{
  "id": "2104.13968",
  "version": "v1",
  "published": "2021-04-28T19:17:34.000Z",
  "updated": "2021-04-28T19:17:34.000Z",
  "title": "Tail-Net: Extracting Lowest Singular Triplets for Big Data Applications",
  "authors": [
    "Gurpreet Singh",
    "Soumyajit Gupta"
  ],
  "categories": [
    "cs.LG",
    "cs.AI"
  ],
  "abstract": "SVD serves as an exploratory tool in identifying the dominant features in the form of top rank-r singular factors corresponding to the largest singular values. For Big Data applications it is well known that Singular Value Decomposition (SVD) is restrictive due to main memory requirements. However, a number of applications such as community detection, clustering, or bottleneck identification in large scale graph data-sets rely upon identifying the lowest singular values and the singular corresponding vectors. For example, the lowest singular values of a graph Laplacian reveal the number of isolated clusters (zero singular values) or bottlenecks (lowest non-zero singular values) for undirected, acyclic graphs. A naive approach here would be to perform a full SVD however, this quickly becomes infeasible for practical big data applications due to the enormous memory requirements. Furthermore, for such applications only a few lowest singular factors are desired making a full decomposition computationally exorbitant. In this work, we trivially extend the previously proposed Range-Net to \\textbf{Tail-Net} for a memory and compute efficient extraction of lowest singular factors of a given big dataset and a specified rank-r. We present a number of numerical experiments on both synthetic and practical data-sets for verification and bench-marking using conventional SVD as the baseline.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-28T19:17:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "big data applications",
      "extracting lowest singular triplets",
      "lowest singular factors",
      "lowest singular values",
      "large scale graph data-sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}