Here’s a very good introduction to HMM:

Introduction

Hidden Markov models are widely used in science, engineering and many other areas (speech recognition, optical character recognition, machine translation, bioinformatics, computer vision, finance and economics, and in social science). 

Definition: The Hidden Markov Model (HMM) is a variant of a finite state machine having a set of hidden states, Q, an output alphabet (observations), O, transition probabilities, A, output (emission) probabilities, B, and initial state probabilities, Π. The current state is not observable. Instead, each state produces an output with a certain probability (B). Usually the states, Q, and outputs, O, are understood, so an HMM is said to be a triple, ( A, B, Π ).

Formal Definition:

Hidden states Q = { q_i }, i = 1, . . . , N .

Transition probabilities A = {a_ij = P(q_j at t +1 | q_i at t)}, where P(a | b) is the conditional probability of a given b, t = 1, . . . , T is time, and q_i in Q. Informally, A is the probability that the next state is q_j given that the current state is q_i.

 Observations (symbols) O = { o_k }, k = 1, . . . , M .

Emission probabilities B = { b_ik = b_i(o_k) = P(o_k | q_i) }, where o_k in O. Informally, B is the probability that the output is o_k given that the current state is q_i.

Initial state probabilities Π = {p_i = P(q_i at t = 1)}.

Canonical problems

There are 3 canonical problems to solve with HMMs:

1. Given the model parameters, compute the probability of a particular output sequence. This problem is solved by the Forward and Backward algorithms (described below).
2. Given the model parameters, find the most likely sequence of (hidden) states which could have generated a given output sequence. Solved by the Viterbi algorithm and Posterior decoding.
3. Given an output sequence, find the most likely set of state transition and output probabilities. Solved by the Baum-Welch algorithm

Forward Algorithm

Let α_t(i) be the probability of the partial observation sequence O_t = {o(1), o(2), … , o(t)} to be produced by all possible state sequences that end at the i-th state. 

α_t(i) = P(o(1), o(2), … , o(t) | q(t) = q_i ).

Then the unconditional probability of the partial observation sequence is the sum of α_t(i) over all N states.   

The Forward Algorithm is a recursive algorithm for calculating α_t(i) for the observation sequence of increasing length t . First, the probabilities
for the single-symbol sequence are calculated as a product of initial i-th state probability and emission probability of the given symbol o(1) in the i-th state. Then the recursive formula is applied. Assume we have calculated α_t(i) for some t. To calculate α_t+1(j), we multiply every α_t(i) by the corresponding transition probability from the i-th state to the j-th state, sum the products over all states, and then multiply the result by the emission probability of the symbol o(t+1). Iterating the process, we can eventually calculate α_T(i), and then summing them over all states, we can obtain the required probability.

Formal Definition

Initialization:

  α₁(i) = p_i b_i(o(1)) , i =1, … , N

Recursion:

here  i =1, … , N , t =1, … , T - 1

Termination:

Backward Algorithm

In a similar manner, we can introduce a symmetrical backward variable β_t(i) as the conditional probability of the partial observation sequence from o(t+1) to the end to be produced by all state sequences that start at i-th state (3.13). 

β_t(i) = P(o(t+1), o(t+2), … , o(T) | q(t) = q_i ).

The Backward Algorithm calculates recursively backward variables going backward along the observation sequence. The Forward Algorithm is typically used for calculating the probability of an observation sequence to be emitted by an HMM, but, as we shall see later, both procedures are heavily used for finding the optimal state sequence and estimating the HMM parameters.

Formal Definition

Initialization:

  β_T (i) = 1 , i =1, … , N

According to the above definition, β_T(i) does not exist. This is a formal extension of the below recursion to t = T.

Recursion:

here  i =1, … , N , t = T - 1,  T - 2 , . . . , 1

Termination:

Obviously both Forward and Backward algorithms must give the same results for total probabilities P(O) = P(o(1), o(2), … , o(T) ).

