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.

翻译：本文提出了一种新颖的快速机器学习方法，该技术融合了两种关键技术：正交基向量嵌入和谱变换。正交基向量嵌入通过将原始数据编码转换为在正交基上投影坐标的向量嵌入表示。采用奇异值分解技术计算向量基与投影坐标，从而增强嵌入空间中的距离度量，并通过保留最大奇异值对应的投影向量实现数据压缩。另一方面，谱变换将向量序列数据转换至谱空间。通过应用离散余弦变换并选取最显著的分量，有效简化了长向量序列的处理流程。本文以Word嵌入、文本块嵌入和图像嵌入为例，依托Julia语言与向量数据库实现该算法。同时探讨了该方法在无监督学习和监督学习中的应用，以及应对大规模数据处理的策略。