引言

客户流失这个术语通常用来描述在特定时间或合同期内停止与公司进行业务往来的客户倾向性[1]。传统上，关于客户流失的研究始于客户关系管理（CRM）[2]。在运营服务时，防止客户流失至关重要。过去，客户获取相对于流失数量的效率是良好的。然而，随着市场因服务全球化和激烈竞争而饱和，客户获取成本迅速上升[3][4]。

Reinartz, Werner, Jacquelyn S. Thomas 和 Viswanathan Kumar（2005）表明，从长期业务运营来看，在CRM方面努力提高所有客户的留存率不如在少数目标客户获取活动上投入更有效[22]。同样，Sasser, W. Earl（1990）建议，保留的客户通常比随机获取的新客户带来更高的利润率[23]。此外，Mozer, Michael C., 等人（2000）提出，从净投资回报率来看，保留现有客户的营销活动比吸引新客户更有效[16]。Reichheld 等人（1996）表明，客户留存率提高5%分别使一家软件公司和一家广告公司的客户净现值增加了35%和95%[29]。因此，流失预测可以作为一种方法来提高忠实客户的留存率，从而最终增加公司的价值。

在各种服务领域已经提出了关于客户流失的研究。这些流失分析研究试图使用各种指标提前识别或预测客户流失的可能性。客户流失率[5]是典型的客户流失分析指标。这指的是在特定时期内取消服务的订阅者与总订阅者的比例[5][32][41]。流失率是计算大多数服务领域订阅者服务留存期的最广泛使用的指标。由于其重要性和直观性，流失已被引入各种服务领域并发展以适应每个领域的特性。因此，客户流失分析的研究根据各个研究领域而分散，测量标准也各不相同。目前，这导致了许多问题。在行业中，由于在融合异构服务（例如，车辆共享服务/保险，在线音乐服务/百货商店）过程中服务人员之间不同流失标准引起的沟通成本急剧增加。此外，由于流失研究同时涉及工程和工商管理两个领域，研究人员很难在一篇论文中描述两个独立的专业领域或理解它们。

过去，早期的客户流失被用于定义CRM中的客户状态。CRM是一种商业管理方法，最初出现是为了提高零售、营销、销售、客户服务和供应链领域的效率，以及提高组织的效率和客户价值功能[2]。从那时起，从架构角度来看，CRM已经演变并分为操作性CRM和分析性CRM。分析性CRM专注于开发包含客户特征和态度的数据库和资源[24][25][30]。分析性CRM最初用于利用客户状态和客户行为数据创建适当的营销策略，特别是用于满足客户的个人和独特需求[26]。从这一点开始，IT和知识管理相关技术被利用，公司开始应用专门的技术来获取、保留、流失和选择客户[27]，自从IT领域的技术被实施到CRM中以来，各种公司开始在包括数据仓库、网站、电信和银行在内的业务领域使用这些技术[28]。如前所述，CRM研究表明，提高少数现有客户的留存率比获取新客户更有效，流失分析已成为重要的个性化客户管理技术之一[20][28][59]。有一些综述论文收集并总结了电信领域的流失分析技术[6][7][8][9]。然而，这些研究仅限于电信领域，流失分析使用的日志数据不包括时间序列特征、留存和生存以及关键绩效指标（KPI）特征。还有一些论文应用了各种基于深度学习模型的流失分析技术在计算机科学领域[10][11]。然而，这些研究仅限于深度学习算法，缺乏基础模型和参数描述。也有一些关于流失的综述论文，但它们不涵盖最新的深度学习技术，只涵盖特定行业领域的流失[12][13]。建立流失预测模型的趋势正在改变，性能正在迅速提高。然而，由于先前研究的分散，研究人员在启动新的流失研究时面临许多困难。为了解决这些问题，这篇综述论文描述了在工商管理、营销、IT、电信、报纸出版、保险和心理学领域中流失预测算法定义的差异，并比较了流失损失和特征工程的差异。此外，我分类并解释了基于此的流失预测模型案例。我们的研究提供了比以往综述论文更广泛的流失详细技术的分类信息。我们的研究可以减少在多个行业/学术领域中被分散和使用的流失标准的混淆，并在将其应用于预测模型时提供实际帮助。特别是，这篇论文介绍了一种深度学习模型，这种模型是为了应对随着工业发展而出现的非合同客户流失问题而设计的。本文结构如下。第2章介绍了每个业务领域流失的典型定义及其差异。第3章展示了各种业务领域中的流失应用案例。

