The source code of paper "Implicit Multidimensional Projection of Local Subspaces".

• This is a Pychram project. If you have installed Pychram in your computer, you can open it in your Pycharm directly. But it's not necessary.
• This code using Python 3.7, numpy and scikit-learn. If you want to run this code in your computer, you must install them, and we suggest you use Anaconda directly, which has already included them.

You can find an example in Main.py:

def run_example():
    dr_method = 'MDS'  # 'MDS'  't-SNE'  'PCA'  'MDSPlus'  't-SNEPlus'
    X, label = load_data()
    repeat = Preprocess.has_repeat(X)
    if repeat:
        print("Please recheck the input data for duplicate points")
        return
    X = Preprocess.normalize(X)  # Optional
    (n, d) = X.shape

    trans = DRTrans()
    if dr_method == 'MDS':
        trans = MDSTrans(X, label=label, y_init=None, y_precomputed=False)
    elif dr_method == 't-SNE':
        trans = TSNETrans(X, label=label, y_init=None, perplexity=30.0)
    elif dr_method == 'PCA':
        trans = PCATrans(X, label=label)
    elif dr_method == "MDSPlus":
        trans = MDSTransPlus(X, label=label, y_init=None, y_precomputed=False)
    elif dr_method == "t-SNEPlus":
        trans = TSNETransPlus(X, label=label, y_init=None, perplexity=30.0)
    else:
        print("This method is not supported at this time: ", dr_method)
        return

    trans.transform(nbrs_k=20, MAX_EIGEN_COUNT=4, yita=0.1)
    np.savetxt("..\\Data\\"+str(dr_method)+"_Y.csv", trans.Y, fmt='%.18e', delimiter=",")
    if n*d < 1024 ** 3 / 2:
        np.savetxt("..\\Data\\"+str(dr_method)+"_derivative.csv", trans.derivative, fmt='%.18e', delimiter=",")
    json_file = JsonFile(path="..\\Data\\")
    json_file.create_file(trans)

• You could put your data and it's label in the package Data. The file data.csv contains n rows and D columns, and every row is a D-dimensional data point. One thing to note is that there should be no duplicate points in your data. label.csv is the label of the data.
• The output files in Data:
  • XXX_Y.csv is the result of dimension reduction.
  • XXX_derivative.csv is $\frac{\partial Y}{\partial X}$.
  • result.json and scale.json are for visualization.

We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data points. Existing methods focus on the projection of multidimensional data points, and the neighborhood information is ignored. Our method is able to analyze the shape and directional information of the local subspace to gain more insights into the global structure of the data through the perception of local structures. Local subspaces are fitted by multidimensional ellipses that are spanned by basis vectors. An accurate and efficient vector transformation method is proposed based on analytical differentiation of multidimensional projections formulated as implicit functions. The results are visualized as glyphs and analyzed using a full set of specifically-designed interactions supported in our efficient web-based visualization tool. The usefulness of our method is demonstrated using various multi- and high-dimensional benchmark datasets. Our implicit differentiation vector transformation is evaluated through numerical comparisons; the overall method is evaluated through exploration examples and use cases.