Sparse non-negative generalized PCA with applications to metabolomics
نویسندگان
چکیده
منابع مشابه
Sparse non-negative generalized PCA with applications to metabolomics
MOTIVATION Nuclear magnetic resonance (NMR) spectroscopy has been used to study mixtures of metabolites in biological samples. This technology produces a spectrum for each sample depicting the chemical shifts at which an unknown number of latent metabolites resonate. The interpretation of this data with common multivariate exploratory methods such as principal components analysis (PCA) is limit...
متن کاملSupplement to “ Sparse Non - Negative Generalized PCA with Applications to Metabolomics ”
1 Proofs Proof 1 (Proof of Proposition 1) The result for u∗ is straightforward (Allen et al., 2011). We consider the problem in v: maximize v u XRv−λ||v ||1 subject to v Rv ≤ 1 & vj ≥ 0 j = 1, . . . p. (1) As this problem is convex and Slater’s condition is satisfied, the KKT conditions are necessary and sufficient for optimality. These are given by the following: RX u−λ1(p) − 2γ∗ 1 Rv∗+~γ∗ 2 =...
متن کاملSparse Non-negative Matrix Factorization with Generalized Kullback-Leibler Divergence
Non-negative Matrix Factorization (NMF), especially with sparseness constraints, plays a critically important role in data engineering and machine learning. Hoyer (2004) presented an algorithm to compute NMF with exact sparseness constraints. The exact sparseness constraints depends on a projection operator. In the present work, we first give a very simple counterexample, for which the projecti...
متن کاملNon-negative sparse coding
Non-negative sparse coding is a method for decomposing multivariate data into non-negative sparse components. In this paper we briefly describe the motivation behind this type of data representation and its relation to standard sparse coding and non-negative matrix factorization. We then give a simple yet efficient multiplicative algorithm for finding the optimal values of the hidden components...
متن کاملSparse PCA with Oracle Property
In this paper, we study the estimation of the k-dimensional sparse principal subspace of covariance matrix Σ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bioinformatics
سال: 2011
ISSN: 1460-2059,1367-4803
DOI: 10.1093/bioinformatics/btr522