流失的定义

流失在多个行业中有不同的定义。在本章中，我描述了两种典型类型。如表1所示，总结了定义流失的不同标准的典型论文。一般来说，字典中流失的定义是长期的不活跃[14]。然而，“不活跃”和“长期”的标准在各个研究领域中是不同的。由于现代服务采用了更宽松的订阅条款，这种不一致性经常出现，因为竞争的原因。在过去，客户流失通过合同取消明确发生，而在包括互联网和零售服务在内的现代服务中，由于客户投资成本低，频繁发生客户流失[19][20][21][96]。这些非合同客户流失是由于更换服务的低转换成本引起的[31]。因此，我将流失的标准分为合同流失和非合同流失。每种流失的描述如下。

第一个标准是合同流失。合同流失指的是客户在合同续约日期到达时不续约的情况[15][16]。这种流失意味着客户对相关服务领域失去兴趣，并且改变了其状态，使其不再可能重新进入。通常出现在客户关闭银行账户或从一个运营商转移到另一个服务时的流失问题中。此外，合同流失在如音乐和电影流媒体服务等固定费率服务中经常出现。

第二个标准是非合同流失。一般来说，在非合同情况下，客户可以在没有时间限制的情况下离开服务/合同。从服务运营的角度来看，首先构建一个流失标准，然后将符合该标准的客户分类为流失客户。为此，计算客户行为改变的日期[96]。当这种不活跃或行为改变的时间超过阈值时，客户被视为流失客户。在此过程中，设定为不活跃日期阈值的时间称为时间窗口[17]。定义非合同流失使得可以推断出在特定时间段内可能流失的客户的概率。时间窗口方法在分析非合同情况的活动日志时经常使用。当客户在一段时间内不使用服务时，这种方法将客户视为流失。互联网服务通常不会删除账户。因此，互联网服务将登录解释为长期的，即服务的保留，并将一段时间内未连接的访问解释为流失[17]。图1示意性地展示了使用时间窗口方法的非合同流失案例。图1的日志记录了10周。时间窗口设定为第4周到第7周的4周时间。从第4周到第7周没有任何活动日志的用户A、B和C被视为流失，而其他有活动日志的用户D、E和F被视为保留。

流失分析通常是为了改善业务成果进行的。因此，在大多数流失预测问题中，流失期被定义为可以恢复客户信任的时间段。如果选择客户完全流失的时间段作为时间窗口，流失定义的时间段会呈指数增加，并且在业务方面不会带来任何收益，因为改变想要流失的客户的意愿被认为是不可能的[17]。上述的合同流失接近于客户完全从服务中流失。因此，如今大多数基于日志的流失预测问题使用概率方法来确定客户是否流失，并给予客户重新使用其服务的激励。

时间窗口的设置标准因服务特性而异。Yang, Wanshan等人（2019）分析了日志数据以定义移动游戏的流失期，分析结果显示超过95%的客户在连续缺席3天后没有返回。他们将3天设定为时间窗口流失期[43]。Lee, Eunjo等人（2018）考虑到PC游戏服务的特性，将75%的客户持续未连接的时间定义为流失期[17]。他们收集了客户未连接的时间段，并绘制了累积数据图。他们选择了超过75%客户流失的时间段作为时间窗口。图2示意性地展示了Lee, Eunjo等人（2018）收集的连续未连接天数的累积数据。根据图2，客户未连接超过75%的时间段是14周。因此，时间窗口流失期为14周。