Posterior decoding

There are several possible criteria for finding the most likely sequence of hidden states. One is to choose states that are individually most likely at the time when a symbol is emitted. This approach is called posterior decoding. 

Let λ _t(i) be the probability of the model to emit the symbol o(t) being in the i-th state for the given observation sequence O. 

λ _t(i) = P( q(t) = q_i | O ).

It is easy to derive that

λ _t(i) = α_t(i) β_t(i) / P( O ) , i =1, … , N , t =1, … , T

Then at each time we can select the state q(t) that maximizes λ _t(i). 

q(t) = arg max {λ _t(i)}

Posterior decoding works fine in the case when HMM is ergodic, i.e. there is transition from any state to any other state. If applied to an HMM of another architecture, this approach could give a sequence that may not be a legitimate path because some transitions are not permitted. 

Viterbi algorithm

The Viterbi algorithm chooses the best state sequence that maximizes the likelihood of the state sequence for the given observation sequence.

Let δ _t(i) be the maximal probability of state sequences of the length t that end in state i and produce the t first observations for the given model.

δ _t(i) = max{P(q(1), q(2), …, q(t-1) ; o(1), o(2), … , o(t) | q(t) = q_i ).}

 The Viterbi algorithm is a dynamic programming algorithm that uses the same schema as the Forward algorithm except for two differences:

1. It uses maximization in place of summation at the recursion and termination steps.
2. It keeps track of the arguments that maximize δ _t(i) for each t and i, storing them in the N by T matrix ψ. This matrix is used to retrieve the optimal state sequence at the backtracking step.

Initialization:

According to the above definition, β_T(i) does not exist. This is a formal extension of the below recursion to .

Recursion:

Termination:

Path (state sequence) backtracking:

 q^*_t = ψ_t+1( q^*_t+1) , t = T - 1,  T - 2 , . . . , 1

References

1. Hidden Markov model, http://www.nist.gov/dads/HTML/hiddenMarkovModel.html 
2. Hidden Markov model, http://en.wikipedia.org/wiki/Hidden_Markov_model
3. Lawrence R. Rabiner, A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition. Proceedings of the IEEE, 77 (2), p. 257–286, February 1989.
4. V. Petrushin. Hidden Markov Models: Fundamentals and Applications. Part 2: Discrete and Continuous Hidden Markov Models, Online Symposium for Electronics Engineers. 2000 

©Nikolai V. Shokhirev, 2004-2006


/**
* Tarik Guelzim
* This is an indexer/search engine for pdf files
* Version 0.1
*
* OCR funcitonality is still in pre-alpha
*/

package core;

import com.asprise.util.ocr.OCR;
import com.asprise.util.pdf.PDFReader;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.HashMap;
import java.util.logging.Level;
import java.util.logging.Logger;
import org.apache.lucene.analysis.standard.StandardAnalyzer;
import org.apache.lucene.index.IndexWriter;
import org.apache.lucene.document.Document;
import org.apache.lucene.queryParser.ParseException;
import org.apache.lucene.queryParser.QueryParser;
import org.apache.lucene.search.Hits;
import org.apache.lucene.search.IndexSearcher;
import org.apache.lucene.search.Query;
import org.apache.lucene.store.Directory;
import org.apache.lucene.store.FSDirectory;
import org.pdfbox.searchengine.lucene.LucenePDFDocument;

public class Main {

/**
* @param args pdf file o be added
*/
public static void main(String[] args) {
HashMap params = null;
// parse args
params = parseArgs(args);
// dispatch commands
if (((String) params.get(”cmd”)).equals(”index”)) {
// build index
buildIndex((String) params.get(”idxFile”),
(String) params.get(”pdfFile”));

} else if (((String) params.get(”cmd”)).equals(”query”)) {

displayIndex(searchIndex((String) params.get(”idxFile”),
(String) params.get(”qString”),
(String) params.get(”dField”)));
} else if (((String) params.get(”cmd”)).equals(”optimize”)) {
optimizeIndex(((String) params.get(”idxFile”)));
} else if (((String) params.get(”cmd”)).equals(”ocr”)) {
ocrPdf((String) params.get(”pdfFile”));
} else {
System.err.println(”Usage: pdfagent {query | index} index_file pdf_file_name”);
}
}

