Comparing Data Set With a Predefined Data Set Using Matrix Operations In Matlab

This post is related to Matlab. In Matlab it is always recommended to use matrix operations instead of using loops such as for or while.

The following algorithm will compare a given set of data from a predefined data set with only matrix operations without using loops

The algorithm will be explained using an example.

If the predefined dataset is given as $\mathcal{D}$ and the dataset given is $\mathcal{E}$,

$$\mathcal{D}=\begin{bmatrix} 0 &0& 0\\ 0& 0 &1\\ 0& 1 &0\\ 0& 1 &1\\ 1& 0& 0\\ 1& 0& 1\\ 1& 1& 0\\ 1& 1& 1 \\
\end{bmatrix} \qquad \mathcal{E}=\begin{bmatrix}
   1 &0 &1 \\ 1 &1 &1\\ 1 &1 &1\\ 0 &0 &1\\ 0 &1 &0
\end{bmatrix}$$

Define
 $$ \mathcal{S}=\mathcal{E}\cdot\mathcal{D}' $$

then

$$ \mathcal{S}=
\begin{bmatrix}
0& 1& 0& 1& 1& 2& 1& 2\\
0& 1& 1& 2& 1& 2& 2& 3\\
0& 1& 1& 2& 1& 2& 2& 3\\
0& 1& 0& 1& 0& 1& 0& 1\\
0& 0& 1& 1& 0& 0& 1& 1
 \end{bmatrix}$$

Get the sum of the each row of $\mathcal{D}$ and $\mathcal{E}$

$$\mathcal{D}_{r\_sum}= \begin{bmatrix}
 0\\
 1\\
 1\\
 2\\
 1\\
 2\\
 2\\
 3\\
\end{bmatrix}
\qquad
\mathcal{E}_{r\_sum}=\begin{bmatrix}
2\\
3\\
3\\
1\\
1\\
\end{bmatrix}$$

Now define a new matrix with the same dimension as of $\mathcal{S}$ for each $\mathcal{E}_{r\_sum}$ and $\mathcal{D}_{r\_sum}$ as $\mathcal{E}_{sum\_mat}$ and $\mathcal{D}_{sum\_mat}$

$$\mathcal{E}_{sum\_mat}=[\mathcal{E}_{r\_sum}  \mathcal{E}_{r\_sum}  \cdots  \mathcal{E}_{r\_sum}]$$
$$\mathcal{D}_{sum\_mat}=\begin{bmatrix}
\mathcal{D}_{r\_sum}' \\\mathcal{D}_{r\_sum}'\\ \vdots \\ \mathcal{D}_{r\_sum}'
\end{bmatrix}$$

For this example results will be,

$$\mathcal{E}_{sum\_mat}=\begin{bmatrix}
2& 2& 2& 2& 2& 2& 2& 2\\
3& 3& 3& 3& 3& 3& 3& 3\\
3& 3& 3& 3& 3& 3& 3& 3\\
1& 1& 1& 1& 1& 1& 1& 1\\
1& 1& 1& 1& 1& 1& 1& 1\\
\end{bmatrix}$$

$$\mathcal{D}_{sum\_mat}=\begin{bmatrix}
0& 1& 1& 2& 1& 2& 2& 3\\
0& 1& 1& 2& 1& 2& 2& 3\\
0& 1& 1& 2& 1& 2& 2& 3\\
0& 1& 1& 2& 1& 2& 2& 3\\
0& 1& 1& 2& 1& 2& 2& 3\\
\end{bmatrix}$$

Now compare each $\mathcal{E}_{sum\_mat}$ and $\mathcal{D}_{sum\_mat}$ with $\mathcal{S}$ separately and if each of $\mathcal{S}$ is equal to the elements of the two matrices the symbol 1 is recorded. The result of the example is given below

$$\mathcal{E}_{com}=\begin{bmatrix}
  0&     0&     0&     0&     0&     1&     0&     1\\
    0 &    0 &    0 &    0 &    0 &    0 &    0 &    1\\
     0  &   0  &   0  &   0  &   0  &   0  &   0  &   1\\
     0   &  1   &  0   &  1   &  0   &  1   &  0   &  1\\
     0    & 0    & 1    & 1    & 0    & 0    & 1    & 1\\
 \end{bmatrix}$$

$$\mathcal{D}_{comp}=\begin{bmatrix}
     1&     1&     0    & 0&     1    & 1&     0    & 0\\
     1 &    1 &    1   &  1 &    1   &  1 &    1   &  1\\
     1  &   1  &   1  &   1  &   1  &   1  &   1  &   1\\
     1   &  1   &  0 &    0   &  0 &    0   &  0 &    0\\
     1    & 0    & 1&     0    & 0&     0    & 0&     0\\
\end{bmatrix}$$

From these two results at each element mark as 1 if and only if the both elements of each matrix is 1. We will name it as $\mathcal{C}$

$$\mathcal{C}=\begin{bmatrix}
     0&     0    & 0&     0    & 0&     1    & 0&     0\\
     0 &    0   &  0 &    0   &  0 &    0   &  0 &    1\\
     0  &   0  &   0  &   0  &   0  &   0  &   0  &   1\\
     0   &  1 &    0   &  0 &    0   &  0 &    0   &  0\\
     0    & 0&     1    & 0&     0    & 0&     0    & 0\\
\end{bmatrix}$$

So the each column of $\mathcal{C}$ will denote the element of the predefined data set - $\mathcal{D}$ and the rows will represent each data point of $\mathcal{E}$. Element $c_{ij}$ of $\mathcal{C}$ will be 1 if $i^{th}$ data point of $\mathcal{E}$ is same as the $j^{th}$ data point of $\mathcal{D}$

The Matlab code for the above procedure is given below.