Supplement for “ Non - negative Matrix Factorization under Heavy Noise ”
نویسندگان
چکیده
||N ||2 √ |T | ≤ 4σ √ n √ |T | producing the contradiction. If σ ≤ ε 4 /4 √ d, (1) is satisfied. Furthermore, if σ > cε/d, then, with high probability, a CONSTANT FRACTION of the columns j violate the condition ||N·,j ||1 ≤ ε required by previous algorithms to hold for EVERY column. Lemma 2. Suppose k = 1, n ≤ c0d, ||C·,j ||1 = 1 for all j and N has i.i.d. entries drawn from N (0, σ), where, σ > c1/ √ d for a large constant c1. Then, given A = BC +N , the Maximum Likelihood Estimator B̃ of B with high probability satisfies ∣∣∣∣∣∣B̃·,1 −B·,1∣∣∣∣∣∣ 1 > ε.
منابع مشابه
Iterative Weighted Non-smooth Non-negative Matrix Factorization for Face Recognition
Non-negative Matrix Factorization (NMF) is a part-based image representation method. It comes from the intuitive idea that entire face image can be constructed by combining several parts. In this paper, we propose a framework for face recognition by finding localized, part-based representations, denoted “Iterative weighted non-smooth non-negative matrix factorization” (IWNS-NMF). A new cost fun...
متن کاملNon-negative Matrix Factorization under Heavy Noise
The Noisy Non-negative Matrix factorization (NMF) is: given a data matrix A (d × n), find non-negative matrices B,C (d × k, k × n respy.) so that A = BC + N , where N is a noise matrix. Existing polynomial time algorithms with proven error guarantees require each column N·,j to have l1 norm much smaller than ||(BC)·,j ||1, which could be very restrictive. In important applications of NMF such a...
متن کاملVoice-based Age and Gender Recognition using Training Generative Sparse Model
Abstract: Gender recognition and age detection are important problems in telephone speech processing to investigate the identity of an individual using voice characteristics. In this paper a new gender and age recognition system is introduced based on generative incoherent models learned using sparse non-negative matrix factorization and atom correction post-processing method. Similar to genera...
متن کاملA new approach for building recommender system using non negative matrix factorization method
Nonnegative Matrix Factorization is a new approach to reduce data dimensions. In this method, by applying the nonnegativity of the matrix data, the matrix is decomposed into components that are more interrelated and divide the data into sections where the data in these sections have a specific relationship. In this paper, we use the nonnegative matrix factorization to decompose the user ratin...
متن کاملRobust non-negative matrix factorization
Non-negative matrix factorization (NMF) is a recently popularized technique for learning partsbased, linear representations of non-negative data. The traditional NMF is optimized under the Gaussian noise or Poisson noise assumption, and hence not suitable if the data are grossly corrupted. To improve the robustness of NMF, a novel algorithm named robust nonnegative matrix factorization (RNMF) i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016