Nonnegativity constraints in numerical analysis

Chen, Donghui; Plemmons, Robert J.

doi:10.1142/9789812836267_0008

Cited by 163 publications

(145 citation statements)

References 75 publications

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“…The second group consists of the active-set and the active-set-like methods, in which zero and nonzero variables are explicitly kept track of and a system of linear equations is solved at each iteration. For more details, see Lawson and Hanson [64], Bjork [8], and Chen and Plemmons [15].…”

Section: Corollary 4 (Nonnegativity Of Best Rank-one Approximation) Fmentioning

confidence: 99%

Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework

2013

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We review algorithms developed for nonnegative matrix factorization (NMF) and nonnegative tensor factorization (NTF) from a unified view based on the block coordinate descent (BCD) framework. NMF and NTF are low-rank approximation methods for matrices and tensors in which the low-rank factors are constrained to have only nonnegative elements. The nonnegativity constraints have been shown to enable natural interpretations and allow better solutions in numerous applications including text analysis, computer vision, and bioinformatics. However, the computation of NMF and NTF remains challenging and expensive due the constraints. Numerous algorithmic approaches have been proposed to efficiently compute NMF and NTF. The BCD framework in constrained non-linear optimization readily explains the theoretical convergence properties of several efficient NMF and NTF algorithms, which are consistent with experimental observations reported in literature. In addition, we discuss algorithms that do not fit in the BCD framework contrasting them from those based on the BCD framework. With insights acquired from the unified perspective, we also propose efficient algorithms for updating NMF when there is a small change in the reduced dimension or in the data. The effectiveness of the proposed updating algorithms are validated experimentally with synthetic and real-world data sets.

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Section: Corollary 4 (Nonnegativity Of Best Rank-one Approximation) Fmentioning

confidence: 99%

Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework

2013

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“…To find the optimal solution, we use Linear Least Square Methods which are a standard approach to find the solution to a set of unknown factors from a model that has more equations than the unknowns (Chen & Plemmons, 2009;Van de Geer, 2000). This approach searches for the answer by minimizing the sum of the squares of errors (or residuals) made in the results of every single equation.…”

Section: Call Rate and Actual Location Durationmentioning

confidence: 99%

Building a validation measure for activity-based transportation models based on mobile phone data

Liu

Janssens

Cui

et al. 2014

Expert Systems with Applications

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Activity-based micro-simulation transportation models typically predict 24-hour activitytravel sequences for each individual in a study area. These sequences serve as a key input for travel demand analysis and forecasting in the region. However, despite their importance, the lack of a reliable benchmark to evaluate the generated sequences has hampered further development and application of the models. With the wide deployment of mobile phone devices today, we explore the possibility of using the travel behavioral information derived from mobile phone data to build such a validation measure. Our investigation consists of three steps. First, the daily trajectory of locations, where a user performed activities, is constructed from the mobile phone records. To account for the discrepancy between the stops revealed by the call data and the real location traces that the user has made, the daily trajectories are then transformed into actual travel sequences. Finally, all the derived sequences are classified into typical activity-travel patterns which, in combination with their relative frequencies, define an activity-travel profile. The established profile characterizes the current activity-travel behavior in the study area, and can thus be used as a benchmark for the assessment of the activity-based transportation models. By comparing the activity-travel profiles derived from the call data with statistics that stem from traditional activity-travel surveys, the validation potential is demonstrated. In addition, a sensitivity analysis is carried out to assess how the results are affected by the different parameter settings defined in the profiling process.

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“…NNLS is a well studied problem for which many different methods have been proposed [24]. The classic NNLS algorithm [25] is a greedy stepwise algorithm, similar to OMP, that considers a positive only selection criteriâ…”

Section: B Non-negative Methodsmentioning

confidence: 99%

Non-Negative Group Sparsity with Subspace Note Modelling for Polyphonic Transcription

O'Hanlon

Nagano

Keriven

et al. 2016

IEEE/ACM Trans. Audio Speech Lang. Process.

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Abstract-Automatic Music Transcription (AMT) can be performed by deriving a pitch-time representation through decomposition of a spectrogram with a dictionary of pitch-labelled atoms. Typically, Non-negative Matrix Factorisation (NMF) methods are used to decompose magnitude spectrograms. One atom is often used to represent each note. However, the spectrum of a note may change over time. Previous research considered this variability using different atoms to model specific parts of a note, or large dictionaries comprised of datapoints from the spectrograms of full notes. In this paper the use of subspace modelling of note spectra is explored, with group sparsity employed as a means of coupling activations of related atoms into a pitched subspace.Stepwise and gradient-based methods for non-negative group sparse decompositions are proposed. Finally, a group sparse NMF approach is used to tune a generic harmonic subspace dictionary, leading to improved NMF-based AMT results.

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Nonnegativity constraints in numerical analysis

Cited by 163 publications

References 75 publications

Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework

Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework

Building a validation measure for activity-based transportation models based on mobile phone data

Non-Negative Group Sparsity with Subspace Note Modelling for Polyphonic Transcription

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