast gradient method. We also propose a heuristic algorithm inspired by the successive projection algorithm. To verify the effectiveness of our methods, we compare them with several state-of-the-art separable NMF algorithms on synthetic, document and image data sets.Comment: 31 pages, 12 figures, 4 tables. We have added discussions about the identifiability of the model, we have modified the first synthetic experiment, we have clarified some aspects of the contributio

Mosses from the Mascarenes - 5

A list of Pottiaceae specimens is presented. Trichostomum bombayense C.Müll. is transferred to the genus Pseudosymblepharis Broth., and a new combination is made: Pseudosymblepharis bombayensis (C.Müll.) P. Sollman. Five new synonyms are proposed. Gametophyte characters, separating non-fruiting material of Pseudosymblepharis bombayensis from Trichostomum tenuirostre (Hook. & Tayl.) Lindb., are listed