How do I find the mode of an array and verify it using the frequency?

A very basic question, but I am just getting back into it and I'm struggling to find the right answer on the forums (or I very bad at using Google?).

I have an array which is 100x50 and want to find the mode of each row. When I run the below function, it provides a 98% correct solution. Two of the rows have a mix of values and it is not as easy to tell the mode, whereas the other 98 rows have a distint value. Is it possible to set a threshold so that out of the row, if the value is only less than 30% of the total value then ignore it?

So if row 99 has a value of 1 as the mode, but 1 only occurs 20% (10/50) of the time in the total row then ignore it.

mode(a(:,:)); 

Answer 1

[Walter Roberson]

By definition, mode() returns a value such that no other value is more frequent (but other values might be equally frequent.)

If a potential candidate for the mode is not one of the values that is the most frequent, then that candidate will not be selected.

Now consider the possibilities: if "1" is the selected mode() for a row, then every other value in the row is either less frequent or the same frequency as "1". If "1" occurs only 20% of the time and if no other value occurs with equal frequency... then every other value must also be less than 20% of the values. If "1" occurs only 20% of the time and some other value occurs with the same frequency, then those other values must also occur less than 20% of the values.

Thus, your condition of ignoring the candidate mode if it occurs less than some percentage of the time, is equivalent to saying that for that particular row, the returned mode value must be either empty or NaN, since every other value on the row must occur with frequency no greater than the given percentage, However, mode() of an array row-wise cannot return empty in any row slot, so mode() of the array would have to return NaN for that row.

Is that what you want? That you get back NaN for rows with low frequency ??

[Walter Roberson]

If so, then use the syntax

[M,F] = mode(___)

The F array will return the frequency count for each selected M.

cutoff = 20/100;
[M, F] = mode(A, 2);
M(F < size(A,2)*cutoff) = NaN;

Answer 2

[Umar]

Hi @ Caleb Crawdad,

I reviewed your question regarding row-wise mode computation and the 30% dominance threshold. As you noticed, MATLAB’s built-in `mode` function returns the most frequent value but does not consider whether that value is statistically dominant in the row.

Inspired by Walter Roberson’s vectorized approach on MATLAB Answers, I implemented a _row-wise solution_ that is fully transparent and easy to follow.

*This script:*

* Computes the **row-wise mode** explicitly for each row.

* Calculates the **relative frequency** of the mode.

* Applies a **30% threshold**, marking rows with ambiguous modes as `NaN`.

* Handles **tie-breaks deterministically** (chooses the smallest value).

* Provides full transparency for analysis, showing both the candidate mode and its relative frequency.

*Here’s the MATLAB script:*

clear all; clc; close all;
 A = randi([1 5],100,50); % Example 100x50 matrix
 threshold = 0.3; % minimum fraction for mode
 [rowCount, colCount] = size(A);
 RowIndex = (1:rowCount)'; 
 CandidateMode = NaN(rowCount,1); 
 RelFrequency = NaN(rowCount,1); 
 ModeWithThreshold = NaN(rowCount,1);
 for i = 1:rowCount
 row = A(i,:);
 [uniqueVals, ~, idx] = unique(row); 
 counts = accumarray(idx,1); 
 maxCount = max(counts); 
 posTies = find(counts == maxCount); 
 modeVal = min(uniqueVals(posTies)); 
 relFreq = maxCount / colCount; 
 CandidateMode(i) = modeVal; 
 RelFrequency(i) = relFreq;
 if relFreq >= threshold
 ModeWithThreshold(i) = modeVal;
 else
 ModeWithThreshold(i) = NaN; 
 end
 end
 ResultTable = table(RowIndex, CandidateMode, RelFrequency, ModeWithThreshold, ...
 'VariableNames', {'RowIndex','CandidateMode','RelFrequency','ModeWithThreshold'});
 disp(ResultTable);

    RowIndex    CandidateMode    RelFrequency    ModeWithThreshold
    ________    _____________    ____________    _________________

