For an assignment I have to compute the intra-class distance and use it as an objective function to select features. This is for the MNIST dataset.

While I have a fairly good handle on other aspects of this assignment, the term intra-class distance is confusing to me. Google does not result in any concrete answers either.

I understand intra would mean within, but that's exactly what is confusing to me: how can distance be within? Is it the distance of each measurement with another?

For example, I have N measurements for Class C. Is intra-class distance the distance from n to N-1 measurements within that class?


Intraclass distance is the distance between two points that are in the same class.

In your example, an intra-class distance is the distance between measurements $X_i$ and $X_j$ where $(i,j \in 1 \cdots N)$, and $X_i$ and $X_j$ are members of class C. One usually takes an average over the distances from all possible $(i,j)$ pairs within class C, and use it as the objective function. You can also use the distance between $X_i$ and $\bar{X}_C$ (the average coordinate of all measurements in class C), and take the average of this over all measurements in class C.

In contrast, an inter-class distance is the distance between measurements $X_i$ and $X_j$, where $X_i$ and $X_j$ are members of different classes.

  • $\begingroup$ Thank you! I note that you mention one usually takes an average over the all the pairwise distances from class C. My assignment states that "Implement a forward search algorithm using the Intra-class distance (defined by the mean of each class)" - does this mean I take the distance of each point from the mean? $\endgroup$ – saad Mar 6 at 18:20
  • 1
    $\begingroup$ Yes. It means what you said. $\endgroup$ – LambdaPsi Mar 6 at 18:22

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