updated k-means and fixed bugs in refactoring

fixed issues with k-means. fixed bug with variable for loop and numbering in IRWIN-HALL DISTRIBUTION routine in refactoring. also fixed small bug in line 1250.

Author: mdcramer

_apple-2-blog/k-means.md

@@ -8,6 +8,7 @@ tags:
   - K-means
   - machine learning
 date: 2025-09-20
+last_modified_at: 2025-10-06
 ---
 
 Wait. Does k-means count as machine learning? Yes. Yes, it does.
@@ -32,7 +33,7 @@ At the end of each loop I draw a line between the latest estimates of cluster ce
 
 ## K-means explained
 
-[K-means clustering](https://en.wikipedia.org/wiki/K-means_clustering){:target="_blank"} is a recursive algorithm that aims to partition \\(n\\) observations into \\(k\\) clusters in which each observation belongs to the cluster with the nearest mean, called the cluster centroid.
+[K-means clustering](https://en.wikipedia.org/wiki/K-means_clustering){:target="_blank"} is an iterative algorithm that aims to partition \\(n\\) observations into \\(k\\) clusters in which each observation belongs to the cluster with the nearest mean, called the cluster centroid.
 
 |Step|Description|
 |--|--|
@@ -196,7 +197,7 @@ This code is a slog and it's not really critical to understanding ML but I thoug
 3030   IF KM%(I - 1,1) - KM%(I,1) <> 0 THEN M = -1 * (KM%(I - 1,0) - KM%(I,0)) / (KM%(I - 1,1) - KM%(I,1))
 3040   P%(0,0) = (KM%(I,0) - KM%(I - 1,0)) / 2 + KM%(I - 1,0)
 3050   P%(0,1) = (KM%(I,1) - KM%(I - 1,1)) / 2 + KM%(I - 1,1)
-3060   GOSUB 3500
+3060   GOSUB 3080
 3070 NEXT
 3080 REM  -- DRAW LINE FROM SLOPE AND POINT --
 3090 NX = 1 : REM  -- REM NUMBER OF INTERSECTIONS --
@@ -230,4 +231,9 @@ I then iterate through the 4 sides of the 'box' on the screen, using the corners
 
 Yes! Yes, we can.
 
-While k-means is simple, it does not take advantage of our knowledge of the Gaussian nature of the data. If we know that the distributions are Gaussian, which is very frequently the case in machine learning, we can employ a more powerful algorithm: Expectation Maximization (EM). This post is already long enough, so we'll deal with that another day. Eventually, perhaps, we'll also get to deep learning, although developing back propagation for an arbitrary size neural net using APPLESOFT BASIC on an <span class="no-break">Apple ][+</span> is not going to be easy.
+While k-means is simple, it does not take advantage of our knowledge of the Gaussian nature of the data. If we know that the distributions are at least approximately Gaussian, which is frequently the case, we can employ a more powerful application of the Expectation Maximization (EM) framework (k-means is a specific implementation of centroid-based clustering that uses an iterative approach similar to EM with 'hard' clustering) that takes advantage of this. This post is already long enough, so we'll deal with that another day. Eventually, perhaps, we'll also get to deep learning, although developing back propagation for an arbitrary size neural net using APPLESOFT BASIC on an <span class="no-break">Apple ]\[+</span> is not going to be easy.
+
+## Social media sharing
+I shared this post on [Hacker News](https://news.ycombinator.com/item?id=45415510){:target="_blank"} and, to my surprise and delight, got a decent amount of feedback, including some helpful corrections.
+
+My [post on Facebook](https://www.facebook.com/markdcramer/posts/pfbid0eG3AuPSxFTqBm4nggDAjqJrQe8VFv5VUEKf5SQ8qtnDjVFZ4qaSZvauDBcKRxSoFl){:target="_blank"} received _significantly_ less reaction. My friends are apparently a lot less interested in ML algorithms on retro hardware than randos on Hacker News. My share requests to Facebook groups [Apple II Enthusiasts](https://www.facebook.com/groups/5251478676){:target="_blank"} and [Retro Microcomputers](https://www.facebook.com/groups/retrocomputers){:target="_blank"} were both rejected, which is a bit disappointing. Still, those are fun groups to follow. My [post on the VCF forum](https://forum.vcfed.org/index.php?threads/ml-on-an-apple.1254709/){:target="_blank"} also got zilch. (I attend the [Vintage Computer Festival](https://vcfed.org/events/vintage-computer-festival-west/){:target="_blank"} at the [Computer History Museum](https://computerhistory.org/){:target="_blank"}, which was a good time.) Perhaps I'll try Reddit and LinkedIn next to see what happens...

_apple-2-blog/refactoring.md

@@ -135,7 +135,7 @@ The only remaining tweaks were for the plotting routines. The two routines below
 1220 IF X0% < 1 OR X0% > 270 THEN RETURN
 1230 IF X1% < 1 OR X1% > 150 THEN RETURN
 1240 HPLOT X0% - 1,X1% TO X0% + 1,X1%
-1250 HPLOT X0%,X1% - 1 TO X0%,X1 + 1
+1250 HPLOT X0%,X1% - 1 TO X0%,X1% + 1
 1260 RETURN
 
 1300 REM == DRAW BOX AT X0, X1 ==
@@ -153,17 +153,17 @@ The only remaining tweaks were for the plotting routines. The two routines below
 The final chunk of code is interesting. After sharing my [Box-Muller](/apple-2-blog/synthesizing-data#box-muller-to-the-rescue) routine with my friend, [Răzvan Surdulescu](https://www.linkedin.com/in/surdules/){:target="_blank"}, he suggested using the [Irwin-Hall Distribution](https://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution){:target="_blank"}. `SQR` and `COS` are expensive operations in BASIC and Irwin-Hall [approximates a normal distribution](https://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution#Approximating_a_Normal_distribution){:target="_blank"} by sampling 12 uniform random numbers.
 
 ```bbcbasic
-1400 REM == IRWIN-HALL DISTRIBUTION ==
-1490 Z0 = -6:Z1 = -6
-1500 FOR I = 1 TO 12
-1510   Z0 = Z0 + RND(1)
-1520   Z1 = Z1 + RND(1)
-1530 NEXT
-1540 RETURN
-1550 REM == RANDOM GEN SPEED TEST ==
-1560 FOR I = 1 TO 500
-1570   GOSUB 1400
-1580 NEXT
+1500 REM == IRWIN-HALL DISTRIBUTION ==
+1510 Z0 = -6:Z1 = -6
+1520 FOR Z = 1 TO 12
+1530   Z0 = Z0 + RND(1)
+1540   Z1 = Z1 + RND(1)
+1550 NEXT
+1560 RETURN
+1600 REM == RANDOM GEN SPEED TEST ==
+1610 FOR I = 1 TO 500
+1620   GOSUB 1400
+1630 NEXT
 ```
 I gave it a go and ran a comparison by generating 500 pairs of random numbers with each. This took 63s with Box-Muller and 90s with Irwin-Hall, so I will stick with the former. That being said, this was a nifty idea.