Question: I tried uploading to IBM Cloud Object Storage (ICOS) with the following code, and some files could not uploaded.
Failed files contain the symbol "[" or "]" in the file name.

```
TransferUtility Utl = new TransferUtility(objClient);
TransferUtilityUploadDirectoryRequest request = new   TransferUtilityUploadDirectoryRequest
{
    BucketName = "Correct Backet name"
    Directory = "Correct directory name" ex. "C:\\testd1\\testd2"
    KeyPrefix = "Correct prefix"
    SearchOption = SearchOption.AllDirectories,
    SearchPattern = "*.*"
};

Utl.UploadDirectory(request);

```

---

Language:.NET C#

API: AWSSDK.Core 3.3.22.5, AWSSDK.S3 3.3.18.2 

Exception name：Amazon.S3.AmazonS3Exception  

Message："Invalid Argument"

InnerException name：Amazon.Runtime.Internal.HttpErrorResponseException  

Message："The remote server returned an error: (400) Bad Request"

Files with ordinary name such as "test.txt" can be uploaded without problems.  

This phenomenon does not occur with AWS S3 or another S3 compatible storage service.  

(But I have tried on only one of other S3 compatible services...) 

Could you tell me why I can not upload to ICOS and what solutions are there?

Best Regards.

Answer: 
Both the [scikit-Learn User Guide on KMeans](https://scikit-learn.org/stable/modules/clustering.html#k-means) and [Andrew Ng's CS229 Lecture notes on k-means](http://cs229.stanford.edu/notes/cs229-notes7a.pdf) indicate that the elbow method minimizes the **sum** of squared **distances** between cluster points and their cluster centroids. The sklearn documentation calls this "inertia" and points out that it is subject to the drawback of inflated **Euclidean distances** in high-dimensional spaces. Ng calls this minimization of the "distortion function". One can, however, find [examples](https://www.geeksforgeeks.org/elbow-method-for-optimal-value-of-k-in-kmeans/) of the definition of distortion being "the **average** of the squared distances from the cluster centers of the respective clusters" (emphasis mine) in contrast to "inertia" being the **sum** of the squared distances. While confusing, and confirming these terms are not consistently defined, it suggests to me both work.
Reading the documentation for [KMeans](https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans) you can see that both distortion and inertia both are the sum of distance for each point to its center.