智能基础设施下的IMU活动签名自动注释方法
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"这篇文档可能涉及的是智能基础设施中惯性测量单元(IMU)生成的活动签名的自动注释方法，特别是在智能环境下的应用。研究可能深入到如何利用IMU数据来理解和解析人类活动，并可能引入了一种名为DRIPP（DRIVENPOINTPROCESSESTOMODELSTIMULI INDUCEDPATTERNSIN M/EEGSIGNALS）的技术，该技术可能用于建模在脑电图(EEG)和磁脑电图(MEG)信号中由刺激诱导的模式。文档中还提到了Cédric Allain、Alexandre Gramfort和Thomas Moreau等研究人员，他们来自Inria Parietal团队和巴黎萨克雷大学，对非侵入式电生理信号的定量分析进行了探讨，特别是关于如何无监督地提取这些信号中的时间模式，如诱发电位响应、神经振荡的瞬时爆发，以及用于数据清洗的眨眼或心跳事件。文章介绍了一种基于点过程的方法，用于估计这些事件的发生如何受到认知任务和实验操纵的影响。"
文章的主要知识点包括：
1. **智能基础设施与IMU活动签名**：智能基础设施是指融合了各种传感器和计算能力的环境，其中IMU（惯性测量单元）用于收集用户活动的数据，形成活动签名，这有助于理解人类行为和运动。
2. **非侵入式电生理信号分析**：EEG和MEG是非侵入式脑成像技术，用于记录大脑的电和磁活动。通过量化分析这些信号，可以识别出与特定大脑活动相关的时间模式。
3. **DRIPP技术**：这是一种用于建模EEG和MEG信号中由外部刺激诱导的模式的点过程模型。点过程理论在统计学和概率论中用于描述随机事件发生的序列，可能被用来捕捉信号中的异常或响应模式。
4. **无监督学习方法**：文献中提到使用无监督的卷积字典学习方法来有效地提取信号中的模式，这表明无需预先标记的数据，就能识别出数据集中的关键特征和事件。
5. **事件基础描述**：通过无监督学习，可以从数据中识别出事件，比如大脑活动的特定响应、神经振荡的瞬态爆发，甚至生理噪声如眨眼和心跳，为后续的数据处理和分析提供基础。
6. **点过程和事件发生率**：研究提出使用点过程来估计事件的发生如何受到认知任务或实验条件的影响，这可能涉及到计算事件的条件概率，以了解大脑活动如何随外部因素变化。
7. **自动注释系统Accoustate**：虽然标题中提到，但在给出的部分内容中没有详细描述，但可以推测Accoustate可能是一个系统，用于自动标注IMU生成的活动签名，可能是为了提高分析效率和准确性。
这些知识点对于理解智能环境中的活动监测、非侵入式脑信号处理和机器学习在生物信号分析中的应用具有重要意义。
DriPP: Driven Point Processes to Model Stimuli Induced Patterns in M/EEG SignalsA PREPRINT
Algorithm 1: EM-based algorithm
input :A
k
, T
p
, a, b, T, N
output :The estimated values for parameters µ, α, m
and σ
1 Initialize µ
(0)
, α
(0)
, m
(0)
, σ
(0)
;
2 for i = 0, . . . , N − 1 do
3 if α
(i)
= 0
R
#P
then
4 µ
(i+1)
= µ
(MLE)
;
5 break;
6 end
7 Define λ
(i)
using Equation (2);
8 Compute µ
(i+1)
, α
(i+1)
, m
(i+1)
, σ
(i+1)
;
9 end
10 return µ
(i+1)
, α
(i+1)
, m
(i+1)
, σ
(i+1)
Also, when the estimate of parameter m is too
far from the kernel’s support
[a ; b]
, we are in
a pathological case where EM is diverging due
to indeterminacy between setting
α = 0
and
pushing
m
to infinity due to the discrete na-
ture of our events. Thus, we consider that the
stochastic process is not linked to the consid-
ered driver, and fall back to the MLE estimator.
The algorithm is therefore stopped and we set
α = 0
R
#P
.
It is worth noting that if
∀p ∈ P, α
k,p
= 0
,
then the intensity is reduced to its baseline, thus
the negative log-likelihood is
L
k,p
(Θ
k,p
) =
µ
k
T −#A
k
log µ
k
, where
#A
denotes the car-
dinality of the set
A
. Thus, we can terminate
the EM algorithm by directly computing the
MLE for µ
k
, namely: µ
(MLE)
k
= #A
k
/T
Initialization strategy
We propose a "smart
start" initialization strategy, where parameters are initialized based on their role in the model. It reads:
µ
(0)
k
=
#A
k
− #
S
p∈P
D
k,p
T −λ
S
p∈P
S
t
0
∈T
p
[t
0
+ a ; t
0
+ b]
(10)
α
(0)
k,p
=
#D
k,p
λ
S
t
0
∈T
p
[t
0
+ a ; t
0
+ b]
− µ
(0)
k
, ∀p ∈ P (11)
m
(0)
k,p
=
1
#D
k,p
X
d∈D
k,p
d and σ
(0)
k,p
=
v
u
u
t
1
#D
k,p
X
d∈D
k,p
d − m
(0)
2
, ∀p ∈ P
, (12)
where
λ (·)
denotes the Lebesgue measure, and where
D
k,p
:
= {t − t
(p)
∗
(t), t ∈ A
k
} ∩ [a ; b]
is the set
of all empirical delays possibly linked to the driver
p
, with
t
(p)
∗
(t)
:
= max{t
0
, t
0
∈ T
p
, t
0
≤ t}
denoting the
timestamp of the last event on the driver
p
that occurred before time
t
. Here, the baseline intensity
µ
(0)
is
set to the average number of process’ events that occur outside any kernel support, i.e., the events that are
guaranteed to be exogenous or spontaneous. Similarly, the kernel intensity
α
(0)
is computed as the increase in
the average number of activations over the kernel support, compared to
µ
(0)
. The initial guess for
m
(0)
and
σ
(0)
are obtained with their parametric estimates, considering that all event on the kernel support are assigned
to the considered driver.
4 Experiments
We evaluated our model on several experiments, using both synthetic and empirical MEG data. We used
Python
(Python Software Foundation, 2019) and its scientific libraries (Virtanen et al., 2020; Hunter, 2007;
Harris et al., 2020). We relied on
alphacsc
for CDL with rank-1 constraints on MEG (Dupré la Tour et al.,
2018) and we used
MNE
(Gramfort et al., 2013) to load and manipulate the MEG datasets. Computations were
run on CPU Intel(R) Xeon(R) E5-2699, with 44 physical cores.
4.1 Evaluation of the EM convergence on synthetic data
For a given number of drivers and a set of corresponding parameters
Θ
, we first generate the drivers’
processes and then simulate the stochastic process for a pre-determined duration
T
. Each driver’s timestamps
are simulated as follows: given an interstimuli interval (ISI), a set of
S =
T
ISI
equidistant timestamps
is generated – where
b·c
denotes the floor function. Then
P
timestamps are uniformly sampled without
replacement from this set. In all our experiments, we fixed the ISI to
1 s
for the "wide" kernel, and to
1.4 s
for the "sharp" one. Finally, a one-dimensional non-homogeneous Poisson process is simulated following
5
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