# Presentation: 125887

## Chandrika Kamath and Imola K. FodorCenter for Applied Scientific ComputingLawrence Livermore National LaboratoryGatlinburg, TNMarch 26-27, 2002

**Dimension Reduction and Sampling**
** ****First SDM ISIC All-Hands Meeting**

**UCRL. This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract  W-7405-Eng-48.**

## The SDM ISIC aims to minimize the effort researchers spend in managing their data

**LLNL is participating in several of the tasks, including**
**data mining to improve the management of data**
**Problem: data from simulations and experiments is high dimensional (i.e. many features)**
**Querying the features can help in understanding the data**
** ****but, searching in a high-dimensional space is difficult**
**May want to cluster similar objects for efficient access**
**but, clustering is expensive in high dimensions**

****** ****We plan to address the problem of high dimensionality   using techniques for dimension reduction and sampling originally developed in data mining.  **

## Our work on dimension reduction will help both data management and mining

**Reducing the dimensions will improve**
**searching (task 3.1, LBNL)**
**clustering (task 2.1, ORNL)**
**Dimension reduction is expensive if many data items**
**use a sample of the data items **
**techniques for sampling in presence of rare events**
**We will focus on climate and high-energy-physics data**
**complements work at ORNL (climate), LBNL (HEP)**
**but, techniques applicable to other data as well**

****** ****We only report the .8 FTE work funded under SciDAC; however, our data mining research is more extensive. See www.llnl.gov/casc/sapphire**

## There are two different ways in which we can view dimension reduction

**Reduce the number of features representing a data item**
**Reduce the number of basis vectors used to describe the data: if some of the       are small, they can be ignored**

## Our work on climate data focuses on reducing the number of basis vectors

**Domain expert Dr. Benjamin Santer (LLNL climate)**
**Climate scientists are interested in understanding the change in the earth’s surface temperature**
**Simulated and observed data are mixtures of volcano, El Ni****ño, and other effects **
**Our goal is to separate the signals corresponding to different effects**
**traditional approaches such as principal component analysis (PCA) have not worked  **
**separation difficult as**** El Chich****ón and Pinatubo ****volcano eruptions coincided**** ****with El Ni****ño events**
**our approach is to use independent component analysis (ICA)**

****** ****Dimension reduction supporting scientific discovery  **

## The raw data is as monthly temperatures on a 144x73 spatial grid on 17 vertical levels

**January 1979 raw temperatures (Kelvin) on the 144x73 latitude by longitude grid**
**at 1000hPa pressure level.  Data from NCEP.**

## Initially, we applied ICA to global monthly mean anomaly temperatures

**Time series of global monthly mean anomalies, Jan 1979 - Dec 2000**

**17 vertical levels**
** ****level1: 1000hPa,**
** ****lowest altitude**
** ****level17: 10hPa,**
** ****highest altitude **

## Next, we ran experiments with simulated data to understand the behavior of ICA

**(i) Two original sources**

**(ii) Two mixed signals from the original**

**ICA estimates correctly the shapes of the two independent components (ICs).  **
**With additional processing, we can also estimate the relative contributions of the two ICs in the two mixed signals. **

**(iii) Sources (ICs) recovered from (ii)**
**      **

**ICA**

**mix**

## Original decomposition of the two mixed signals (-): sine (--) and volcano (-.) 

**(i) Signal 1**

**(ii) Signal 2**

## 

After proper post-processing, ICA estimates remarkably well the underlying independent components and their appropriate contributions in the mixed signals   

**After proper post-processing, ICA estimates remarkably well the underlying independent components and their appropriate contributions in the mixed signals   **

**(i) Signal 1**

**(ii) Signal 2**

**ICA decomposition of the two mixed signals (-): sine (--) and volcano (-.) **

## ICA can also separate “noise” used as an extra component in the mixing 

**3 original**
**sources**

**3 mixed **
**signals**

**3 estimated**
**ICs**

**mix**

**ICA**

## Original decomposition of 3 mixed signals (-): El Niño (--), volcano (-.), and noise (..)

**Cooling in global series at the arrow is in fact a combination of an ENSO warming and a volcano cooling.   Without the volcano eruption, the El Nino warming would dominate, resulting in warmer global temperatures.**

**(i) Signal 1**

**(ii) Signal 2**

**(iii) Signal 3**

## ICA decomposition of 3 mixed signals (-): El Niño (--), volcano (-.), and noise (..)

** ****Although not perfect in terms of the exact amplitudes, ICA clearly separates the cooling effect of the volcano from the warming effect of El Nino.  **

**(i) Signal 1**

**(ii) Signal 2**

**(iii) Signal 3**

## Our future plans include work with HEP data and collaborators at ORNL and LBNL

**Complete the work on the climate problem**
**our results with artificial data are encouraging**
**identify appropriate ICA model for climate data**
**Make the ICA software accessible to SciDAC scientists**
**Try ICA and other dimension reduction techniques in the context of the STAR high-energy-physics data**
**reduce number of features**
**investigate sampling to reduce computation**
**collaborate with LBNL (data, searching)**
**Investigate incremental PCA**
**monitor climate simulations using indices based on the principal components**
**collaborate with ORNL (data, clustering)**