This paper presents a novel fast machine learning method that leverages two
techniques: Vector Embedding on Orthonormal Basis (VEOB) and Spectral Transform
(ST). The VEOB converts the original data encoding into a vector embedding with
coordinates projected onto orthonormal bases. The Singular Value Decomposition
(SVD) technique is used to calculate the vector basis and projection
coordinates, leading to an enhanced distance measurement in the embedding space
and facilitating data compression by preserving the projection vectors
associated with the largest singular values. On the other hand, ST transforms
sequence of vector data into spectral space. By applying the Discrete Cosine
Transform (DCT) and selecting the most significant components, it streamlines
the handling of lengthy vector sequences. The paper provides examples of word
embedding, text chunk embedding, and image embedding, implemented in Julia
language with a vector database. It also investigates unsupervised learning and
supervised learning using this method, along with strategies for handling large
data volumes.

该论文介绍了一种新颖的快速机器学习方法，利用了两种技术：正交基向量嵌入（VEOB）和谱变换（ST）。该方法通过将原始数据编码转换为在正交基向量上投影的向量嵌入，采用奇异值分解（SVD）技术计算向量基和投影坐标，从而在嵌入空间中实现了增强的距离测量，并通过保留与最大奇异值相关的投影向量来实现数据压缩。同时，它还利用离散余弦变换（DCT）将向量数据序列转换到谱空间，并选择最重要的分量，以简化对于长向量序列的处理。该论文提供了使用这种方法在 Julia 语言中实现的词嵌入、文本块嵌入和图像嵌入的示例，并探讨了使用该方法进行无监督学习和监督学习的策略，以及如何处理大数据量。