一加Ace2 Pro真機(jī)揭曉 鈦空灰配色質(zhì)感拉滿
終于，在經(jīng)過了幾波預(yù)熱之后，一加Ace2 Pro的外觀真機(jī)圖在網(wǎng)上出現(xiàn)了。還是博主數(shù)碼閑聊站曝光的，這次的外觀設(shè)計(jì)還是延續(xù)了一加11的方案，只是細(xì)節(jié)上有了調(diào)整，例如新加入了鈦空灰
我們將使用輪廓分?jǐn)?shù)和一些距離指標(biāo)來執(zhí)行時(shí)間序列聚類實(shí)驗(yàn)，并且進(jìn)行可視化
讓我們看看下面的時(shí)間序列:
如果沿著y軸移動(dòng)序列添加隨機(jī)噪聲，并隨機(jī)化這些序列，那么它們幾乎無法分辨，如下圖所示-現(xiàn)在很難將時(shí)間序列列分組為簇:
上面的圖表是使用以下腳本創(chuàng)建的:
# Import necessary libraries import os import pandas as pd import numpy as np # Import random module with an alias 'rand' import random as rand from scipy import signal # Import the matplotlib library for plotting import matplotlib.pyplot as plt # Generate an array 'x' ranging from 0 to 5*pi with a step of 0.1 x = np.arange(0, 5*np.pi, 0.1) # Generate square, sawtooth, sin, and cos waves based on 'x' y_square = signal.square(np.pi * x) y_sawtooth = signal.sawtooth(np.pi * x) y_sin = np.sin(x) y_cos = np.cos(x) # Create a DataFrame 'df_waves' to store the waveforms df_waves = pd.DataFrame([x, y_sawtooth, y_square, y_sin, y_cos]).transpose() # Rename the columns of the DataFrame for clarity df_waves = df_waves.rename(columns={0: 'time', 1: 'sawtooth', 2: 'square', 3: 'sin', 4: 'cos'}) # Plot the original waveforms against time df_waves.plot(x='time', legend=False) plt.show() # Add noise to the waveforms and plot them again for col in df_waves.columns: if col != 'time': for i in range(1, 10): # Add noise to each waveform based on 'i' and a random value df_waves['{}_{}'.format(col, i)] = df_waves[col].apply(lambda x: x + i + rand.random() * 0.25 * i) # Plot the waveforms with added noise against time df_waves.plot(x='time', legend=False) plt.show()現(xiàn)在我們需要確定聚類的基礎(chǔ)。這里有兩種方法:
把接近于一組的波形分組——較低歐幾里得距離的波形將聚在一起。
把看起來相似的波形分組——它們有相似的形狀，但歐幾里得距離可能不低。
一般來說，我們希望根據(jù)形狀對(duì)時(shí)間序列進(jìn)行分組，對(duì)于這樣的聚類-可能希望使用距離度量，如相關(guān)性，這些度量或多或少與波形的線性移位無關(guān)。
讓我們看看上面定義的帶有噪聲的波形對(duì)之間的歐幾里得距離和相關(guān)性的熱圖:
可以看到歐幾里得距離對(duì)波形進(jìn)行分組是很困難的，因?yàn)槿魏我唤M波形對(duì)的模式都是相似的。例如，除了對(duì)角線元素外，square & cos之間的相關(guān)形狀與square和square之間的相關(guān)形狀非常相似
所有的形狀都可以很容易地使用相關(guān)熱圖組合在一起——因?yàn)轭愃频牟ㄐ尉哂蟹浅８叩南嚓P(guān)性(sin-sin對(duì))，而像sin和cos這樣的波形幾乎沒有相關(guān)性。
通過上面熱圖和分析，根據(jù)高相關(guān)性分配組看起來是一個(gè)好主意，但是我們?nèi)绾味x相關(guān)閾值呢？看起來像一個(gè)迭代過程，容易出現(xiàn)不準(zhǔn)確和大量的人工工作。
在這種情況下，我們可以使用輪廓分?jǐn)?shù)（Silhouette score），它為執(zhí)行的聚類分配一個(gè)分?jǐn)?shù)。我們的目標(biāo)是使輪廓分?jǐn)?shù)最大化。
輪廓分?jǐn)?shù)（Silhouette Score）是一種用于評(píng)估聚類質(zhì)量的指標(biāo)，它可以幫助你確定數(shù)據(jù)點(diǎn)是否被正確地分配到它們的簇中。較高的輪廓分?jǐn)?shù)表示簇內(nèi)數(shù)據(jù)點(diǎn)相互之間更加相似，而不同簇之間的數(shù)據(jù)點(diǎn)差異更大，這通常是良好的聚類結(jié)果。
輪廓分?jǐn)?shù)的計(jì)算方法如下：
其中，N 是數(shù)據(jù)點(diǎn)的總數(shù)。
輪廓分?jǐn)?shù)的取值范圍在 -1 到 1 之間，具體含義如下：
一些重要的知識(shí)點(diǎn):
在所有點(diǎn)上的高平均輪廓分?jǐn)?shù)(接近1)表明簇的定義良好且明顯。