/**
* OCR text from images
* @param fname pdf file
*/
private static void ocrPdf(String fname) {
try {
OCR ocr = new OCR();
PDFReader reader = new PDFReader(new File(fname));
reader.open();
int pages = reader.getNumberOfPages();
for (int i = 0; i < pages; i++) {
BufferedImage image = reader.getPageAsImage(i);
System.out.println(ocr.recognizeEverything(image));
}
reader.close();
} catch (IOException ex) {
Logger.getLogger(Main.class.getName()).log(Level.SEVERE, null, ex);
}
}

/**
* optimize index
* @param idxFile index path
*/
private static void optimizeIndex(String idxFile) {
try {
IndexWriter iw = new IndexWriter(idxFile, new StandardAnalyzer(), isIndexExist(idxFile));
iw.optimize();
} catch (IOException ex) {
Logger.getLogger(Main.class.getName()).log(Level.SEVERE, null, ex);
}
}

/**
* build pd index
* @param idxFile index file path
* @param pdfFile pdf file
*/
private static void buildIndex(String idxFile, String pdfFile) {

IndexWriter iw = null;
LucenePDFDocument pdfDoc = null;
Document luceneDoc = null;

try {
// lucene index

iw = new IndexWriter(idxFile, new StandardAnalyzer(),
isIndexExist(idxFile));

pdfDoc = new LucenePDFDocument();
luceneDoc = LucenePDFDocument.getDocument(new FileInputStream(pdfFile));

// luceneDoc = pdfDoc.convertDocument(new File(pdfFile));
addDoc(iw, luceneDoc);

iw.optimize();
iw.close();

} catch (IOException ex) {
Logger.getLogger(Main.class.getName()).log(Level.SEVERE, null, ex);
}
}

private static void displayIndex(Hits hits) {
try {
if (hits.length() == 0) {
System.out.println(”No results found.”);
} else {
for (int i = 0; i < hits.length(); i++) {
System.out.println(”————————-”);
System.out.println(”URL: ” + hits.doc(i).get(”url”));
System.out.println(”Modified: ” + hits.doc(i).get(”modified”));
System.out.println(”————————-”);

System.out.println(hits.doc(i).get(”contents”));
}
}
} catch (IOException ex) {
Logger.getLogger(Main.class.getName()).log(Level.SEVERE, null, ex);
}
}

/**
* search the index for a stri  ng
* @param indexFile index file path
* @param qString string query
* @param idxField the field to search
* @return hits for the query
*/
private static Hits searchIndex(String indexFile, String qString, String idxField) {
Hits hits = null;
IndexSearcher searcher = null;
Directory fsDir = null;
Query query = null;
QueryParser qParser = null;

try {
//query index
System.out.println(”Searching for ” + qString + ” in ” + indexFile + ” — field: ” + idxField);

// create index searcher
fsDir = FSDirectory.getDirectory(indexFile, false);
searcher = new IndexSearcher(fsDir);
// parse query
qParser = new QueryParser(idxField, new StandardAnalyzer());
query = qParser.parse(qString);
//query = QueryParser.parse(qString, idxField, new StandardAnalyzer());
System.out.println(query.toString());
// search
hits = searcher.search(query);

} catch (IOException ex) {
System.err.println(”Index file” + indexFile + ” doesn’t exist”);
Logger.getLogger(Main.class.getName()).log(Level.SEVERE, null, ex);
System.exit(1);
} catch (ParseException ex) {
System.err.println(”Error while parsing the index.”);
Logger.getLogger(Main.class.getName()).log(Level.SEVERE, null, ex);
} finally {
return hits;
}

}

/**
* Singelton for indx file
* @param idxFile file to check
* @return exist or not
*/
private static boolean isIndexExist(String idxFile) {
File file;
boolean create = true;

if (((file = new File(idxFile)).exists() && file.isDirectory())) {
create = false;
}

return create;
}

/**
* parse cmd line args
* @param args params
* @return array of params
*/
private static HashMap parseArgs(String[] args) {
HashMap cmdMap = new HashMap();
switch (args.length) {
case 2:
cmdMap.put(”cmd”, (String) args[0]);
cmdMap.put(”idxFile”, (String) args[1]);
cmdMap.put(”pdfFile”, (String) args[1]);
break;
case 3:
cmdMap.put(”cmd”, (String) args[0]);
cmdMap.put(”idxFile”, (String) args[1]);
cmdMap.put(”pdfFile”, (String) args[2]);
break;
case 4:
cmdMap.put(”cmd”, (String) args[0]);
cmdMap.put(”idxFile”, (String) args[1]);
cmdMap.put(”qString”, (String) args[2]);
cmdMap.put(”dField”, (String) args[3]);
break;
default:
System.err.println(”Usage: pdfagent {query | index} index_file pdf_file_name”);
System.exit(1);
break;
}
return cmdMap;
}

/**
* Add document to the index
* @param iw
* @param doc
*/
private static void addDoc(IndexWriter iw, Document doc) {
try {
iw.addDocument(doc);

} catch (IOException ex) {
Logger.getLogger(Main.class.getName()).log(Level.SEVERE, null, ex);
}
}
}

1- download ndiswrapper src files from the sourceforge site

2- logging as root using

• # su -

• #make && make install

3- after the sources compile and the software installs you need to get install the windows drivers for the mini pci 1350

• #cd /to/wlan/card/windows/drivers
• #ndiswrapper -i bcmwl5.inf
• #ndiswrapper -l ( you should see hardware present)
  
• #ndiswrapper -m

4- note that if you are using kernel > 2.6.15, it is precompiled with the bcm43xx drivers so you need to prevent loading it during boot up.

• #echo “blacklist bcm43xx” >> /etc/modprobe.d/blacklist

5- unload the bcm43xx driver using

• #rmmod bcm43x

6- load the ndiswrapper module

• #modprobe ndiswrapper

7- scan for networks and connect

• #iwlist wlan0 scan
• #ifup wlan0

and voila!!

This situation happens to most of Careless! Linux users, but thanks to the GRUB flags, one might

able to overcome this situation with ease.

my /boot/grub/grub.conf looks like this

on your machine, you can do

1. $more /boot/grub/grub.conf to view yours

default 0

timeout 30

splashimage=(hd0,0)/grub/splash.xpm.gz

title=Gentoo Linux

root (hd0,0)

kernel /kernel-genkernel-x86-2.6.17-gentoo-r7 root=/dev/ram0 init=/linuxrc ramdisk=8192 real_root=/dev/sda3 doscsi

initrd /initramfs-genkernel-x86-2.6.17-gentoo-r7

2. Now reboot the machine, and at the grub menu press ‘e’ then ‘e’

now what do you wanna do is boot the machine to single mode.

3. Go down to the line kernel /kernel… and add ‘1′ to its end. you’ll wind up with:

kernel /kernel-genkernel-x86-2.6.17-gentoo-r7 root=/dev/ram0 init=/linuxrc ramdisk=8192 real_root=/dev/sda3 doscsi 1

4. Now press ENTER and ‘b’ et voila.

PXE Server Setup

Install the tftp server and pxe server

yum install tftp-server pxe

Get the pxelinux boot loader. The pxelinux boot loader is bundled in the syslinux tar file. Retrieve this from http://www.kernel.org/pub/linux/utils/boot/syslinux/syslinux-2.00.tar.gz. (Or latest version in that directory.)

Copy the boot loader into place. After expanding the compressed tar archive, copy the file ‘pxelinux.0′ into your tftpboot area. As in the following example:

cp syslinux-2.00/pxelinux.0 /tftpboot/X86PC/UNDI/linux-install/

Create the pxelinux configuration directory. The boot loader expects a directory to be present in the same directory it was loaded from. It expects this directory to be named pxelinux.cfg, and looks for a file in that directory based on the IP address of the machine. If it does not find a file whose name is based on the IP address, it will look for a file named default.

