MoMA

KO | EN

gitlite — search

#hacktoberfest #llm #golang #go #android #deep-learning #macos #java #windows #security #ios #mcp #openai #open-source

(★ 22)

MoMA: Modern Multivariate Analysis in R

MoMA 최신버젼 다운로드

최종 버전 다운로드 (.zip)

// repository documentation

Was this content helpful?

★ 0 (0 ratings)

# MoMA: Modern Multivariate Analysis

[![TravisCI Build
Status](https://travis-ci.com/DataSlingers/MoMA.svg?branch=develop)](https://travis-ci.com/DataSlingers/MoMA)
[![codecov Coverage
Status](https://codecov.io/gh/DataSlingers/MoMA/branch/develop/graph/badge.svg)](https://codecov.io/gh/DataSlingers/MoMA/branch/develop)
[![License: GPL
v2](https://img.shields.io/badge/License-GPL%20v2-brightgreen.svg)](https://www.gnu.org/licenses/old-licenses/gpl-2.0.en.html)
[![CRAN\_Status\_Badge](http://www.r-pkg.org/badges/version/MoMA)](https://cran.r-project.org/package=MoMA)
[![Project Status: WIP – Initial development is in progress, but there
has not yet been a stable, usable release suitable for the
public.](http://www.repostatus.org/badges/latest/wip.svg)](http://www.repostatus.org/#wip)

MoMA is a penalized SVD framework that supports a wide range of
sparsity-inducing penalties. For a matrix *X*, MoMA gives the solution
to the following optimization
problem:

</center>

The penalties (the *P* functions) we support so far include

- `moma_lasso()`: LASSO (least absolute shrinkage and selection
    operator).

- `moma_scad()`: SCAD (smoothly clipped absolute deviation).

- `moma_mcp()` MCP (minimax concave penalty).

- `moma_slope()`: SLOPE (sorted \(\ell\)-one penalized estimation).

- `moma_grplasso()`: Group LASSO.

- `moma_fusedlasso()`: Fused LASSO.

- `moma_spfusedlasso()`: Sparse fused LASSO.

- `moma_l1tf()`: \(\ell\)-one trend filtering.

- `moma_cluster()`: Cluster penalty.

With this at hand, we can easily extend classical multivariate models:

- `moma_sfpca()` performs penalized principal component analysis.

- `moma_sfcca()` performs penalized canonical component analysis.

- `moma_sflda()` performs penalized linear discriminant analysis.

We also provide Shiny App support to facilitate interaction with the
results. If you are new to MoMA, the best place to start is
`vignette("MoMA")`.

## Installation

The newest version of the package can be installed from Github:

``` r
library(devtools)
install_github("DataSlingers/MoMA", ref = "master")
```

## Usage

Perform sparse linear discriminant analysis on the Iris data set.

``` r
library(MoMA)

## collect data
X <- iris[, 1:4]
Y_factor <- as.factor(rep(c("s", "c", "v"), rep(50, 3)))

## range of penalty
lambda <- seq(0, 1, 0.1)

## run!
a <- moma_sflda(
    X = X,
    Y_factor = Y_factor,
    x_sparse = moma_lasso(lambda = lambda),
    rank = 3
)

plot(a) # start a Shiny app and play with it!
```

</center>

## Background

Multivariate analysis – the study of finding meaningful patterns in
datasets – is a key technique in any data scientist’s toolbox. Beyond
its use for Exploratory Data Analysis (“EDA”), multivariate analysis
also allows for principled *Data-Driven Discovery*: finding meaningful,
actionable, and reproducible structure in large data sets. Classical
techniques for multivariate analysis have proven immensely successful
through history, but modern Data-Driven Discovery requires new
techniques to account for the specific complexities of modern data. This
package provides a new unified framework for **Modern Multivariate
Analysis** (“MoMA”), which will provide a unified and flexible baseline
for future research in multivariate analysis. Even more importantly, we
anticipate that this easy-to-use `R` package will increase adoption of
these powerful new models by end users and, in conjunction with `R`’s
rich graphics libraries, position `R` as the leading platform for modern
exploratory data analysis and data-driven discovery.

