How To Determine Number Of Clusters In T-SNE And Best Clustering Algorithm?

Question

I used TSNE method to cluster my DataSet.

X_embedded = TSNE(n_components=2, verbose=1, perplexity=10, n_iter=600).fit_transform(binary)
kmeans = KMeans(init="k-means++", n_clusters=6, n_init=4)
kmeans.fit(X_embedded) 

1. Why it just clusters my DataSet into 2 clusters?
2. What is The best method for clustering that?
3. How to determine Number Of Clusters ?

Here is my clusters's dispersion :

import seaborn as sns

sns.scatterplot(data = X_embedded)

Answer 1

1. There are not only two clusters. What happens is that when plotting the data we do not define how the dots should be coloured, something like: plt.scatter(x = ..., y = ..., c = kmeans.predict(...)) should give you what you are after. (Side-note: the scatter-plot shown appears quite unstructured so I would not be very optimistic about a clustering algorithm doing well here)
2. There is never a best method to cluster. As clustering is a unsupervised learning procedure, the good of a particular clustering in related to the relevance of the "structure discovery" we gain out of it. e.g. Clustering customer behaviour and finding that female and male costumers have different spending patterns might be very relevant ("so clustering was good") or might be something everyone in the business knew already ("so clustering is bad").
3. Determining the exact number of cluster is usually not a clear-cut question. That said, we have multiple threads within CV.SE discussing this question in detail. For example see the threads:

• Chosing optimal k and optimal distance-metric for k-means
• Elbow criteria to determine number of cluster
• Determine the number of clusters for K-means automatically

In the absence of any other context using something like the Gap statistic (see: Gap Statistic in plain English?) or the Elbow method (Elbow criteria to determine number of cluster - same above) is probably OK as a first step. After getting an idea of what these heuristics do and why they give their respective answers, more involved metrics might be relevant.