Create configuration files. Here is an example pxelinux configuration file named default.

serial 0 9600 0xab3
default localboot
timeout 100
prompt 1
display display.msg

label localboot
        LOCALBOOT 0

label 7.3
        kernel vmlinuz-7.3
        append initrd=initrd-7.3.img lang= lowres devfs=nomount ramdisk_size=8192 console=ttyS0,9600

Create the display message file. In the above pxelinux configuration file, there was a display.msg reference with the display keyword. Below is an example file:

PXE Booting to install Red Hat Linux.

Current images are:
Localboot -- Exit PXE, boot locally

7.3 --- For Red Hat Linux 7.3 interactive installation

Make available the kernel and initrd. The kernel and initrd images are available from the images/pxeboot directory of the install image. (The install image is either on the CD or the base of the individual version’s filesystem tree on an ftp/http/file server.)

Rename the files to suit the boot loader configuration. The filenames of the kernel and the initial RAM disk must match the configuration entries in the pxelinux configuration file. To suit the running example:

mv initrd-everything.img initrd-7.3.img
mv vmlinuz ../vmlinuz-7.3

Configure the PXE server configuration file. With the Red Hat Linux RPM, the PXE server is configured by default to work with the NBP (Network Boot Prompt), which does not work with this example. Additionally, this example opts to have workstations boot off the network by default, load the pxelinux, and then time out to local boot from the pxelinux boot loader.

The two sections that need to be changed look like:

[X86PC/UNDI/linux-install/ImageFile_Name]
0
2
linux

and

[X86PC/UNDI/MENU]
0,Local Boot
13,Remote Install Linux
# 14,Remote Boot Linux

Those sections should look like:

[X86PC/UNDI/linux-install/ImageFile_Name]
0
0
pxelinux

and

[X86PC/UNDI/MENU]
#0,Local Boot
13,Remote Install Linux
# 14,Remote Boot Linux

Confirm that the appropriate services are accessible. The main services that must be started and accessible for the PXE booting process are:

• tftpdxinetd (for tftpd)pxe

The way to check is to use           chkconfig.

[root linux-install]# /sbin/chkconfig --list tftp
tftp            off
[root linux-install]# /sbin/chkconfig tftp on
[root linux-install]# /sbin/chkconfig --list xinetd
xinetd          0:off   1:off   2:off   3:on    4:on    5:on    6:off
[root linux-install]# /sbin/chkconfig --list pxe
pxe             0:off   1:off   2:off   3:off   4:off   5:off   6:off
[root linux-install]# /sbin/chkconfig pxe on

In the above example, tftp was not configured to start by           default, nor was pxe. However, xinetd was.  To configure           tftp and pxe to start automatically,  chkconfig           <service> on was run. Since tftp is a part of           xinetd, as long as xinetd is running, nothing past the           chkconfig tftp on needs to be done to use           the tftp service. However, pxe must be started at this point           to begin using it prior to a reboot. The below example           illustrates confirming that xinetd is running as well as           starting pxe.

[root etc]# /sbin/service xinetd status
xinetd (pid 821) is running...
[root etc]# /sbin/service pxe status
pxe is stopped
[root etc]# /sbin/service pxe start
Starting pxe:                                              [  OK  ]

Add the PXE entries to /etc/services. While not required, it may be helpful to add the PXE service entries to the /etc/services file.

pxe 67/udp
pxe 4011/udp

PS. This article is an ongoing progress!

  #yum install libXp

  assuming you're using bash
  $ echo "export AWT_TOOLKIT='MToolkit'" >> ~/.bashrc
  $ echo "export AWT_TOOLKIT='MToolkit'" >> ~/.bash_profile

  $source ~/.bashrc
  $~/.bash_profile

and this should work.