Multimodal deep learning methods capture synergistic features from multiple
modalities and have the potential to improve accuracy for stress detection
compared to unimodal methods. However, this accuracy gain typically comes from
high computational cost due to the high-dimensional feature spaces, especially
for intermediate fusion. Dimensionality reduction is one way to optimize
multimodal learning by simplifying data and making the features more amenable
to processing and analysis, thereby reducing computational complexity. This
paper introduces an intermediate multimodal fusion network with manifold
learning-based dimensionality reduction. The multimodal network generates
independent representations from biometric signals and facial landmarks through
1D-CNN and 2D-CNN. Finally, these features are fused and fed to another 1D-CNN
layer, followed by a fully connected dense layer. We compared various
dimensionality reduction techniques for different variations of unimodal and
multimodal networks. We observe that the intermediate-level fusion with the
Multi-Dimensional Scaling (MDS) manifold method showed promising results with
an accuracy of 96.00\% in a Leave-One-Subject-Out Cross-Validation (LOSO-CV)
paradigm over other dimensional reduction methods. MDS had the highest
computational cost among manifold learning methods. However, while
outperforming other networks, it managed to reduce the computational cost of
the proposed networks by 25\% when compared to six well-known conventional
feature selection methods used in the preprocessing step.

通过多模态深度学习方法和流形学习的降维技术，本文提出了一种中间多模态融合网络，成功地在处理和分析数据时降低了计算复杂度，并在准确性方面优于其他网络。

一种具有多模态中间融合网络和流形学习的应对压力检测方法

A Multimodal Intermediate Fusion Network with Manifold Learning for  Stress Detection

Multi-dimensional Scaling (MDS) is a family of methods for embedding
pair-wise dissimilarities between $n$ objects into low-dimensional space. MDS
is widely used as a data visualization tool in the social and biological
sciences, statistics, and machine learning. We study the Kamada-Kawai
formulation of MDS: given a set of non-negative dissimilarities $\{d_{i,j}\}_{i
, j \in [n]}$ over $n$ points, the goal is to find an embedding
$\{x_1,\dots,x_n\} \subset \mathbb{R}^k$ that minimizes \[ \text{OPT} =
\min_{x} \mathbb{E}_{i,j \in [n]} \left[ \left(1-\frac{\|x_i -
x_j\|}{d_{i,j}}\right)^2 \right] \]
Despite its popularity, our theoretical understanding of MDS is extremely
limited. Recently, Demaine, Hesterberg, Koehler, Lynch, and Urschel
(arXiv:2109.11505) gave the first approximation algorithm with provable
guarantees for Kamada-Kawai, which achieves an embedding with cost $\text{OPT}
+\epsilon$ in $n^2 \cdot 2^{\tilde{\mathcal{O}}(k \Delta^4 / \epsilon^2)}$
time, where $\Delta$ is the aspect ratio of the input dissimilarities. In this
work, we give the first approximation algorithm for MDS with quasi-polynomial
dependency on $\Delta$: for target dimension $k$, we achieve a solution with
cost $\mathcal{O}(\text{OPT}^{ \hspace{0.04in}1/k } \cdot \log(\Delta/\epsilon)
)+ \epsilon$ in time $n^{ \mathcal{O}(1)} \cdot 2^{\tilde{\mathcal{O}}( k^2
(\log(\Delta)/\epsilon)^{k/2 + 1} ) }$.
Our approach is based on a novel analysis of a conditioning-based rounding
scheme for the Sherali-Adams LP Hierarchy. Crucially, our analysis exploits the
geometry of low-dimensional Euclidean space, allowing us to avoid an
exponential dependence on the aspect ratio $\Delta$. We believe our
geometry-aware treatment of the Sherali-Adams Hierarchy is an important step
towards developing general-purpose techniques for efficient metric optimization
algorithms.

我们研究了多维缩放（Multi-dimensional Scaling，MDS）的 Kamada-Kawai 公式，提出了一种基于 Sherali-Adams 线性规划层次的近似算法，该算法实现了在目标维度下成本和时间复杂度之间的平衡，为高效度量优化算法的开发奠定了基础。