低或負(fù)的平均輪廓分?jǐn)?shù)(接近-1)表明重疊或形成不良的集群。
0左右的分?jǐn)?shù)表示該點(diǎn)位于兩個(gè)簇的邊界上。
現(xiàn)在讓我們嘗試對(duì)時(shí)間序列進(jìn)行分組。我們已經(jīng)知道存在四種不同的波形，因此理想情況下應(yīng)該有四個(gè)簇。
pca = decomposition.PCA(n_compnotallow=2) pca.fit(df_man_dist_euc) df_fc_cleaned_reduced_euc = pd.DataFrame(pca.transform(df_man_dist_euc).transpose(), index = ['PC_1','PC_2'], columns = df_man_dist_euc.transpose().columns) index = 0 range_n_clusters = [2, 3, 4, 5, 6, 7, 8] # Iterate over different cluster numbers for n_clusters in range_n_clusters: # Create a subplot with silhouette plot and cluster visualization fig, (ax1, ax2) = plt.subplots(1, 2) fig.set_size_inches(15, 7) # Set the x and y axis limits for the silhouette plot ax1.set_xlim([-0.1, 1]) ax1.set_ylim([0, len(df_man_dist_euc) + (n_clusters + 1) * 10]) # Initialize the KMeans clusterer with n_clusters and random seed clusterer = KMeans(n_clusters=n_clusters, n_init="auto", random_state=10) cluster_labels = clusterer.fit_predict(df_man_dist_euc) # Calculate silhouette score for the current cluster configuration silhouette_avg = silhouette_score(df_man_dist_euc, cluster_labels) print("For n_clusters =", n_clusters, "The average silhouette_score is :", silhouette_avg) sil_score_results.loc[index, ['number_of_clusters', 'Euclidean']] = [n_clusters, silhouette_avg] index += 1 # Calculate silhouette values for each sample sample_silhouette_values = silhouette_samples(df_man_dist_euc, cluster_labels) y_lower = 10 # Plot the silhouette plot for i in range(n_clusters): # Aggregate silhouette scores for samples in the cluster and sort them ith_cluster_silhouette_values = sample_silhouette_values[cluster_labels == i] ith_cluster_silhouette_values.sort() # Set the y_upper value for the silhouette plot size_cluster_i = ith_cluster_silhouette_values.shape[0] y_upper = y_lower + size_cluster_i color = cm.nipy_spectral(float(i) / n_clusters) # Fill silhouette plot for the current cluster ax1.fill_betweenx(np.arange(y_lower, y_upper), 0, ith_cluster_silhouette_values, facecolor=color, edgecolor=color, alpha=0.7) # Label the silhouette plot with cluster numbers ax1.text(-0.05, y_lower + 0.5 * size_cluster_i, str(i)) y_lower = y_upper + 10 # Update y_lower for the next plot # Set labels and title for the silhouette plot ax1.set_title("The silhouette plot for the various clusters.") ax1.set_xlabel("The silhouette coefficient values") ax1.set_ylabel("Cluster label") # Add vertical line for the average silhouette score ax1.axvline(x=silhouette_avg, color="red", linestyle="--") ax1.set_yticks([]) # Clear the yaxis labels / ticks ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1]) # Plot the actual clusters colors = cm.nipy_spectral(cluster_labels.astype(float) / n_clusters) ax2.scatter(df_fc_cleaned_reduced_euc.transpose().iloc[:, 