title: Joint analysis of multiple high-dimensional data types using sparse matrix approximations of rank-1 with applications to ovarian and liver cancer.
abstract: BACKGROUND
  Technological advances enable the cost-effective acquisition of Multi-Modal Data Sets (MMDS) composed of measurements for multiple, high-dimensional data types obtained from a common set of bio-samples. The joint analysis of the data matrices associated with the different data types of a MMDS should provide a more focused view of the biology underlying complex diseases such as cancer that would not be apparent from the analysis of a single data type alone. As multi-modal data rapidly accumulate in research laboratories and public databases such as The Cancer Genome Atlas (TCGA), the translation of such data into clinically actionable knowledge has been slowed by the lack of computational tools capable of analyzing MMDSs. Here, we describe the Joint Analysis of Many Matrices by ITeration (JAMMIT) algorithm that jointly analyzes the data matrices of a MMDS using sparse matrix approximations of rank-1.
  
  
  METHODS
  The JAMMIT algorithm jointly approximates an arbitrary number of data matrices by rank-1 outer-products composed of "sparse" left-singular vectors (eigen-arrays) that are unique to each matrix and a right-singular vector (eigen-signal) that is common to all the matrices. The non-zero coefficients of the eigen-arrays identify small subsets of variables for each data type (i.e., signatures) that in aggregate, or individually, best explain a dominant eigen-signal defined on the columns of the data matrices. The approximation is specified by a single "sparsity" parameter that is selected based on false discovery rate estimated by permutation testing. Multiple signals of interest in a given MDDS are sequentially detected and modeled by iterating JAMMIT on "residual" data matrices that result from a given sparse approximation.
  
  
  RESULTS
  We show that JAMMIT outperforms other joint analysis algorithms in the detection of multiple signatures embedded in simulated MDDS. On real multimodal data for ovarian and liver cancer we show that JAMMIT identified multi-modal signatures that were clinically informative and enriched for cancer-related biology.
  
  
  CONCLUSIONS
  Sparse matrix approximations of rank-1 provide a simple yet effective means of jointly reducing multiple, big data types to a small subset of variables that characterize important clinical and/or biological attributes of the bio-samples from which the data were acquired.
authors.affiliation: University of Hawaii Cancer Center, 701 Ilalo Street, Honolulu, HI 96813 USA.
authors.forename: Gordon
authors.identifier: 0000-0003-4669-0396
authors.initials: G
authors.lastname: Okimoto
authors.affiliation: University of Hawaii Cancer Center, 701 Ilalo Street, Honolulu, HI 96813 USA.
authors.forename: Ashkan
authors.initials: A
authors.lastname: Zeinalzadeh
authors.affiliation: SNR Analytics, LLC, 45-115E Waikalua Road, Kaneohe, HI 96744 USA.
authors.forename: Tom
authors.initials: T
authors.lastname: Wenska
authors.affiliation: University of Hawaii Cancer Center, 701 Ilalo Street, Honolulu, HI 96813 USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Loomis
authors.affiliation: Department of Mathematics, University of Hawaii, Manoa, Honolulu, HI 96822 USA.
authors.forename: James B
authors.initials: JB
authors.lastname: Nation
authors.affiliation: Interactive Biosoftware, Rouen, France.
authors.forename: Tiphaine
authors.initials: T
authors.lastname: Fabre
authors.affiliation: University of Hawaii Cancer Center, 701 Ilalo Street, Honolulu, HI 96813 USA.
authors.forename: Maarit
authors.initials: M
authors.lastname: Tiirikainen
authors.affiliation: University of Hawaii Cancer Center, 701 Ilalo Street, Honolulu, HI 96813 USA.
authors.forename: Brenda
authors.initials: B
authors.lastname: Hernandez
authors.affiliation: University of Hawaii Cancer Center, 701 Ilalo Street, Honolulu, HI 96813 USA.
authors.forename: Owen
authors.initials: O
authors.lastname: Chan
authors.affiliation: University of Hawaii Cancer Center, 701 Ilalo Street, Honolulu, HI 96813 USA.
authors.forename: Linda
authors.initials: L
authors.lastname: Wong
authors.affiliation: The Hamamatsu/Queen's PET (Positron Emission Tomography) Imaging Center, Queen's Medical Center, Honolulu, HI 96816 USA.
authors.forename: Sandi
authors.initials: S
authors.lastname: Kwee
keywords: Generalized singular value decomposition; Hepatocellular carcinoma; Joint data analysis; LASSO; Ovarian cancer; Sparse signal detection; The Cancer Genome Atlas