Dimensionality reduction represents a critical preprocessing step in order to
increase the efficiency and the performance of many hyperspectral imaging
algorithms. However, dimensionality reduction algorithms, such as the Principal
Component Analysis (PCA), suffer from their computationally demanding nature,
becoming advisable for their implementation onto high-performance computer
architectures for applications under strict latency constraints. This work
presents the implementation of the PCA algorithm onto two different
high-performance devices, namely, an NVIDIA Graphics Processing Unit (GPU) and
a Kalray manycore, uncovering a highly valuable set of tips and tricks in order
to take full advantage of the inherent parallelism of these high-performance
computing platforms, and hence, reducing the time that is required to process a
given hyperspectral image. Moreover, the achieved results obtained with
different hyperspectral images have been compared with the ones that were
obtained with a field programmable gate array (FPGA)-based implementation of
the PCA algorithm that has been recently published, providing, for the first
time in the literature, a comprehensive analysis in order to highlight the pros
and cons of each option.

应用 PCA 算法在高性能设备上实现降维以增加高光谱成像算法的效率和性能，并与 FPGA 实现进行比较以揭示各自的优缺点。

高性能计算设施上对高光谱数据进行主成分分析的实现：结果与比较

Implementation of the Principal Component Analysis onto High-Performance  Computer Facilities for Hyperspectral Dimensionality Reduction: Results and  Comparisons

Sentence embeddings produced by Pretrained Language Models (PLMs) have
received wide attention from the NLP community due to their superior
performance when representing texts in numerous downstream applications.
However, the high dimensionality of the sentence embeddings produced by PLMs is
problematic when representing large numbers of sentences in memory- or
compute-constrained devices. As a solution, we evaluate unsupervised
dimensionality reduction methods to reduce the dimensionality of sentence
embeddings produced by PLMs. Our experimental results show that simple methods
such as Principal Component Analysis (PCA) can reduce the dimensionality of
sentence embeddings by almost $50\%$, without incurring a significant loss in
performance in multiple downstream tasks. Surprisingly, reducing the
dimensionality further improves performance over the original high-dimensional
versions for the sentence embeddings produced by some PLMs in some tasks.

使用预训练语言模型（PLMs）生成的句子嵌入引起了自然语言处理界的广泛关注，因为它们在多种下游应用中以优越的性能表示文本。然而，当在内存或计算受限设备中表示大量句子时，由 PLMs 生成的句子嵌入的高维度会带来问题。作为解决方案，我们评估了无监督的降维方法来降低由 PLMs 生成的句子嵌入的维度。我们的实验结果表明，如主成分分析（PCA）等简单方法可以将句子嵌入的维度降低近 50%，而不会在多个下游任务中造成显著性能损失。令人惊讶的是，在某些任务中，进一步降低维度可以提高某些 PLMs 生成的句子嵌入的性能。

评估预训练句子嵌入的无监督降维方法

Evaluating Unsupervised Dimensionality Reduction Methods for Pretrained  Sentence Embeddings

Estimating intrinsic dimensionality of data is a classic problem in pattern
recognition and statistics. Principal Component Analysis (PCA) is a powerful
tool in discovering dimensionality of data sets with a linear structure; it,
however, becomes ineffective when data have a nonlinear structure. In this
paper, we propose a new PCA-based method to estimate intrinsic dimension of
data with nonlinear structures. Our method works by first finding a minimal
cover of the data set, then performing PCA locally on each subset in the cover
and finally giving the estimation result by checking up the data variance on
all small neighborhood regions. The proposed method utilizes the whole data set
to estimate its intrinsic dimension and is convenient for incremental learning.
In addition, our new PCA procedure can filter out noise in data and converge to
a stable estimation with the neighborhood region size increasing. Experiments
on synthetic and real world data sets show effectiveness of the proposed
method.

本文介绍了一种基于 PCA 的新方法，用于估计具有非线性结构的数据的内在维数，该方法利用整个数据集估计其内在维数，并方便增量学习。该方法使用数据的最小覆盖来处理数据集的非线性结构，并通过检查所有小邻域区域的数据方差来确定估计结果。实验结果表明，该方法可以过滤数据中的噪声，并在邻域区域大小增加时收敛到稳定的估计值。