如上所述，有两种客户流失类型，分别是合同流失和非合同流失。此外，还有三种流失观察标准：月度、日常和二元。月度和日常流失观察与客户状态在数据库中更新的周期有关。二元流失观察是通过操作这个数据库获得的。一般来说，在合同设置中，二元流失由合同的存在与否决定。在非合同设置中，公司定义客户的不活跃特征，当客户符合不活跃或不忠诚客户特征时，客户被视为二元流失[96]。定义客户流失的多种方式是为了定期监控客户状态的变化。通过这种观察，可以通过预测客户流失率并为可能流失的客户提供激励来增加预期的净业务价值[16][23]。

各个业务领域的流失分析

早期的大多数流失研究都是从管理角度进行的，特别是客户关系管理（CRM）[30][31]。CRM流失涵盖了客户识别、客户吸引、客户保留和客户开发过程中可能发生的所有流失问题。现代流失预测问题主要使用日志数据进行分析。日志是使用互联网服务时留下的跟踪数据。因此，使用日志数据实现的流失预测模型可以用于各个行业的互联网服务。有12个业务领域进行了流失预测。

电信行业占据了之前大多数流失研究。尽管客户获取成本高，电信服务的客户粘性也很高。因此，如果防止客户流失并提供适当的激励，有助于维持销售[16][32][33][34]。

金融和保险行业也预测客户流失。张荣等人（2017）强调了建立流失预测模型和防止流失的必要性，提到保险行业的高客户获取成本和高客户价值[11]。蒋丁安等人（2003）提到在线金融市场的客户价值高，并使用Apriori算法根据金融产品选择和客户的金融产品选择顺序创建了流失情景[35]。拉里维埃尔·巴特和德克·范登波尔（2004）基于客户群体根据金融产品属性的不同，通过测量每种产品的生存时间，证明了选择金融产品的客户倾向不同，流失的可能性也不同[36]。佐普尼迪斯·康斯坦丁、玛丽亚·马夫里和乔治·伊奥安努（2008）测量了金融产品的转换率和每种产品的客户生存期，以发现有吸引力的产品[37]。在这里，由于生存期短，流失更频繁，这被用作衡量需要补充金融产品的指标。格拉迪·尼古拉斯、巴特·巴森斯和克里斯托夫·克鲁克斯（2009）测量了客户生命周期价值和预期收益随时间的减少，作为对应客户忠诚度的指标[38]。在此过程中，使用机器学习计算流失率，用于估计客户生命周期价值。

后来，流失研究在游戏领域如同在电信领域一样积极进行。这些服务由于大量竞争，客户流入和流失的周期很快。然而，如果单一服务运行时间长，服务竞争加剧，客户获取成本（CAC）往往会增加[16][39][128]。随着CAC的增加，预测和防止流失的技术变得更加重要。维尔亚宁·马库斯等人（2016）将生存分析应用于移动游戏，并计算了流失率，类似于金融服务的流失预测[40]。由于日志数据量大，游戏领域在进行流失研究时积极使用机器学习技术[10][42][43]。米洛舍维奇·米洛斯、内纳德·兹维奇和伊戈尔·安杰尔科维奇（2017）在游戏流失研究中创建了流失预测模型，通过找出并将可能流失的客户分为A/B组，提供流失预防激励，并统计证明了实际效果[44]。朗格·朱利安等人（2014）进行了一项类似的研究，揭示了与一般营销目标相比，现有高可能性流失客户的营销响应率更高[45]。

此外，音乐流媒体服务领域甚至举办了构建预测模型的比赛，流失研究也在互联网服务和报纸订阅领域进行。报纸订阅和音乐流媒体服务提供固定费率服务，客户流失与合同续约期一致。另一方面，由于互联网服务根据客户的意愿进入不活跃状态，合同续约几乎是实时进行的。流失预测研究还在在线约会、在线商务、问答服务和社交网络服务领域进行[46]。

有些研究从心理学角度探讨客户流失。博博拉·佐赫布等人（2011）结合动机理论与客户使用MMORPG游戏，分析了客户动机改变时的流失情况[47]。尼克·易（2016）调查了大约25万名玩家，显示客户对游戏的态度按国家、种族和年龄分组[48]。

在营销领域，格拉迪·尼古拉斯、巴特·巴森斯和克里斯托夫·克鲁克斯（2009）使用了RFM（最近一次、频率和货币）和CLV（客户生命周期价值）等营销视角的特征进行流失预测[38]。

尽管少数，但在人力资源和能源领域也进行了流失预测研究。萨拉迪·V·维贾亚和吉里什·凯沙夫·帕尔希卡尔（2011）在员工流失时进行流失研究，以降低再培训成本并证明员工价值[50]。莫耶尔松·朱莉和大卫·马滕斯（2015）基于客户提供的能源数据和社会人口数据，估计客户是否会流失到另一能源供应商[51]。

结论

在本研究中，我比较了使用日志数据的流失预测分析技术。流失分析用于互联网服务和游戏、保险和管理领域。流失预测研究通常是为了改善业务成果。因此，时间窗口被用来选择潜在的流失客户，而不是测量客户的完全流失。客户流失的损失成本通过CAC或CLV计算。在过去，预测客户流失时，研究人员使用生存分析或时间序列分析，结合统计学、图论和传统的机器学习算法。最近，使用深度学习算法的流失预测分析出现了。深度学习算法被发现优于其他算法。这可能是由于通过计算机收集了大量的客户日志数据，并使用这些数据集的全部来进行流失预测。本论文的流失预测模型使用深度学习进行流失预测，数据时间戳按秒级顺序或总量巨大的客户日志数据。在这种情况下，处理日志的特征工程技术对模型性能的提升有显著影响。与其他建模技术不同，深度学习模型能够通过嵌入时间序列特征将高维稀疏日志数据转换为低维密集特征。此外，深度学习模型可以通过层叠神经元结构从大量数据中学习客户的行为模式。因此，给定细微的时间戳和大量的观察数据，将这些数据应用于深度学习算法以生成潜在特征预计会比传统的流失预测模型表现更好。

这是因为如今的日志数据被收集的时间更长，深度学习算法相比旧算法更能捕捉客户的潜在状态。换句话说，深度学习算法今天受到关注的原因在于现代流失预测使用的大量数据及其捕捉细微变化的能力。如前文所述，传统的流失预测算法，包括统计方法，仍然在今天被积极使用。这是因为哪种流失预测模型在性能上表现最佳取决于数据格式的不同。使用深度学习的流失预测模型是一种新的解决方案，具有良好的结构来预测现代流失数据集。因此，为了解决当前的问题，读者需要了解流失数据集的格式，并应用合适的算法来解决流失预测问题。

此外，我还概述了一种性能评估方法，用于比较过去到现在使用的各种流失预测算法。大多数流失预测模型都与客户关系管理相关。例如，流失预测模型是否对假阳性或假阴性具有鲁棒性可能会导致性能差异。根据本文的研究，许多文章除了标准的精度外，还使用AUC作为性能衡量方法。一般来说，由于流失客户比非流失客户少，需要一种专注于流失客户的性能特定方法。ROC曲线是模型正确预测流失客户的比率和预测剩余客户为流失客户的比率的图形。因此，它是一种专注于流失客户预测的性能衡量方法。

在本研究中，我全面比较了流失预测问题。本文有助于在各种流失预测算法中找到满足研究人员需求的方法。此外，本文预计将用于改善服务和构建更好的流失分析模型。

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