Multivariate analysis techniques date back to the earliest days of
statistics, pre-dating other foundational concepts like hypothesis
testing by several decades. Classical techniques such as Principal
Components Analysis (“PCA”) \[1, 2\], Partial Least Squares (“PLS”),
Canonical Correlation Analysis (“CCA”) \[3\], and Linear Discriminant
Analysis (“LDA”), have a long and distinguished history of use in
statistics and are still among the most widely used methods for EDA.
Their importance is reflected in the CRAN Task View dedicated to
Multivariate Analysis \[4\], as well as the specialized implementations
available for a range of application areas. Somewhat surprisingly, each
of these techniques can be interpreted as a variant of the well-studied
eigendecomposition problem, allowing statisticians to build upon a rich
mathematical and computational literature.

In the early 2000s, researchers noted that naive extensions of classical
multivariate techniques to the high-dimensional setting produced
unsatisfactory results, a finding later confirmed by advances in random
matrix theory \[5\]. In response to these findings, multivariate
analysis experienced a renaissance as researchers developed a wide array
of new techniques to incorporate sparsity, smoothness, and other
structure into classical techniques \[6,7,8,9,10,11,12,13,14 among many
others\], resulting in a rich literature on “modern multivariate
analysis.” Around the same time, theoretical advances showed that these
techniques avoided many of the pitfalls associated with naive extensions
\[15,16,17,18,19,20\].

While this literature is vast, it relies on a single basic principle: it
is essential to adapt classical techniques to account for known
characteristics and complexities of the dataset at hand for multivariate
analysis to succeed. For example, a neuroscientist investigating the
brain’s response to an external stimulus may expect a response which is
simultaneously spatially smooth and sparse: spatially smooth because the
brain processes related stimuli in well-localized areas (*e.g.*, the
visual cortex) and sparse because not all regions of the brain are used
to respond to a given stimulus. Alternatively, a statistical factor
model used to understand financial returns may be significantly improved
by incorporating known industry sector data, motivating a form of group
sparsity. A sociologist studying how pollution leads to higher levels of
respiratory illnesses may combine spatial smoothness and sparsity
(indicating “pockets” of activity) with a non-negativity constraint,
knowing that pollution and illness have a positive effect.

To incorporate these different forms of prior knowledge into
multivariate analysis, a wide variety of algorithms and approaches have
been proposed. In 2013, Allen proposed a general framework that unified
existing techniques for “modern” PCA, as well as proposing a number of
novel extensions \[21\]. The recently developed `MoMA` algorithm builds
on this work, allowing more forms of regularization and structure, as
well as supporting more forms of multivariate analysis.

The principal aim of this package is to make modern multivariate
analysis available to a wide audience. This package will allow for
fitting PCA, PLS, CCA, and LDA with all of the modern
“bells-and-whistles:” sparsity, smoothness, ordered and unordered
fusion, orthogonalization with respect to arbitrary bases, and
non-negativity constraints. Uniting this wide literature under a single
umbrella using the `MoMA` algorithm will provide a unified and flexible
platform for data-driven discovery in `R`.

## Authors

- [Michael Weylandt](http://github.com/michaelweylandt)
    
    Department of Statistics, Rice University

- [Genevera Allen](http://www.stat.rice.edu/~gallen)
    
    Departments of Statistics, CS,and ECE, Rice University
    
    Jan and Dan Duncan Neurological Research Institute Baylor College of
    Medicine and Texas Children’s Hospital

- [Luofeng “Luke” Liao](http://github.com/Banana1530)
    
    School of Data Science, Fudan University

## Acknowledgements

- MW was funded by an NSF Graduate Research Fellowship 1450681.
  - LL was funded by Google Summer of Code 2019.

## References

\[1\] K. Pearson. “On Lines and Planes of Closest Fit to Systems of
Points in Space.” The London, Edinburgh, and Dublin Philosophical
Magazine and Journal of Science 2, p.559-572, 1901.
<https://doi.org/10.1080/14786440109462720>

\[2\] H. Hotelling. Analysis of a Complex of Statistical Variables into
Principal Components. Journal of Educational Psychology 24(6),
p.417-441, 1933. <http://dx.doi.org/10.1037/h0071325>

\[3\] H. Hotelling. “Relations Between Two Sets of Variates” Biometrika
28(3-4), p.321-377, 1936. <https://doi.org/10.1093/biomet/28.3-4.321>

\[4\] See [CRAN Task View: Multivariate
Statistics](https://cran.r-project.org/web/views/Multivariate.html)

\[5\] I. Johnstone, A. Lu. “On Consistency and Sparsity for Principal
Components Analysis in High Dimensions.” Journal of the American
Statistical Association: Theory and Methods 104(486), p.682-693, 2009.
<https://doi.org/10.1198/jasa.2009.0121>

