scholarly journals Structured Low-Rank Algorithms: Theory, Magnetic Resonance Applications, and Links to Machine Learning

2020 ◽  
Vol 37 (1) ◽  
pp. 54-68 ◽  
Author(s):  
Mathews Jacob ◽  
Merry P. Mani ◽  
Jong Chul Ye
Processes ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1071
Author(s):  
Lucia Billeci ◽  
Asia Badolato ◽  
Lorenzo Bachi ◽  
Alessandro Tonacci

Alzheimer’s disease is notoriously the most common cause of dementia in the elderly, affecting an increasing number of people. Although widespread, its causes and progression modalities are complex and still not fully understood. Through neuroimaging techniques, such as diffusion Magnetic Resonance (MR), more sophisticated and specific studies of the disease can be performed, offering a valuable tool for both its diagnosis and early detection. However, processing large quantities of medical images is not an easy task, and researchers have turned their attention towards machine learning, a set of computer algorithms that automatically adapt their output towards the intended goal. In this paper, a systematic review of recent machine learning applications on diffusion tensor imaging studies of Alzheimer’s disease is presented, highlighting the fundamental aspects of each work and reporting their performance score. A few examined studies also include mild cognitive impairment in the classification problem, while others combine diffusion data with other sources, like structural magnetic resonance imaging (MRI) (multimodal analysis). The findings of the retrieved works suggest a promising role for machine learning in evaluating effective classification features, like fractional anisotropy, and in possibly performing on different image modalities with higher accuracy.


2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Zhikuan Zhao ◽  
Jack K. Fitzsimons ◽  
Patrick Rebentrost ◽  
Vedran Dunjko ◽  
Joseph F. Fitzsimons

AbstractMachine learning has recently emerged as a fruitful area for finding potential quantum computational advantage. Many of the quantum-enhanced machine learning algorithms critically hinge upon the ability to efficiently produce states proportional to high-dimensional data points stored in a quantum accessible memory. Even given query access to exponentially many entries stored in a database, the construction of which is considered a one-off overhead, it has been argued that the cost of preparing such amplitude-encoded states may offset any exponential quantum advantage. Here we prove using smoothed analysis that if the data analysis algorithm is robust against small entry-wise input perturbation, state preparation can always be achieved with constant queries. This criterion is typically satisfied in realistic machine learning applications, where input data is subjective to moderate noise. Our results are equally applicable to the recent seminal progress in quantum-inspired algorithms, where specially constructed databases suffice for polylogarithmic classical algorithm in low-rank cases. The consequence of our finding is that for the purpose of practical machine learning, polylogarithmic processing time is possible under a general and flexible input model with quantum algorithms or quantum-inspired classical algorithms in the low-rank cases.


2017 ◽  
Vol 56 (6) ◽  
pp. 806-812 ◽  
Author(s):  
Turid Torheim ◽  
Eirik Malinen ◽  
Knut Håkon Hole ◽  
Kjersti Vassmo Lund ◽  
Ulf G. Indahl ◽  
...  

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