        1             2               0.3                 2       
        2             5               0.3                 5       
        3             4              0.32                 4       
        4             2              0.22               NaN       
        5             3              0.24               NaN       
        6             5               0.3                 5       
        7             3              0.24               NaN       
        8             3               0.3                 3       
        9             1               0.3                 1       
       10             4              0.24               NaN       
       11             4              0.28               NaN       
       12             5              0.24               NaN       
       13             4              0.32                 4       
       14             3              0.24               NaN       
       15             3              0.34                 3       
       16             2               0.3                 2       
       17             1              0.26               NaN       
       18             1              0.28               NaN       
       19             1              0.26               NaN       
       20             1              0.24               NaN       
       21             3              0.26               NaN       
       22             5              0.24               NaN       
       23             4              0.28               NaN       
       24             4              0.24               NaN       
       25             5              0.26               NaN       
       26             5              0.26               NaN       
       27             5               0.3                 5       
       28             4              0.34                 4       
       29             5              0.36                 5       
       30             4              0.24               NaN       
       31             2              0.26               NaN       
       32             5              0.28               NaN       
       33             3              0.26               NaN       
       34             3               0.3                 3       
       35             4              0.28               NaN       
       36             3              0.28               NaN       
       37             1              0.24               NaN       
       38             4              0.24               NaN       
       39             2               0.3                 2       
       40             2               0.3                 2       
       41             3              0.34                 3       
       42             1              0.26               NaN       
       43             4              0.24               NaN       
       44             3              0.26               NaN       
       45             5               0.3                 5       
       46             2              0.26               NaN       
       47             2               0.3                 2       
       48             4              0.26               NaN       
       49             3              0.24               NaN       
       50             5              0.28               NaN       
       51             5              0.34                 5       
       52             3              0.26               NaN       
       53             5              0.26               NaN       
       54             3              0.26               NaN       
       55             2               0.3                 2       
       56             4              0.32                 4       
       57             3              0.26               NaN       
       58             3               0.3                 3       
       59             5              0.24               NaN       
       60             3              0.26               NaN       
       61             2               0.3                 2       
       62             2              0.26               NaN       
       63             3              0.24               NaN       
       64             3               0.3                 3       
       65             4               0.3                 4       
       66             2               0.3                 2       
       67             2              0.26               NaN       
       68             1              0.28               NaN       
       69             5              0.28               NaN       
       70             5              0.24               NaN       
       71             1              0.24               NaN       
       72             3              0.24               NaN       
       73             5              0.26               NaN       
       74             4              0.28               NaN       
       75             5              0.28               NaN       
       76             3              0.24               NaN       
       77             3               0.3                 3       
       78             2              0.32                 2       
       79             2              0.24               NaN       
       80             4              0.32                 4       
       81             2              0.22               NaN       
       82             3               0.3                 3       
       83             1              0.28               NaN       
       84             1              0.34                 1       
       85             5              0.26               NaN       
       86             5              0.24               NaN       
       87             2              0.24               NaN       
       88             2              0.28               NaN       
       89             5              0.28               NaN       
       90             3              0.28               NaN       
       91             2              0.24               NaN       
       92             1              0.22               NaN       
       93             3               0.3                 3       
       94             1              0.24               NaN       
       95             1              0.28               NaN       
       96             5              0.32                 5       
       97             4              0.28               NaN       
       98             1              0.32                 1       
       99             4              0.26               NaN       
      100             1              0.24               NaN       

*Please see attached*

<</matlabcentral/answers/uploaded_files/1839255/IMG_4536.jpeg>>

*How this addresses your concerns:*

1. Row-wise mode:Computed explicitly per row.

2. Threshold enforcement:Modes below 30% are ignored (`NaN`).

3. Ambiguous rows:Easily identifiable with `NaN`.

4. Mixed-value rows:Tie-break handled deterministically.

5. Transparency: `CandidateMode` and `RelFrequency` show exactly how dominant the mode is.

This solution ensures accurate mode detection while clearly filtering non-dominant rows.