\[6\] B. Silverman. “Smoothed Functional Frincipal Fomponents Analysis
by Choice of Norm.” Annals of Statistics 24(1), p.1-24, 1996.
<https://projecteuclid.org/euclid.aos/1033066196>

\[7\] J. Huang, H. Shen, A. Buja. “Functional Principal Components
Analysis via Penalized Rank One Approximation.” Electronic Journal of
Statistics 2, p.678-695, 2008.
<https://projecteuclid.org/euclid.ejs/1217450800>

\[8\] I.T. Jolliffe, N.T. Trendafilov, M. Uddin. “A Modified Principal
Component Technique Based on the Lasso.” Journal of Computational and
Graphical Statistics 12(3), p.531-547, 2003.
<https://doi.org/10.1198/1061860032148>

\[9\] H. Zou, and T. Hastie, and R. Tibshirani. “Sparse Principal
Component Analysis.” Journal of Computational and Graphical Statistics
15(2), p.265-286, 2006. <https://doi.org/10.1198/106186006X113430>

\[10\] A. d’Aspremont, L. El Gahoui, M.I. Jordan, G.R.G. Lanckriet. “A
Direct Formulation for Sparse PCA Using Semidefinite Programming.” SIAM
Review 49(3), p.434-448, 2007. <https://doi.org/10.1137/050645506>

\[11\] A. d’Aspremont, F. Bach, L. El Gahoui. “Optimal Solutions for
Sparse Principal Component Analysis.” Journal of Machine Learning
Research 9, p.1269-1294, 2008.
<http://www.jmlr.org/papers/v9/aspremont08a.htm>

\[12\] D. Witten, R. Tibshirani, T. Hastie. “A Penalized Matrix
Decomposition, with Applications to Sparse Principal Components and
Canonical Correlation Analysis.” Biostatistics 10(3), p.515-534, 2009.
<https://doi.org/10.1093/biostatistics/kxp008>

\[13\] R. Jenatton, G. Obozinski. F. Bach. “Structured Sparse Principal
Component Analysis.” Proceedings of the 13th International Conference on
Artificial Intelligence and Statistics (AISTATS) 2010.
<http://proceedings.mlr.press/v9/jenatton10a.html>

\[14\] G.I. Allen, M. Maletic-Savatic. “Sparse Non-Negative Generalized
PCA with Applications to Metabolomics.” Bioinformatics 27(21),
p.3029-3035, 2011. <https://doi.org/10.1093/bioinformatics/btr522>

\[15\] A.A. Amini, M.J. Wainwright. “High-Dimensional Analysis of
Semidefinite Relaxations for Sparse Principal Components.” Annals of
Statistics 37(5B), p.2877-2921, 2009.
<https://projecteuclid.org/euclid.aos/1247836672>

\[16\] S. Jung, J.S. Marron. “PCA Consistency in High-Dimension, Low
Sample Size Context.” Annals of Statistics 37(6B), p.4104-4130, 2009.
<https://projecteuclid.org/euclid.aos/1256303538>

\[17\] Z. Ma. “Sparse Principal Component Analysis and Iterative
Thresholding.” Annals of Statistics 41(2), p.772-801, 2013.
<https://projecteuclid.org/euclid.aos/1368018173>

\[18\] T.T. Cai, Z. Ma, Y. Wu. “Sparse PCA: Optimal Rates and Adaptive
Estimation.” Annals of Statistics 41(6), p.3074-3110, 2013.
<https://projecteuclid.org/euclid.aos/1388545679>

\[19\] V.Q. Vu, J. Lei. “Minimax Sparse Principal Subspace Estimation in
High Dimensions.” Annals of Statistics 41(6), p.2905-2947, 2013.
<https://projecteuclid.org/euclid.aos/1388545673>

\[20\] D. Shen, H. Shen, J.S. Marron. “Consistency of Sparse PCA in High
Dimension, Low Sample Size Contexts.” Journal of Multivariate Analysis
115, p.317-333, 2013. <https://doi.org/10.1016/j.jmva.2012.10.007>

\[21\] G.I. Allen. “Sparse and Functional Principal Components
Analysis.” ArXiv Pre-Print 1309.2895 (2013).
<https://arxiv.org/abs/1309.2895>

MoMA

MoMA 최신버젼 다운로드

오늘의 추천 프로젝트

Was this content helpful?

Recent Feedback

MoMA

MoMA 최신버젼 다운로드

오늘의 추천 프로젝트

Was this content helpful?

Recent Feedback

Download README