[python, k-means, 1d] How to use K-means to classify a histogram of a 1D data set using two features in time and value

How to use K-means to classify a histogram of a 1D data set using two features in time and value

井民全, Jing, mqjing@gmail.com

At first step, we crate a demo dataset by generating a 100 samples data array with mixed two distribution in which the first distribution has 30 samples with properties of means as 40 with standard deviation 1 and the second distribution has 70 samples with means as 60 and the standard deviation as 10. The second step, let k-means to classify the histogram of data and provide the cut result.

Key points

(1) How to get the histogram bin for k-means

i = 1     bins = np.linspace(0, len(X), len(X))     axes[i].hist(X, bins=bins, fc='#AAAAFF')     axes[i].set_title("(b) Show the frequency histogram of X.")     axes[i].set_ylabel("Histogram")     axes[i].set_xlabel("Values")          # get distributed bins     p = axes[i].patches     lstHistogram = [patch.get_height() for patch in p]

(2) How to use k-means to classify the 1D data

# run k-means     kmeans = KMeans(n_clusters=2)     lstLabel = kmeans.fit_predict(list(zip([x for x in range(0, len(lstHistogram))], lstHistogram)))     print(lstLabel)     # get the k-means result     lstIndex =   np.where(np.abs(np.diff(lstLabel)) == 1)[0]     print("The cut points, lstIndex = ", lstIndex)

Code

np.random.seed(1)     N = 100 # total samples     # normal distribution list. mean = 40, std= 1, number of samples = 30%     arrA = np.random.normal(40, 1, int(0.3 * N))          # normal distribution list. mean = 60, std= 10, number of samples = 70%     arrB = np.random.normal(60, scale=10, size=int(0.7 * N))      X = np.concatenate((arrA, arrB))         fig, axes = plt.subplots(nrows=3, sharex=True, gridspec_kw={"height_ratios": [1,1,1]})     fig.suptitle('Fig. Test of Normal Distribution and K-means.')     fig.canvas.set_window_title('Test of Normal Distribution and K-means')          # show all samples     i = 0     axes[i].plot([x for x in range(0, X.size)], X, "tab:red", label="X")     axes[i].set_title("(a) Data X with two distributions.")     axes[i].set_ylabel("Value")     axes[i].set_xlabel("Samples")     axes[i].grid()     axes[i].legend()          # show histogram     i = 1     bins = np.linspace(0, N, N)     axes[i].hist(X, bins=bins, fc='#AAAAFF')     axes[i].set_title("(b) Show the frequency histogram of X.")     axes[i].set_ylabel("Histogram")     axes[i].set_xlabel("Values")     # get distributed bins     p = axes[i].patches     lstHistogram = [patch.get_height() for patch in p]     # run k-means     kmeans = KMeans(n_clusters=2)     lstLabel = kmeans.fit_predict(list(zip([x for x in range(0, len(lstHistogram))], lstHistogram)))     print(lstLabel)     lstIndex =   np.where(np.abs(np.diff(lstLabel)) == 1)[0]     print("The cut points, lstIndex = ", lstIndex)     # show k-means result     i = 2     axes[i].plot([x for x in range(0, len(lstLabel))], lstLabel, "tab:red", label="k-means label")     axes[i].set_title("(c) Show K-means result for the X distribution.")     axes[i].set_ylabel("Label{0/1}")     axes[i].set_xlabel("Values")     axes[i].grid()     axes[i].legend()          plt.tight_layout() # Prvent the figure title overlaps axes label     plt.show()

Result

Figure

Stdout

fig.canvas.set_window_title('Test of Normal Distribution and K-means') [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] The cut points, lstIndex =  [49]

References

1. https://numpy.org/doc/stable/reference/random/generated/numpy.random.normal.html

2. https://numpy.org/doc/stable/reference/generated/numpy.where.html

3. https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html