Learning the parts of objects by non-negative matrix factorization

By Daniel D. Lee, H. S. Seung. 1999

Subfields: Representation & Self-Supervised Learning

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In Representation & Self-Supervised Learning

Citations in the corpus

Adafactor: Adaptive Learning Rates with Sublinear Memory Cost (2018, background): “In addition to the Frobenius norm, another popular cost function in the literature is the generalized Kullback-Leibler divergence, also known as the I-divergence (Lee & Seung, 1999).”
Unsupervised Speech Representation Learning Using WaveNet Autoencoders (2019, methodology): “such representations may be difficult to interpret because the reconstruction of an input depends on all latent features [36].”
From Frequency to Meaning: Vector Space Models of Semantics (2010, methodology): “A low-RAM algorithm, Multislice Projection, for large sparse tensors is presented and evaluated.17 Since the work of Deerwester et al. (1990), subsequent research has discovered many alternative matrix smoothing processes, such as Nonnegative Matrix Factorization (NMF) (Lee & Seung, 1999), Probabili”
Counterfactuals uncover the modular structure of deep generative models (2018, background): “The choice of NMF is justiﬁed by its success in isolating meaningful parts of images in different components [Lee and Seung, 1999].”
Group invariance principles for causal generative models (2017, methodology): “ this strategy to speciﬁc unsupervised learning algorithms that have been used in a wide range of areas: Non-negative Matrix factorization (NMF) [Lawton and Sylvestre, 1971; Paatero and Tapper, 1994; Lee and Seung, 1999] and the classical Gaussian mixture model for clustering. Finally, we draw a con”
Automatic Differentiation Variational Inference (2016, methodology): “We continue by exploring two nonconjugate non-negative matrix factorization models (Lee and Seung, 1999): a constrained Gamma Poisson model (Canny, 2004) and a Dirichlet Exponential Poisson model.”
Sparse Overcomplete Word Vector Representations (2015, background): “Nonnegativity in the feature space has often been shown to correspond to interpretability (Lee and Seung, 1999; Cichocki et al., 2009; Murphy et al., 2012; Fyshe et al., 2014; Fyshe et al., 2015).”
Deep Exponential Families (2014, background): “network [25]; Gamma latent variables give something akin to deep version of nonnegative matrix factorization [20]; Gaussian latent variables lead to the types of models that have recently been explored in the context”
Domain and Function: A Dual-Space Model of Semantic Relations and Compositions (2012, methodology): “…xi > 0 0 otherwise (20) Our version of element-wise multiplication may be expressed as follows: c = (nn(aΣ1−pk V T k )⊙ nn(bΣ 1−p k V T k ))VkΣ p−1 k (21) Another way to deal with element-wise multiplication would be to use nonnegative matrix factorization (NMF) (Lee & Seung, 1999) instead of SVD.”
Unsupervised Learning of Image Manifolds by Semidefinite Programming (2004, background): “Though one can imagine other types of hidden structure in ensembles of images, such as clusters (Gordon et al., 2003) or parts ( Lee & Seung, 1999 ), in this paper, we shall focus solely on the continuous structure that arises from image manifolds.”
Independent component analysis: recent advances (2013, background): “chemometrics, and later popularized by Lee & Seung [87] under the name ‘non-negative matrix factorization’ (NMF).”
Feature dimensionality reduction: a review (2022, unknown): “Nonnegative matrix factorization (NMF) [72], also known as non-negative matrix approximation or positive matrix factorization, is an unsupervised learning method.”
Self-Supervised Speech Representation Learning: A Review (2022, unknown): “niques include k-means clustering [11], mixture models [12], autoencoders [13], and non-negative matrix factorization [14].”
The Impact of Missing Labels and Overlapping Sound Events on Multi-label Multi-instance Learning for Sound Event Classification (2019, background): “NMD is an extension of non-negative matrix factorization (NMF) and is capable of identifying components with a temporal structure [12, 13].”