[Steven Lord]

clear all; clc; close all;

Please don't start your scripts like this. If you run this script hoping to compare one run of the script with another, these three commands make it very difficult if not impossible to do so. Get out of the habit of including these commands in your scripts.

[Umar]

@Steven Lord, Thanks for your feedback. I understand the concern regarding clear all, clc, and close all—it's definitely something to avoid if you're debugging or running the script multiple times. However, in this case, the intent was to provide a self-contained example to ensure the code runs without residual data interfering, especially for new users who might not know the best practices yet.

That said, I'm happy to focus on optimizing the solution and any further suggestions you may have regarding the implementation itself—such as improving the mode calculation or handling edge cases more efficiently. Would love to hear your thoughts on that.

[Walter Roberson]

My code is much much shorter.

 A = randi([1 5],100,50); % Example 100x50 matrix
 threshold = 0.3; % minimum fraction for mode
[M, F] = mode(A, 2);
M1 = M;
M1(F < size(A,2)*threshold) = NaN;
table((1:size(M,1)).', M, F./size(A,2), M1)

ans = 100×4 table
    Var1    M    Var3    M1 
    ____    _    ____    ___

      1     1    0.34      1
      2     5    0.32      5
      3     4    0.26    NaN
      4     2    0.24    NaN
      5     2    0.26    NaN
      6     1     0.3      1
      7     3    0.28    NaN
      8     4     0.3      4
      9     1    0.24    NaN
     10     4    0.24    NaN
     11     3    0.26    NaN
     12     2    0.28    NaN
     13     4     0.3      4
     14     5     0.3      5
     15     1    0.34      1
     16     5    0.28    NaN

 [rowCount, colCount] = size(A);
 RowIndex = (1:rowCount)'; 
 CandidateMode = NaN(rowCount,1); 
 RelFrequency = NaN(rowCount,1); 
 ModeWithThreshold = NaN(rowCount,1);
 for i = 1:rowCount
 row = A(i,:);
 [uniqueVals, ~, idx] = unique(row); 
 counts = accumarray(idx,1); 
 maxCount = max(counts); 
 posTies = find(counts == maxCount); 
 modeVal = min(uniqueVals(posTies)); 
 relFreq = maxCount / colCount; 
 CandidateMode(i) = modeVal; 
 RelFrequency(i) = relFreq;
 if relFreq >= threshold
 ModeWithThreshold(i) = modeVal;
 else
 ModeWithThreshold(i) = NaN; 
 end
 end
 ResultTable = table(RowIndex, CandidateMode, RelFrequency, ModeWithThreshold, ...
 'VariableNames', {'RowIndex','CandidateMode','RelFrequency','ModeWithThreshold'})

ResultTable = 100×4 table
    RowIndex    CandidateMode    RelFrequency    ModeWithThreshold
    ________    _____________    ____________    _________________

        1             1              0.34                 1       
        2             5              0.32                 5       
        3             4              0.26               NaN       
        4             2              0.24               NaN       
        5             2              0.26               NaN       
        6             1               0.3                 1       
        7             3              0.28               NaN       
        8             4               0.3                 4       
        9             1              0.24               NaN       
       10             4              0.24               NaN       
       11             3              0.26               NaN       
       12             2              0.28               NaN       
       13             4               0.3                 4       
       14             5               0.3                 5       
       15             1              0.34                 1       
       16             5              0.28               NaN       

[Umar]

Absolutely right, @Walter Robertson! That's a beautifully elegant solution - much more concise and leverages MATLAB's built-in functions perfectly.Your approach using mode(A, 2) directly is brilliant:

• Gets both the mode values AND frequencies in one function call
• The threshold filtering with M1(F < size(A,2)*threshold) = NaN is clean and vectorized
• No loops needed at all!

This is exactly why I appreciate working with experienced MATLAB developers - there's always a more elegant built-in solution than the verbose manual approach. Your code is not just shorter, it's also more readable and computationally efficient.

Thanks for sharing this - definitely learning from your approach here. Sometimes the best solutions are the simplest ones that fully utilize MATLAB's strengths!