• Algorithmic Complexity of Clustering and Low-Rank Approximation Problems 

      Simonov, Kirill (Doctoral thesis, 2021-03-29)
      The two most popular unsupervised learning problems are k-Clustering and Low-Rank Approximation. Consider a set of n datapoints, in the k-Clustering problem, the objective is to partition these points into k clusters and ...
    • Building large k-cores from sparse graphs 

      Fomin, Fedor; Sagunov, Danil; Simonov, Kirill (Journal article; Peer reviewed, 2020)
      A popular model to measure network stability is the k-core, that is the maximal induced subgraph in which every vertex has degree at least k. For example, k-cores are commonly used to model the unraveling phenomena in ...
    • Low-Rank Binary Matrix Approximation in Column-Sum Norm 

      Fomin, Fedor; Golovach, Petr; Panolan, Fahad; Simonov, Kirill (Journal article; Peer reviewed, 2020)
      We consider 𝓁₁-Rank-r Approximation over {GF}(2), where for a binary m× n matrix 𝐀 and a positive integer constant r, one seeks a binary matrix 𝐁 of rank at most r, minimizing the column-sum norm ‖ 𝐀 -𝐁‖₁. We show ...
    • Parameterized complexity of PCA 

      Fomin, Fedor; Golovach, Petr; Simonov, Kirill (Journal article; Peer reviewed, 2020)
      We discuss some recent progress in the study of Principal Component Analysis (PCA) from the perspective of Parameterized Complexity.
    • Parameterized k-Clustering: Tractability Island 

      Fomin, Fedor; Golovach, Petr; Simonov, Kirill (Peer reviewed; Journal article, 2019)
      In k-Clustering we are given a multiset of n vectors X subset Z^d and a nonnegative number D, and we need to decide whether X can be partitioned into k clusters C_1, ..., C_k such that the cost sum_{i=1}^k min_{c_i in R^d} ...
    • Refined Complexity of PCA with Outliers 

      Fomin, Fedor; Golovach, Petr; Panolan, Fahad; Simonov, Kirill (Conference object; Peer reviewed; Journal article, 2019)
      Principal component analysis (PCA) is one of the most fundamental procedures in exploratory data analysis and is the basic step in applications ranging from quantitative finance and bioinformatics to image analysis and ...