0], df_fc_cleaned_reduced_euc.transpose().iloc[:, 1], marker=".", s=30, lw=0, alpha=0.7, c=colors, edgecolor="k") # Label the clusters and cluster centers centers = clusterer.cluster_centers_ ax2.scatter(centers[:, 0], centers[:, 1], marker="o", c="white", alpha=1, s=200, edgecolor="k") for i, c in enumerate(centers): ax2.scatter(c[0], c[1], marker="$%d$" % i, alpha=1, s=50, edgecolor="k") # Set labels and title for the cluster visualization ax2.set_title("The visualization of the clustered data.") ax2.set_xlabel("Feature space for the 1st feature") ax2.set_ylabel("Feature space for the 2nd feature") # Set the super title for the whole plot plt.suptitle("Silhouette analysis for KMeans clustering on sample data with n_clusters = %d" % n_clusters, fnotallow=14, fnotallow="bold") plt.savefig('sil_score_eucl.png') plt.show()
可以看到無論分成多少簇，數(shù)據(jù)都是混合的，并不能為任何數(shù)量的簇提供良好的輪廓分?jǐn)?shù)。這與我們基于歐幾里得距離熱圖的初步評(píng)估的預(yù)期一致
pca = decomposition.PCA(n_compnotallow=2) pca.fit(df_man_dist_corr) df_fc_cleaned_reduced_corr = pd.DataFrame(pca.transform(df_man_dist_corr).transpose(), index = ['PC_1','PC_2'], columns = df_man_dist_corr.transpose().columns) index=0 range_n_clusters = [2,3,4,5,6,7,8] for n_clusters in range_n_clusters: # Create a subplot with 1 row and 2 columns fig, (ax1, ax2) = plt.subplots(1, 2) fig.set_size_inches(15, 7) # The 1st subplot is the silhouette plot # The silhouette coefficient can range from -1, 1 but in this example all # lie within [-0.1, 1] ax1.set_xlim([-0.1, 1]) # The (n_clusters+1)*10 is for inserting blank space between silhouette # plots of individual clusters, to demarcate them clearly. ax1.set_ylim([0, len(df_man_dist_corr) + (n_clusters + 1) * 10]) # Initialize the clusterer with n_clusters value and a random generator # seed of 10 for reproducibility. clusterer = KMeans(n_clusters=n_clusters, n_init="auto", random_state=10) cluster_labels = clusterer.fit_predict(df_man_dist_corr) # The silhouette_score gives the average value for all the samples. # This gives a perspective into the density and separation of the formed # clusters silhouette_avg = silhouette_score(df_man_dist_corr, cluster_labels) print( "For n_clusters =", n_clusters, "The average silhouette_score is :", silhouette_avg, ) sil_score_results.loc[index,['number_of_clusters','corrlidean']] = [n_clusters,silhouette_avg] index=index+1 sample_silhouette_values = silhouette_samples(df_man_dist_corr, cluster_labels) y_lower = 10 for i in range(n_clusters): # Aggregate the silhouette scores for samples belonging to # cluster i, and sort them ith_cluster_silhouette_values = sample_silhouette_values[cluster_labels == i] ith_cluster_silhouette_values.sort() size_cluster_i = ith_cluster_silhouette_values.shape[0] y_upper = y_lower + size_cluster_i color = cm.nipy_spectral(float(i) / n_clusters) ax1.fill_betweenx( np.arange(y_lower, y_upper), 0, ith_cluster_silhouette_values, facecolor=color, edgecolor=color, alpha=0.7, ) # Label the silhouette plots with their cluster numbers at the middle ax1.text(-0.05, y_lower + 0.5 * size_cluster_i, str(i)) # Compute the new y_lower for next plot y_lower = y_upper + 10 # 10 for the 0 samples ax1.set_title("The silhouette plot for the various clusters.") ax1.set_xlabel("The silhouette coefficient values") ax1.set_ylabel("Cluster label") # The vertical line for average silhouette score of all the values ax1.axvline(x=silhouette_avg, color="red", linestyle="--") ax1.set_yticks([]) # Clear the yaxis labels / ticks ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1]) # 2nd Plot showing the actual clusters formed colors = cm.nipy_spectral(cluster_labels.astype(float) / n_clusters) ax2.scatter( df_fc_cleaned_reduced_corr.transpose().iloc[:, 0], df_fc_cleaned_reduced_corr.transpose().iloc[:, 1], marker=".", s=30, lw=0, alpha=0.7, c=colors, edgecolor="k" ) # for i in range(len(df_fc_cleaned_cleaned_reduced.transpose().iloc[:, 0])): # ax2.annotate(list(df_fc_cleaned_cleaned_reduced.transpose().index)[i], # (df_fc_cleaned_cleaned_reduced.transpose().iloc[:, 0][i], # df_fc_cleaned_cleaned_reduced.transpose().iloc[:, 1][i] + 0.2)) # Labeling the clusters centers = clusterer.cluster_centers_ # Draw white circles at cluster centers ax2.scatter( centers[:, 0], centers[:, 1], marker="o", c="white", alpha=1, s=200, edgecolor="k", ) for i, c in enumerate(centers): ax2.scatter(c[0], c[1], marker="$%d$" % i, alpha=1, s=50, edgecolor="k") ax2.set_title("The visualization of the clustered data.") ax2.set_xlabel("Feature space for the 1st feature") ax2.set_ylabel("Feature space for the 2nd feature") plt.suptitle( "Silhouette analysis for KMeans clustering on sample data with n_clusters = %d" % n_clusters, fnotallow=14, fnotallow="bold", ) plt.show()
當(dāng)選擇的簇?cái)?shù)為4時(shí)，我們可以清楚地看到分離的簇，其他結(jié)果通常比歐氏距離要好得多。
輪廓分?jǐn)?shù)表明基于相關(guān)性的距離矩陣在簇?cái)?shù)為4時(shí)效果最好，而在歐氏距離的情況下效果就不那么明顯了結(jié)論
在本文中，我們研究了如何使用歐幾里得距離和相關(guān)度量執(zhí)行時(shí)間序列聚類，并觀察了這兩種情況下的結(jié)果如何變化。如果我們?cè)谠u(píng)估聚類時(shí)結(jié)合Silhouette，我們可以使聚類步驟更加客觀，因?yàn)樗峁┝艘环N很好的直觀方式來查看聚類的分離情況。
本文鏈接：http://www.www897cc.com/showinfo-26-13365-0.html使用輪廓分?jǐn)?shù)提升時(shí)間序列聚類的表現(xiàn)
聲明：本網(wǎng)頁內(nèi)容旨在傳播知識(shí)，若有侵權(quán)等問題請(qǐng)及時(shí)與本網(wǎng)聯(lián)系，我們將在第一時(shí)間刪除處理。郵件：2376512515@qq.com
Copyright ? 2016-2023 天津谷騏科技有限公司 版權(quán)所有 sitemap.xml
違法及侵權(quán)請(qǐng)聯(lián)系：2376512515@qq.com 津ICP備18001702號(hào)
津公網(wǎng)安備 12010102000574號(hào)