arXiv subjects

Yichuan Deng

Publications and source records attributed to Yichuan Deng.

22 records · Page 2Linked to original sources

arXiv2023

Streaming Kernel PCA Algorithm With Small Space

Principal Component Analysis (PCA) is a widely used technique in machine learning, data analysis and signal processing. With the increase in the size and complexity of datasets, it has become important to develop low-space usage algorithms for PCA. Streaming PCA has gained significant attention in recent years, as it can handle large datasets efficiently. The kernel method, which is commonly used in learning algorithms such as Support Vector Machines (SVMs), has also been applied in PCA algorithms. We propose a streaming algorithm for Kernel PCA problems based on the traditional scheme by Oja. Our algorithm addresses the challenge of reducing the memory usage of PCA while maintaining its accuracy. We analyze the performance of our algorithm by studying the conditions under which it succeeds. Specifically, we show that, when the spectral ratio $R := λ_1/λ_2$ of the target covariance matrix is lower bounded by $C \cdot \log n\cdot \log d$, the streaming PCA can be solved with $O(d)$ space cost. Our proposed algorithm has several advantages over existing methods. First, it is a streaming algorithm that can handle large datasets efficiently. Second, it employs the kernel method, which allows it to capture complex nonlinear relationships among data points. Third, it has a low-space usage, making it suitable for applications where memory is limited.

cs.LG↗

arXiv2022

A Nearly Optimal Size Coreset Algorithm with Nearly Linear Time

A coreset is a point set containing information about geometric properties of a larger point set. A series of previous works show that in many machine learning problems, especially in clustering problems, coreset could be very useful to build efficient algorithms. Two main measures of an coreset construction algorithm's performance are the running time of the algorithm and the size of the coreset output by the algorithm. In this paper we study the construction of coresets for the $(k,z)$-clustering problem, which is a generalization of $k$-means and $k$-median problem. By properly designing a sketching-based distance estimation data structure, we propose faster algorithms that construct coresets with matching size of the state-of-the-art results.

cs.DS↗

arXiv2022

Fast Distance Oracles for Any Symmetric Norm

In the Distance Oracle problem, the goal is to preprocess $n$ vectors $x_1, x_2, \cdots, x_n$ in a $d$-dimensional metric space $(\mathbb{X}^d, \| \cdot \|_l)$ into a cheap data structure, so that given a query vector $q \in \mathbb{X}^d$ and a subset $S\subseteq [n]$ of the input data points, all distances $\| q - x_i \|_l$ for $x_i\in S$ can be quickly approximated (faster than the trivial $\sim d|S|$ query time). This primitive is a basic subroutine in machine learning, data mining and similarity search applications. In the case of $\ell_p$ norms, the problem is well understood, and optimal data structures are known for most values of $p$. Our main contribution is a fast $(1+\varepsilon)$ distance oracle for any symmetric norm $\|\cdot\|_l$. This class includes $\ell_p$ norms and Orlicz norms as special cases, as well as other norms used in practice, e.g. top-$k$ norms, max-mixture and sum-mixture of $\ell_p$ norms, small-support norms and the box-norm. We propose a novel data structure with $\tilde{O}(n (d + \mathrm{mmc}(l)^2 ) )$ preprocessing time and space, and $t_q = \tilde{O}(d + |S| \cdot \mathrm{mmc}(l)^2)$ query time, for computing distances to a subset $S$ of data points, where $\mathrm{mmc}(l)$ is a complexity-measure (concentration modulus) of the symmetric norm. When $l = \ell_{p}$ , this runtime matches the aforementioned state-of-art oracles.

cs.DS↗

arXiv2022

SODA: Site Object Detection dAtaset for Deep Learning in Construction

Computer vision-based deep learning object detection algorithms have been developed sufficiently powerful to support the ability to recognize various objects. Although there are currently general datasets for object detection, there is still a lack of large-scale, open-source dataset for the construction industry, which limits the developments of object detection algorithms as they tend to be data-hungry. Therefore, this paper develops a new large-scale image dataset specifically collected and annotated for the construction site, called Site Object Detection dAtaset (SODA), which contains 15 kinds of object classes categorized by workers, materials, machines, and layout. Firstly, more than 20,000 images were collected from multiple construction sites in different site conditions, weather conditions, and construction phases, which covered different angles and perspectives. After careful screening and processing, 19,846 images including 286,201 objects were then obtained and annotated with labels in accordance with predefined categories. Statistical analysis shows that the developed dataset is advantageous in terms of diversity and volume. Further evaluation with two widely-adopted object detection algorithms based on deep learning (YOLO v3/ YOLO v4) also illustrates the feasibility of the dataset for typical construction scenarios, achieving a maximum mAP of 81.47%. In this manner, this research contributes a large-scale image dataset for the development of deep learning-based object detection methods in the construction industry and sets up a performance benchmark for further evaluation of corresponding algorithms in this area.

cs.CV↗