| Sentence Completion via Latent Semantic Analysis | The method is based on applying singular value decomposition ( SVD ) to a matrix W representing the occurrence of words in documents. |
| Sentence Completion via Latent Semantic Analysis | SVD results in an approximation of W by the product of three matrices, one in which each word is represented as a low—dimensional vector, one in which each document is represented as a low dimensional vector, and a diagonal scaling matrix. |
| Sentence Completion via Latent Semantic Analysis | An important property of SVD is that the rows of US — which represents the words — behave similarly to the original rows of W, in the sense that the cosine similarity between two rows in US approximates the cosine similarity between the corre— |
| Estimating the Tensor Model | The following lemma justifies the use of an SVD calculation as one method for finding values for U a and Va that satisfy condition 2: |
| Introduction | These algorithms use spectral methods: that is, algorithms based on eigenvector decompositions of linear systems, in particular singular value decomposition ( SVD ). |
| Introduction | The first step is to take an SVD of the training examples, followed by a projection of the training examples down to a low-dimensional space. |