70 research outputs found
Computational complexity of decomposing a symmetric matrix as a sum of positive semidefinite and diagonal matrices
We study several variants of decomposing a symmetric matrix into a sum of a
low-rank positive semidefinite matrix and a diagonal matrix. Such
decompositions have applications in factor analysis and they have been studied
for many decades. On the one hand, we prove that when the rank of the positive
semidefinite matrix in the decomposition is bounded above by an absolute
constant, the problem can be solved in polynomial time. On the other hand, we
prove that, in general, these problems as well as their certain approximation
versions are all NP-hard. Finally, we prove that many of these low-rank
decomposition problems are complete in the first-order theory of the reals;
i.e., given any system of polynomial equations, we can write down a low-rank
decomposition problem in polynomial time so that the original system has a
solution iff our corresponding decomposition problem has a feasible solution of
certain (lowest) rank
Efficient and Direct Inference of Heart Rate Variability using Both Signal Processing and Machine Learning
Heart Rate Variability (HRV) measures the variation of the time between
consecutive heartbeats and is a major indicator of physical and mental health.
Recent research has demonstrated that photoplethysmography (PPG) sensors can be
used to infer HRV. However, many prior studies had high errors because they
only employed signal processing or machine learning (ML), or because they
indirectly inferred HRV, or because there lacks large training datasets. Many
prior studies may also require large ML models. The low accuracy and large
model sizes limit their applications to small embedded devices and potential
future use in healthcare. To address the above issues, we first collected a
large dataset of PPG signals and HRV ground truth. With this dataset, we
developed HRV models that combine signal processing and ML to directly infer
HRV. Evaluation results show that our method had errors between 3.5% to 25.7%
and outperformed signal-processing-only and ML-only methods. We also explored
different ML models, which showed that Decision Trees and Multi-level
Perceptrons have 13.0% and 9.1% errors on average with models at most hundreds
of KB and inference time less than 1ms. Hence, they are more suitable for small
embedded devices and potentially enable the future use of PPG-based HRV
monitoring in healthcare
PPG-based Heart Rate Estimation with Efficient Sensor Sampling and Learning Models
Recent studies showed that Photoplethysmography (PPG) sensors embedded in
wearable devices can estimate heart rate (HR) with high accuracy. However,
despite of prior research efforts, applying PPG sensor based HR estimation to
embedded devices still faces challenges due to the energy-intensive
high-frequency PPG sampling and the resource-intensive machine-learning models.
In this work, we aim to explore HR estimation techniques that are more suitable
for lower-power and resource-constrained embedded devices. More specifically,
we seek to design techniques that could provide high-accuracy HR estimation
with low-frequency PPG sampling, small model size, and fast inference time.
First, we show that by combining signal processing and ML, it is possible to
reduce the PPG sampling frequency from 125 Hz to only 25 Hz while providing
higher HR estimation accuracy. This combination also helps to reduce the ML
model feature size, leading to smaller models. Additionally, we present a
comprehensive analysis on different ML models and feature sizes to compare
their accuracy, model size, and inference time. The models explored include
Decision Tree (DT), Random Forest (RF), K-nearest neighbor (KNN), Support
vector machines (SVM), and Multi-layer perceptron (MLP). Experiments were
conducted using both a widely-utilized dataset and our self-collected dataset.
The experimental results show that our method by combining signal processing
and ML had only 5% error for HR estimation using low-frequency PPG data.
Moreover, our analysis showed that DT models with 10 to 20 input features
usually have good accuracy, while are several magnitude smaller in model sizes
and faster in inference time
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