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This paper presents a novel fast machine learning method that leverages twotechniques: Vector Embedding on Orthonormal Basis (VEOB) and Spectral Transform(ST). The VEOB converts the original data encoding into a vector embedding withcoordinates projected onto orthonormal bases. The Singular Value Decomposition(SVD) technique is used to calculate the vector basis and projectioncoordinates, leading to an enhanced distance measurement in the embedding spaceand facilitating data compression by preserving the projection vectorsassociated with the largest singular values. On the other hand, ST transformssequence of vector data into spectral space. By applying the Discrete CosineTransform (DCT) and selecting the most significant components, it streamlinesthe handling of lengthy vector sequences. The paper provides examples of wordembedding, text chunk embedding, and image embedding, implemented in Julialanguage with a vector database. It also investigates unsupervised learning andsupervised learning using this method, along with strategies for handling largedata volumes.

Fast Machine Learning Method with Vector Embedding on Orthonormal Basis and Spectral Transform