Monday, September 7, 2009

Singular Value Decomposition (SVD) and Latent Semantic Indexing (LSI) in C#

LSI is used in a variety of information retrieval and text processing applications. It uses uses a mathematical technique called Singular Value Decomposition (SVD) to identify patterns in the relationships between the terms and concepts contained in an unstructured collection of text.

Tutorials for LSI and SVD can be found online. I will use Bluebit .Net Matrix Library to calculate SVD and other matrix and vector operations needed in LSI.

I implemented LSI in C# using the example described in Mi Ishlita. The program will display the name of each document and its similarity value. You can use any sorting algorithm to sort the results by the similarity values. Like in the previous example, the program assumes that there is a string array "docs" which contains the query's (at zero index) and the documents' text.

To use the code (below), you need to download and install .NET Matrix Library (NML™) 4.3 and then reference .NET Matrix Library from within your project using the following instructions:
  1. Open the Visual Studio a and open a new Visual Basic or C# project.
  2. Select Project | Add Reference...
  3. Select the .NET tab and find Bluebit .NET Matrix Library listed, double click on it and then press OK.
Here is the code:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using Bluebit.MatrixLibrary;
using System.Collections;
using System.Text.RegularExpressions;

namespace LSI
class Program
static double[,] A; //term-document Array
static double[] q; //term-query Array
static List wordlist = new List(); //List of terms found in documents
static SortedDictionary sortedList = new SortedDictionary(); //Documents ranked by VSM with angle value
static string[] docs ={"gold silver truck", //Query
"shipment of gold damaged in a fire",//Doc 1
"delivery of silver arrived in a silver truck", //Doc 2
"shipment of gold arrived in a truck"}; //Doc 3

static void Main(string[] args)

foreach (KeyValuePair kvp in sortedList)

Console.WriteLine(kvp.Value + " " + kvp.Key);

public static void createWordList()
foreach (string doc in docs)
wordlist = getWordList(wordlist, doc);
wordlist.Sort(); //sort the wordlist alphabetically

public static List getWordList(List wordlist, string query)
Regex exp = new Regex("\\w+", RegexOptions.IgnoreCase);
MatchCollection MCollection = exp.Matches(query);

foreach (Match match in MCollection)
if (!wordlist.Contains(match.Value))

return wordlist;

public static void createVector()
double[] queryvector;
q = new double[wordlist.Count];
A = new double[wordlist.Count, docs.Length-1];
for (int j = 0; j < docs.Length; j++)
queryvector = new double[wordlist.Count];

for (int i = 0; i < wordlist.Count; i++)
//calculate Term Frequency
double tf = getTF(docs[j], wordlist[i]);

if (j == 0) //if Query term then add it to query array
q[i] = tf;
else //if document term then add it to document array
A[i, j-1] = tf;



private static void LatentSemanticIndexing()
//Singular Value Decomposition
Matrix docMatrix = new Matrix(A);
SVD svd = new SVD(docMatrix);

//A = U S VT
Matrix U = svd.U;
Matrix S = svd.S;
Matrix V = svd.V;
Matrix VT = svd.VH;

//Dimensionality Reduction: Computing Uk, Sk, Vk and VkT
Matrix Uk = new Matrix(U.ToArray(), U.Rows, U.Cols - 1);
Matrix Sk = new Matrix(S.ToArray(), S.Rows - 1, S.Cols - 1);
Matrix Vk = new Matrix(V.ToArray(), V.Rows, V.Cols - 1);
Matrix VkT = Vk.Transpose();

//q = qT Uk Sk-1
Matrix queryMatrix = new Matrix(q,q.Length,1);
queryMatrix = queryMatrix.Transpose() * Uk * Sk.Inverse();

//sim(q, d) = sim(qT Uk Sk-1, dT Uk Sk-1) using cosine similarities
for (int i = 0; i < V.Rows; i++)
Vector docVector = Vk.RowVector(i);
Vector queryVector = queryMatrix.RowVector(0);
double sim = Vector.DotProduct(docVector, queryVector) / (docVector.Length * queryVector.Length);

Console.WriteLine("Doc " + (i + 1).ToString() + " :" + sim);

private static double getTF(string document, string term)
string[] queryTerms = Regex.Split(document, "\\s");
double count = 0;

foreach (string t in queryTerms)
if (t == term)
return count;



After you have sorted the results in descending order using the similarity values, your results will be as follows: