Patent Publication Number: US-2023162197-A1

Title: Methods and apparatus for fraud detection

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. patent application Ser. No. 16/256,903, filed Jan. 24, 2019, and entitled “METHODS AND APPARATUS FOR FRAUD DETECTION,” which is incorporated herein in its entirety by reference. 
    
    
     TECHNICAL FIELD 
     The disclosure relates generally to fraud detection and, more specifically, to identifying fraudulent retail activities. 
     BACKGROUND 
     Some transactions, such as some in-store or online retail transactions, are fraudulent. For example, a customer may attempt to return an item to a store from which it was not purchased. For example, the item may have been stolen from a different store. As another example, a customer may attempt to return an item with another&#39;s receipt that includes the same or a similar item. In some cases, a customer may present another&#39;s identification (ID) card (e.g., driver&#39;s license) when attempting to return an item. In some cases, a customer may buy and use an item, and may attempt to return the item when the person no longer has a need for the item. 
     In each of these examples, the customer is involved in a fraudulent activity. Fraudulent activities may cause financial harm to a company, such as a retailer. For example, the company may incur expense in accepting the item and returning payment for the item. The company may also incur expenses related to inventorying and stocking the item, attempting to resell the item, returning the item to a manufacturer, or disposing the item. In addition, workers, such as retail workers, must spend time in processing the return, for example. As such, a retailer may benefit from identifying fraudulent transactions before the transaction is complete. 
     SUMMARY 
     The embodiments described herein are directed to automatically identifying fraudulent transactions. The embodiments may identify a fraudulent activity as it is taking place, for example, allowing a retailer to stop or not allow the transaction. For example, the embodiments may allow a retailer to identify a suspected fraudulent activity. The retailer may then more closely scrutinize the transaction to determine if fraud is indeed involved. As a result, the embodiments may allow a retailer to decrease expenses related to fraudulent transactions. 
     In accordance with various embodiments, exemplary systems may be implemented in any suitable hardware or hardware and software, such as in any suitable computing device. For example, in some embodiments, a computing device is configured to receive return data identifying the return of at least one item. For example, the return data may be received from a computing device located at a store as a customer is attempting to return an item. The computing device may also be configured to obtain modified strategy data identifying at least one rule of a modified strategy. The rule may be based on the application of at least one discrete stochastic gradient descent (DSGD) algorithm to an initial strategy. The computing device may be configured to apply the modified strategy to the received return data identifying the return of the at least one item, and determine whether the return of the at least one item is fraudulent based on the application of the modified strategy. The computing device may be further configured to generate fraud data identifying whether the return of the at least one item is fraudulent based on the determination. The computing device may also be configured to transmit, in response to the received return data, the fraud data identifying whether the return of the at least one item is fraudulent. For example, the computing device may transmit the fraud data to the computing device located at the store. 
     In some embodiments, a method is provided that includes receiving return data identifying the return of at least one item. The method may also include obtaining modified strategy data identifying at least one rule of a modified strategy that is based on the application of at least one discrete stochastic gradient descent (DSGD) algorithm to an initial strategy. The method may also include applying the modified strategy to the received return data identifying the return of the at least one item, and determining whether the return of the at least one item is fraudulent based on the application of the modified strategy. The method may further include generating fraud data identifying whether the return of the at least one item is fraudulent based on the determination. The method may also include transmitting, in response to the received return data, the fraud data identifying whether the return of the at least one item is fraudulent. 
     In yet other embodiments, a non-transitory computer readable medium has instructions stored thereon, where the instructions, when executed by at least one processor, cause a computing device to perform operations that include receiving return data identifying the return of at least one item. The operations may also include obtaining modified strategy data identifying at least one rule of a modified strategy that is based on the application of at least one discrete stochastic gradient descent (DSGD) algorithm to an initial strategy. The operations may also include applying the modified strategy to the received return data identifying the return of the at least one item, and determining whether the return of the at least one item is fraudulent based on the application of the modified strategy. The operations may further include generating fraud data identifying whether the return of the at least one item is fraudulent based on the determination. The operations may also include transmitting, in response to the received return data, the fraud data identifying whether the return of the at least one item is fraudulent. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The features and advantages of the present disclosures will be more fully disclosed in, or rendered obvious by the following detailed descriptions of example embodiments. The detailed descriptions of the example embodiments are to be considered together with the accompanying drawings wherein like numbers refer to like parts and further wherein: 
         FIG.  1    is a block diagram of a fraud detection system in accordance with some embodiments; 
         FIG.  2    is a block diagram of the fraud detection computing device of the fraud detection system of  FIG.  1    in accordance with some embodiments; 
         FIG.  3    is a block diagram illustrating examples of various portions of the fraud detection system of  FIG.  1    in accordance with some embodiments; 
         FIG.  4    is a block diagram illustrating examples of various portions of the fraud detection computing device of  FIG.  1    in accordance with some embodiments; 
         FIG.  5    is a flowchart of an example method that can be carried out by the fraud detection system  100  of  FIG.  1    in accordance with some embodiments; 
         FIG.  6    is a flowchart of another example method that can be carried out by the fraud detection system  100  of  FIG.  1    in accordance with some embodiments; and 
         FIG.  7    is an example software listing of an example algorithm that may be executed by the fraud detection computing device of  FIG.  1   . 
     
    
    
     DETAILED DESCRIPTION 
     The description of the preferred embodiments is intended to be read in connection with the accompanying drawings, which are to be considered part of the entire written description of these disclosures. While the present disclosure is susceptible to various modifications and alternative forms, specific embodiments are shown by way of example in the drawings and will be described in detail herein. The objectives and advantages of the claimed subject matter will become more apparent from the following detailed description of these exemplary embodiments in connection with the accompanying drawings. 
     It should be understood, however, that the present disclosure is not intended to be limited to the particular forms disclosed. Rather, the present disclosure covers all modifications, equivalents, and alternatives that fall within the spirit and scope of these exemplary embodiments. The terms “couple,” “coupled,” “operatively coupled,” “operatively connected,” and the like should be broadly understood to refer to connecting devices or components together either mechanically, electrically, wired, wirelessly, or otherwise, such that the connection allows the pertinent devices or components to operate (e.g., communicate) with each other as intended by virtue of that relationship. 
     Turning to the drawings,  FIG.  1    illustrates a block diagram of a fraud detection system  100  that includes a fraud detection computing device  102  (e.g., a server, such as an application server), a server  104  (e.g., a web server), workstation(s)  106 , database  116 , and multiple customer computing devices  110 ,  112 ,  114  operatively coupled over network  118 . Fraud detection computing device  102 , workstation(s)  106 , server  104 , and multiple customer computing devices  110 ,  112 ,  114  can each be any suitable computing device that includes any hardware or hardware and software combination for processing and handling information. In addition, each can transmit data to, and receive data from, communication network  118 . 
     For example, fraud detection computing device  102  can be a computer, a workstation, a laptop, a server such as a cloud-based server, or any other suitable device. Each of multiple customer computing devices  110 ,  112 ,  114  can be a mobile device such as a cellular phone, a laptop, a computer, a table, a personal assistant device, a voice assistant device, a digital assistant, or any other suitable device. 
     Additionally, each of fraud detection computing device  102 , server  104 , workstations  106 , and multiple customer computing devices  110 ,  112 ,  114  can include one or more processors, one or more field-programmable gate arrays (FPGAs), one or more application-specific integrated circuits (ASICs), one or more state machines, digital circuitry, or any other suitable circuitry. 
     Although  FIG.  1    illustrates three customer computing devices  110 ,  112 ,  114 , fraud detection system  100  can include any number of customer computing devices  110 ,  112 ,  114 . Similarly, fraud detection system  100  can include any number of workstation(s)  106 , fraud detection computing devices  102 , servers  104 , and databases  116 . 
     Workstation(s)  106  are operably coupled to communication network  118  via router (or switch)  108 . Workstation(s)  106  and/or router  108  may be located at a store  109 , for example. Workstation(s)  106  can communicate with fraud detection computing device  102  over communication network  118 . The workstation(s)  106  may send data to, and receive data from, fraud detection computing device  102 . For example, the workstation(s)  106  may transmit data related to a return, such as the return of an item, to fraud detection computing device  102 . In response, fraud detection computing device  102  may transmit an indication of whether the return of the item is suspected of being fraudulent. Workstation(s)  106  may also communicate with server  104 . For example, server  104  may be a web server and host one or more web pages, such as a retailer&#39;s website. Workstation(s)  106  may be operable to access and program (e.g., configure) the webpages hosted by server  104 . 
     Fraud detection computing device  102  is operable to communicate with database  116  over communication network  118 . For example, fraud detection computing device  102  can store data to, and read data from, database  116 . Database  116  can be a remote storage device, such as a cloud-based server, a memory device on another application server, a networked computer, or any other suitable remote storage. Although shown remote to fraud detection computing device  102 , in some examples, database  116  can be a local storage device, such as a hard drive, a non-volatile memory, or a USB stick. 
     Communication network  118  can be a WiFi® network, a cellular network such as a 3GPP® network, a Bluetooth® network, a satellite network, a wireless local area network (LAN), a network utilizing radio-frequency (RF) communication protocols, a Near Field Communication (NFC) network, a wireless Metropolitan Area Network (MAN) connecting multiple wireless LANs, a wide area network (WAN), or any other suitable network. Communication network  118  can provide access to, for example, the Internet. 
     First customer computing device  110 , second customer computing device  112 , and N th  customer computing device  114  may communicate with web server  104  over communication network  118 . For example, web server  104  may host one or more webpages of a website. Each of multiple computing devices  110 ,  112 ,  114  may be operable to view, access, and interact with the webpages hosted by web server  104 . In some examples, web server  104  hosts a web page for a retailer that allows for the purchase of items. For example, an operator of one of multiple computing devices  110 ,  112 ,  114  may access the web page hosted by web server  104 , add one or more items to an online shopping cart of the web page, and perform an online checkout of the shopping cart to purchase the items. 
     In some examples, the web page may be operated by a retailer and allow for the initiation of the return of an item. For example, an operator of one of multiple computing devices  110 ,  112 ,  114  may submit information on the web page to return an item. In these examples, web server  104  may transmit data that identifies the attempted return to fraud detection computing device  102 . In response, fraud detection computing device  102  may transmit an indication of whether the attempted return is suspected of being fraudulent. The customer may complete the return of the item by dropping the item off at a retail location of the retailer. In some examples, the customer may complete the return of the item by mailing the item to the retailer. In some examples, the customer may return the item at a service desk at the retail location. 
     Fraud detection system  100  may allow for the identification of activities that may be fraudulent. For example, fraud detection system  100  may identify an attempted in-store return of an item as fraudulent. Fraud detection system  100  may also identify online initiated returns as fraudulent. In some examples, fraud detection system  100  may identify completed returns as fraudulent (e.g., the item has been returned to a retailer and the customer has received payment for the returned item). 
     In some examples, fraud detection system  100  collects a set of training examples and builds a set of features for these examples (e.g., feature engineering). Possible features may include the total amount of a return, the number of items returned, whether or not a receipt is presented, how many returns a particular customer has made over a previous period of time (e.g., in the past few days, etc.). The set of training examples may be based on previous transactions, such as the return of previous items either in-store or online, and are identified (e.g., by a reviewer) as either fraudulent or not fraudulent. For example, fraud instances may be identified as positive (e.g., 1), and non-fraud instances may be identified as negative (e.g., 0). The training examples may be stored in database  116 , for example. 
     Fraud detection computing device  102  may employ a classifier, such as one based on Logistic Regression, Support Vector Machines, Random Forest, or Gradient Boosting Machines. The classifier may be trained with the set of training examples. Based on being trained with the training examples, the classifier may be configured to identify a probability that a provided data set identifying a transaction, such as the return of an item, is fraudulent. 
     Fraud detection computing device  102  may generate a strategy (e.g., one or more rules) that captures the fraud instances of the training examples. The strategy may be a logical expression of the feature space, such as the feature space used to train the classifier. For example, the strategy may include the output of the classifier (e.g., the probability that a particular data set identifying a fraudulent transaction), and/or other conditions, such as conditions identified by human reviewers. For example, the strategy may include a requirement that the output of the classifier be greater than or equal to a threshold amount. In other words, given a feature set “x” provided to the classifier, a strategy (e.g., strategy S) could be as simple as C(x)&gt;0.75, where C is the trained classifier. In this example, to be identified as fraudulent, the output of the classifier must be greater than 0.75. In other words, the classifier, for a particular feature set, determines that the probability that the feature set is associated with fraudulent activity is greater than 75%. 
     The strategy generated by fraud detection computing device  102  may also include required or alternate conditions of the feature set for a particular transaction, such as the requirement that the amount of a return be beyond (e.g., greater than) a threshold amount. For example, a more sophisticated strategy (e.g., strategy S) may be: 
         C ( x )&gt;0.75 OR ( x   1 &gt;30 AND ( x   5 &lt;0.27 OR  x   9 =0)) OR  x   4 &gt;13  eq. (1)
 
     where each x i  is the i-th feature of x. 
     Here, “OR” indicates an alternative condition such that at least one of two conditions must be true for the overall expression to be true, and “AND” indicates a required condition such that both conditions must be true for the overall expression to be true. In this example, a transaction may be identified as fraudulent if one of three conditions are met. Specifically, for the classifier to identify a transaction as fraudulent (e.g., S(x)=true), the output of the classifier must be at least 0.75, the first feature must be greater than 30 and either the fifth feature must be less than 0.27 or the ninth feature must be 0, or the fourth feature must be greater than 13. Each of the conditions may be referred to as the rules of the strategy, were the action space of the strategy may be defined as: 
         A={x∈X|S ( x )=true}  eq. (2).
 
     Based on the initial strategy (e.g., strategy S) and the output of the classifier (e.g., C(x)), fraud detection computing device  102  may generate a modified strategy (e.g., strategy S′). Modified strategy S′ may include a larger “action space” than the initial strategy S. In other words, modified strategy S′ may identify more examples in the training set as fraudulent than the initial strategy S identifies. Modified strategy S′ may be based on the same set of features as in the initial strategy, or a different, yet reduced, set of features. In some examples, the modified strategy is based on applying one or more discrete stochastic gradient descent (DSGD) algorithms to the initial strategy. In some examples, the modified strategy is based on applying one or more dimensionality reduction (DR) algorithms to the initial strategy. In some examples, at least one of each of a DSGD algorithm and DR algorithm is applied. 
     Once the modified strategy is applied, in some examples, the accuracy of the modified strategy is determined. For example, fraud detection computing device  102  may compare the output of the modified strategy (e.g., indicating whether a transaction is fraudulent) to a predetermine determination for the same feature set. In some examples, the classifier may be retrained, and the initial strategy S and modified strategy S′ may be updated based on the retrained classifier. In some examples, the classifier is retrained with training sets, such as refreshed training sets (e.g., by incorporating the output of the modified strategy), and the initial strategy and modified strategy are updated until the modified strategy produces no false positives (e.g., transactions identified by the modified strategy as fraudulent that should not be identified as such). In some examples, the initial strategy and modified strategy are updated until a certain stopping criteria is met (e.g., false positive rate or percentage of transactions that are misclassified are below some threshold value). 
     Once finalized, fraud detection computing device  102  may employ the modified classifier to determine whether in-store or online transactions are fraudulent. For example, upon the attempted return of an item to a store  109 , workstation  106  may transmit data related to the attempted return to fraud detection computing device  102 . Fraud detection computing device  102  may apply the modified strategy to the received data, and determine whether the transaction is should be suspected of being fraudulent (e.g., associated with fraudulent activities). Fraud detection computing device  102  may transmit data indicating whether the attempted return is fraudulent to workstation  106 . If the data indicates that the transaction may be fraudulent, an operator of workstation  106 , such as a retailer&#39;s associate, may undergo precautionary measures to either verify that the transaction is fraudulent, which the associated may then stop, or not fraudulent, which the associate may then allow. On the other hand, if both the initial strategy S and the modified strategy S′ have little or no false positive transactions, fraud detection computing device  102  may deny the attempted return directly, such as be denying a credit card transaction, for example. 
       FIG.  2    illustrates the fraud detection computing device  102  of  FIG.  1   . Fraud detection computing device  102  can include one or more processors  201 , working memory  202 , one or more input/output devices  203 , instruction memory  207 , a transceiver  204 , one or more communication ports  207 , and a display  206 , all operatively coupled to one or more data buses  208 . Data buses  208  allow for communication among the various devices. Data buses  208  can include wired, or wireless, communication channels. 
     Processors  201  can include one or more distinct processors, each having one or more cores. Each of the distinct processors can have the same or different structure. Processors  201  can include one or more central processing units (CPUs), one or more graphics processing units (GPUs), application specific integrated circuits (ASICs), digital signal processors (DSPs), and the like. 
     Processors  201  can be configured to perform a certain function or operation by executing code, stored on instruction memory  207 , embodying the function or operation. For example, processors  201  can be configured to perform one or more of any function, method, or operation disclosed herein. 
     Instruction memory  207  can store instructions that can be accessed (e.g., read) and executed by processors  201 . For example, instruction memory  207  can be a non-transitory, computer-readable storage medium such as a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), flash memory, a removable disk, CD-ROM, any non-volatile memory, or any other suitable memory. 
     Processors  201  can store data to, and read data from, working memory  202 . For example, processors  201  can store a working set of instructions to working memory  202 , such as instructions loaded from instruction memory  207 . Processors  201  can also use working memory  202  to store dynamic data created during the operation of fraud detection computing device  102 . Working memory  202  can be a random access memory (RAM) such as a static random access memory (SRAM) or dynamic random access memory (DRAM), or any other suitable memory. 
     Input-output devices  203  can include any suitable device that allows for data input or output. For example, input-output devices  203  can include one or more of a keyboard, a touchpad, a mouse, a stylus, a touchscreen, a physical button, a speaker, a microphone, or any other suitable input or output device. 
     Communication port(s)  207  can include, for example, a serial port such as a universal asynchronous receiver/transmitter (UART) connection, a Universal Serial Bus (USB) connection, or any other suitable communication port or connection. In some examples, communication port(s)  207  allows for the programming of executable instructions in instruction memory  207 . In some examples, communication port(s)  207  allow for the transfer (e.g., uploading or downloading) of data, such as impression data and/or engagement data. 
     Display  206  can display user interface  205 . User interfaces  205  can enable user interaction with fraud detection computing device  102 . For example, user interface  205  can be a user interface for an application of a retailer that allows a customer to initiate the return of an item to the retailer. In some examples, a user can interact with user interface  205  by engaging input-output devices  203 . In some examples, display  206  can be a touchscreen, where user interface  205  is displayed on the touchscreen. 
     Transceiver  204  allows for communication with a network, such as the communication network  118  of  FIG.  1   . For example, if communication network  118  of  FIG.  1    is a cellular network, transceiver  204  is configured to allow communications with the cellular network. In some examples, transceiver  204  is selected based on the type of communication network  118  fraud detection computing device  102  will be operating in. Processor(s)  201  is operable to receive data from, or send data to, a network, such as communication network  118  of  FIG.  1   , via transceiver  204 . 
       FIG.  3    is a block diagram illustrating examples of various portions of the fraud detection system of  FIG.  1   . In this example, fraud detection computing device  102  receives from a store  109  (e.g., from a computing device, such as workstation  106 , at a store location) return attempt data  324  identifying data associated with the return of an item. Return attempt data  324  may include, for example, one or more of the following: an identification of one or more items being returned; an indication of whether a receipt has been presented; an identification of the customer (e.g., customer ID, passport ID, driver&#39;s license number, etc.); a monetary amount (e.g., price) of each item being returned; the method of payment used to purchase the items (e.g., credit card, cash, check); an item Universal Product Code (UPC) number; an indication of the reason for returning the item (e.g., defect, exchange, etc.); an indication of whether the items are currently in stock; an indication of a time period of when the items where in stock; or any other data related to the return of the items. 
     Fraud detection computing device  102  may process return attempt data  324  to determine feature data relevant to the application of a modified strategy (e.g., strategy S′). For example, fraud detection computing device  102  may parse return attempt data  324  to store relevant feature data  302  in database  116 . Feature data  302  may include any features the modified strategy may take in as an input (e.g., feature set “x”). In this example, feature data  302  includes an amount of return  304 , which may identify the total price of all items being returned, a number of items  306 , which may identify the total number of items being returned, receipt presented  308 , which may identify whether a receipt has been presented for the return, and customer history data  310 . In some examples, fraud detection computing device  102  receives customer history data  310  in return attempt data  324 . Customer history data  310  may include previous purchase data  312  and previous return data  314 . Previous purchase data  312  may identify previous purchase history (e.g., items purchased, date of purchase, price of each item, etc.), while previous return data  314  may identify previous return history (e.g., items returned, dates when returned, amount of each return, etc.). 
     In some examples, fraud detection computing device  102  determines customer history data  310  based on return attempt data  324 . For example, return attempt data  324  may identify a customer ID. The customer ID may be associated with a customer account stored in database  116  (not shown) that includes the customer&#39;s previous transactions. For example, a customer&#39;s previous transactions may include previous purchase history (e.g., items purchased, date of purchase, price of each item, etc.), and previous return history (e.g., items returned, dates when returned, amount of each return, etc.). Based on the customer ID, fraud detection computing device  102  may identify the associated customer account in database  116 , and may obtain data identifying the customer&#39;s previous transactions. 
     Once fraud detection computing device  102  has identified feature data  302 , fraud detection computing device  102  may obtain modified strategy data  316  from database  116 . Modified strategy data  316  may identify one or more rules for the modified strategy. For example, modified strategy data  316  may include data identifying any number of rules, such as first rule data  318 , second rule data  320 , up to N th  rule data  322 . Each of first rule data  318 , second rule data  320 , and up to N th  rule data  322  may identify a rule for modified strategy S′ based on a classifier output requirement (e.g., C(x)&gt;minimum value, C(x)&lt;maximum value), an initial strategy or feature requirement (e.g., x i &gt;minimum value, x i &lt;maximum value), or any combination of any of these requirements (e.g., using “OR” or “AND”). 
     Fraud detection computing device  102  may apply a classifier to the feature set identified by feature data  302 , such as a classifier based on Logistic Regression, Support Vector Machines, Random Forest, or Gradient Boosting Machines, for example. Fraud detection computing device  102  may provide the output of the classifier (which may identify a probability that return attempt data  324  is associated with a fraudulent transaction), and the feature set identified by feature data  302 , to the modified strategy S′ to apply the one or more rules of modified strategy data  316  to determine whether the transaction associated with return attempt data  324  is fraudulent. If, for example, the modified strategy S′ identifies feature data  302  as associated with a fraudulent transaction (e.g., one or more of the rules associated with modified strategy data  316  are satisfied), fraud detection computing device  102  may respond to store  109  with return attempt allowance data  328  indicating that the transaction may be fraudulent. Otherwise, if modified strategy S′ does not identify feature data  302  as being associated with a fraudulent transaction, fraud detection computing device  102  may respond to store  109  with return attempt allowance data  328  indicating that the transaction is not fraudulent. 
     In some examples, fraud detection computing device  102  may receive digital return initiation data  326 , indicating an online initiation of a return of an item. For example, an operator of customer computing device  112  may initiate the return of an item on a web site for a retailer hosted on web server  104 . Digital return initiation data  326 , similar to return attempt data  324 , may identify data associated with the return of the item. Digital return initiation data  326  may include, for example, one or more of the following: an identification of one or more items being returned; an indication of a digital receipt for the item; an identification of the customer (e.g., online customer ID, driver&#39;s license number, etc.); a monetary amount (e.g., price) of each item being returned; the method of payment used to purchase the items (e.g., credit card); an item Universal Product Code (UPC) number; an indication of the reason for returning the item (e.g., defect, exchange, etc.); an indication of whether the items are currently in stock; an indication of a time period of when the items where in stock; or any other data related to the return of the items. 
     Fraud detection computing device  102  may process digital return initiation data  326  to determine feature data relevant to the application of a modified strategy (e.g., strategy S′). For example, fraud detection computing device  102  may parse digital return initiation data  326  to store relevant feature data  302  in database  116 . Feature data  302  may include any features the modified strategy may take in as an input (e.g., feature set “x”). 
     Fraud detection computing device  102  may then apply the classifier to the feature set identified by feature data  302 . Fraud detection computing device  102  may provide the output of the classifier (which may identify a probability that return attempt data  324  is associated with a fraudulent transaction), and the feature set identified by feature data  302 , to the modified strategy S′ to apply the one or more rules of modified strategy data  316  to determine whether the transaction associated with return attempt data  324  is fraudulent. If, for example, the modified strategy S′ identifies feature data  302  as associated with a fraudulent transaction (e.g., one or more of the rules associated with modified strategy data  316  are satisfied), fraud detection computing device  102  may respond to customer computing device  112  with return initiation allowance data  330  indicating that the transaction may be fraudulent. Otherwise, if modified strategy S′ does not identify feature data  302  as being associated with a fraudulent transaction, fraud detection computing device  102  may respond to customer computing device  112  with return initiation allowance data  330  indicating that the transaction is not fraudulent. 
     As indicated in the figure, customer computing device  112  may present a website  302  on display  206 . In some examples, display  206  may be a touchscreen display. Website  302  may be a retailer&#39;s website, such as one hosted by server  104 . Website  302  includes a search bar  304 , which allows a user to search the retailer&#39;s website based on input provided to the search bar  304 . The input may include, for example, one or more search terms. A user may provide the input with the use of, for example, I/O device  203 . The user may initiate a search request  306  by providing the input to the search bar  304  and selecting the “Submit” icon  308 . The search request  306  may include the one or more search terms provided by the user. 
       FIG.  4    is a block diagram illustrating examples of various portions of the fraud detection computing device  102  of  FIG.  1   . As indicated in the figure, fraud detection computing device  102  includes classifier engine  402 , initial strategy engine  404 , strategy expansion engine  406 , discrete stochastic gradient descent (DSGD) engine  408 , and dimensionality reduction (DR) engine  410 . In some examples, one or more of classifier engine  402 , initial strategy engine  404 , strategy expansion engine  406 , discrete stochastic gradient descent (DSGD) engine  408 , and dimensionality reduction (DR) engine  410  may be implemented in hardware. In some examples, one or more of classifier engine  402 , initial strategy engine  404 , strategy expansion engine  406 , discrete stochastic gradient descent (DSGD) engine  408 , and dimensionality reduction (DR) engine  410  may be implemented as an executable program maintained in a tangible, non-transitory memory, such as instruction memory  207  of  FIG.  2   , that may be executed by one or processors, such as processor  201  of  FIG.  2   . 
     Classifier engine  402  may be operable to obtain training data  420  from database  116  so that the employed classifier may be trained. Training data  420  may include, for example, fraud activity data  422  that identifies data associated with fraudulent transactions (as determined, for example, by a human reviewer), and non-fraud activity data  424  that identifies data associated with non-fraudulent transactions. Classifier engine  402  may be based on a supervised learning algorithm such as Logic Regression, Support Vector Machines, Random Forest, Gradient Boosting Machines, or any other suitable learning algorithm (e.g., machine learning algorithm). 
     Once classifier engine  402  is trained, classifier engine  402  may determine class data  412  for a particular transaction example of training data  420 . Class data  412  identifies the class of a transaction example of training data  420 . For example, class data  412  may identify each transaction as fraudulent, or not fraudulent. Classifier engine  402  may also determine fraud probability data  414 , which identifies a probability that a transaction is fraudulent. For example, classifier engine  402  may determine a probability that a particular transaction example of training data  420  is fraudulent. 
     Initial strategy engine  404  may obtain class data  412  and fraud probability data  414  from classifier engine  402 , and transaction data  420  from database  116 , for one or more transactions to generate an initial strategy (e.g., initial strategy S). For example, initial strategy engine  404  may parse feature data from fraud activity data  422  and non-fraud activity data  424 . Based on the parsed feature data and fraud probability data  414  (e.g., C(x)), initial strategy engine  404  may generate an initial strategy. The generated initial strategy may be, for example, the strategy defined in equation 1 described above. In some examples, a user adjusts a rule of the initial strategy, such as editing a rule, providing a new rule, or deleting a rule, by providing input. For example, the user may provide input via I/O device  203  to fraud detection computing device  102  to adjust the initial strategy. Initial strategy engine  404  generates strategy data  416  which identifies and characterizes the rules for the initial strategy. Strategy data  416  may identify and characterize, for example, a classifier requirement (e.g., C(x)&lt;maximum value, C(x)&gt;minimum value), a feature requirement (e.g., x i &lt;maximum value, x i &gt;minimum value), or any other suitable strategy rule. 
     Strategy expansion engine  406  obtains strategy data  416  from initial strategy engine  404 , and generates a modified strategy, which is identified and characterized by modified strategy data  316 . The modified strategy may be generated based on the same set of features used to generate the initial strategy as identified by strategy data  416 , or may be based on a different set of features, as identified by training data  420 . In some examples, the modified strategy is based on the application of one or more discrete stochastic gradient descent (DSGD) algorithms by DSGD engine  408 . In some examples, the modified strategy is based on the application of one or more dimensionality reduction (DR) algorithms by DR engine  410 . In some examples, the modified strategy is based on one or more DR algorithms by DSGD engine  408 , and one or more DR algorithms by DR engine  410 . For example, the one or more DR algorithms by DSGD engine  408 , and the one or more DR algorithms by DR engine  410 , may be complementary to each other. In some examples, strategy expansion engine  406  determines whether to employ a DSGD algorithm, a DR algorithm, or both based on user input. For example, user interface  205  may provide a selection (e.g., enable/disable buttons) of any number of algorithms. 
     DSGD engine  408  may obtain strategy data  416  and execute a discrete stochastic gradient descent (SGD) algorithm to generate a new strategy, which may be an optimized version of the initial strategy generated by initial strategy engine  404 . For example, the new strategy may include more rules that are more relaxed than the rules for the initial strategy. For example, suppose initial strategy engine  404  generates an initial strategy S as: 
         C ( x )&gt;0.75 OR ( x   1 &gt;30 AND ( x   5 &lt;0.27 OR  x   9 =0)) OR  x   4 &gt;13  eq. (3)
 
     After running an SGD algorithm, a new strategy S′ may be: 
         C ( x )&gt;0.685 OR ( x   1 &gt;27 AND ( x   5 &lt;0.27 OR  x   9 =0)) OR  x   4 &gt;12  eq. (4)
 
     While in this example the structure of the strategy remains the same, the decision boundaries (i.e., threshold values such as 0.75 in (3) and 0.685 in (4)) are modified or relaxed. In other words the rules (e.g., conditions) in strategy S′ are less restrictive than in the initial strategy S, thereby providing a larger action space in new strategy S′ than in initial strategy S. DSGD engine  408  may generate optimal threshold values for the action space expansion in new strategy S′ as follows. 
     DSGD engine  408  may assign θ 1 , θ 2 , . . . , θ k  to be the set of all numerical thresholds for inequalities in the initial strategy S. For example, in the above initial strategy (3), θ 1 =0.75, θ 2 =30, θ 3 =0.27, and θ 4 =13. In this example, there is no threshold assigned for the x 9  term because there is not an inequality (rather, x 9 =0). DSGD engine  408  assigns θ=(θ 1 , θ 2  . . . , θ k ) to be the vector of all thresholds in the strategy, and assigns S θ  to be the strategy whose thresholds are set to θ. DSGD engine  408  may assign D to denote the training set, such as training data  420 , and DSGD engine  408  assigns A D  (S θ ) to denote the subset of the training set D that are rejected (e.g., associated with a fraudulent transaction) by strategy S θ , i.e.: 
         A   D ( S   θ )={ x∈D|S   θ ( x )=true}  eq. (5)
 
     Given initial strategy S and classifier output C, DSGD engine  408  may optimize the initial strategy S according to the object function below: 
     
       
         
           
             
               
                 
                   
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     where “c” is a parameter representing a threshold probability of a fraudulent transaction. 
     The parameter “c” may be specified by a user, for example, via user interface  205  using I/O device  203 . The optimization equations in (6) and (7) attempt to maximize the action space of the initial strategy while maintain a sufficiently high average fraud probability, as identified by parameter “c.” 
     During training, in lieu of updating all thresholds simultaneously, DSGD engine  408  modifies one threshold at a time while holding all others constant. In addition, DSGD engine  408  assigns each threshold an individual learning rate. At each iteration, DSGD engine  408  updates the threshold that renders the highest average bad probability (e.g., fraudulent probability). Depending on the complexity of the strategy and learning rate design, the learning duration varies. Eventually, the learning process either converges to an optimal threshold subject to the constraints in equation (6) or terminates when a stopping criteria is met. The stopping criteria may be, for example, when an individual learning rate is less than a threshold value, or when a maximum number of learning iterations (e.g., epochs) have been executed. 
     Specifically, DSGD engine  408  generates a learning rate a i  for each threshold θ i  where the absolute value for each a i  is given as a function a of the strategy variable (e.g., feature) on which θ i  acts on. The sign of α i  depends on the direction of the inequality that immediately precedes (acts on) θ i  in the strategy. For example, if an inequality is “greater than” or “greater than or equal to” (e.g., &gt; or ≥),” then a i  is positive. Otherwise, if an inequality is “less than” or “less than or equal to” (e.g., &lt; or ≤),” then of α i  is negative. 
     For example, taking the initial strategy defined in equation (3) above, DSGD engine  408  may generate learning rates of α 1 =σ(C(x)), α 2 =σ(x 1 ), α 3 =−σ(x 5 ), α 4 =σ(x 4 ), where σ stands for the standard deviation of the acting variable (e.g., feature) calculated based on the training set (e.g., training data  420 ). DSGD engine  408  may also generate a minimum value δ i  for each learning rate α i . In some examples, if θ i  is an integer, DSGD engine  408  assigns δ i =1. Otherwise, DSGD engine  408  may assign δ i  to a small positive real number, such as 10 −5 . 
     Given a vector of thresholds θ=(θ 1 , . . . , θ k ) and the corresponding vector of learning rates α=(α 1 , . . . , α k ). For each i=1, . . . , k, DSGD engine  408  assigns θ i ′=(θ i , . . . , θ i −α i , . . . , θ k ). That is, θ i ′ is a copy of θ except that the i th  entry, θ i , is changed to θ i −α i . Given a training data set D, DSGD engine  408  calculates a gain for the i th  dimension (with respect to training set D) as: 
     
       
         
           
             
               
                 
                   
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     The gain for each i th  dimension indicates a change in average bad probability of the action space after the i th  dimension value is changed from θ i  to θ i −α i . DSGD engine  408  evaluates, for each iteration, the gains of all thresholds θ 1 , . . . , θ k  according to equation (8), and updates the threshold θ i  whose partial derivative is the largest. For example, for the threshold θ i  with the largest gain ∂ i , θ i  is updated with θ i −α i  (e.g., θ=(θ 1 , . . . , θ k ) is updated to become θ i ′=(θ 1 , . . . , θ i −α i , . . . , θ k ). 
     Additionally, DSGD engine  408  updates the learning rates α i , where i=1, . . . , k. That is, if a learning rate is too large such that the optimization constraint is violated (i.e., after updating the threshold, the new average bad probability is lower than parameter “c”), DSGD engine  408  shrinks α i  linearly or exponentially. However, DSGD engine  408  may stop optimizing θ i  when α i  is too small and can be ignored, e.g., α i &lt;δ i . This is because there is not much room for improvement if the learning rate becomes negligible. DSGD engine  408  will continue to optimize thresholds in this manner until every threshold has been optimized, or until the stopping criteria is met.  FIG.  7    shows a software listing in the form of pseudo code describing the above described DSGD algorithm. The software listing illustrates a factor ‘e’ which is employed to shrink learning rate α i . In addition, δ i  is a threshold value to prevent learning rate a i  from becoming too small to be negligible. For example, one may set e to 2 and δ i  to 1 or 10 −5  as indicated above. 
     DR engine  410  may obtain strategy data  416  and execute a dimensionality reduction (DR) algorithm to generate a new strategy, which may be an extension to or an optimized version of the initial strategy generated by initial strategy engine  404 . DR engine  410  produces a new strategy S″ whose action space is a super set of the action space of an input strategy (e.g., initial strategy S). For example, suppose the input strategy is the strategy defined in equation 3 above. After executing the dimensionality reduction algorithm, the new strategy S″ may become: 
         C ( x )&gt;0.685 OR ( x   1 &gt;27 AND ( x   5 &lt;0.27)) OR  x   4 &gt;13  eq. (9)
 
       or 
         C ( x )&gt;0.75 OR ( x   1 &gt;30) AND  x   3 &gt;0.25  eq. (10)
 
     In the strategy defined by equation (9) the existing features/variables have been reduced from five in the initial strategy to four in the new strategy while keeping the thresholds the same or slightly modified. The new strategy is less restrictive than the input strategy and thereby enjoys a larger action space. However, in the strategy defined by equation (10), not only is the existing feature set reduced from five to three, but some existing features are replaced with new ones (e. g., x 3 ). The new features defined by equation (10) may identify an action space that is either adjacent to or distant from the initial space defined by the initial strategy. In that regard, DR engine  410  identifies the key (e.g., predominant) features from the input strategy and uses them to compose a new set of strategies. As such, the new strategy S″ may have a different structure than the input strategy. 
     The dimensionality reduction algorithm that DR engine  410  executes may employ the steps of feature selection, feature transformation, separation factor, and feature importance factor. 
     01 Feature Selection (Fs) 
     At the feature selection step, a training data set is prepared with all the features (X1, X 2 , X 3  . . . . X n ) extracted from the existing strategies (e.g., such as an initial strategy that may include the output of a classifier) and class/tagging/labels (e.g., the identification of whether a particular transaction is good or bad, e.g., fraudulent). The training data set may be stored in database  116 , for example. Next, DR engine  410  employs a federated feature selection approach by polling recommendations from various feature selection algorithms such as filter methods, wrapper methods such as recursive feature elimination algorithms, and embedded methods such as regularization techniques. For example, DR engine  410  may select the top five features recommended by each algorithm, or a subset of features that make to the top 50 percent of features as ranked by each algorithm. In some examples, a user selects the selection criteria from user interface  205  using an I/O device  203 . In some examples, DR engine  410  selects a maximum number of features, such as the top few features from each algorithm. DR engine  410  then proceeds to the next step—feature transformation. 
     02 Feature Transformation (Ft) 
     At this step, DR engine  410  discretizes and normalizes the features selected at the feature selection step through one or more binning algorithms. The binning algorithms may be, for example, feature scaling and normalization, weight of the evidence, variations of principal component analysis (PCA), or any other suitable binning algorithm. In some examples, a user selects the number of bins and the underlying binning algorithm, for example, from user interface  205  using an I/O device  203 . The output of the binning algorithm may be a numeric (real) value ranging between 0 and 1. The transformed features (i.e., as transformed by the binning algorithm) may be denoted by X j   i  where: 
         X   j   i ∈[0,1]  eq. (11)
 
     where: 
     i=1, . . . , k (number of bins), and 
     j=1, . . . , n (number of features) 
     DR engine  410  then proceeds to the next step—separation factor. 
     03 Separation Factor (Fsf) 
     At this step, the transformed features from the feature transformation step are weighted based on characteristics of the transactions (e.g., a type of transaction) the transformed features are associated with. For example, to create a wider separation effect between good (e.g., not fraudulent) and bad (e.g., fraudulent) transactions, DR engine  410  may weigh the transformed features based on whether they are associated with a good, or bad, transaction. DR engine  410  generates a Multiplication Factor or Index M j   i  for the normalized features. M j   i  is defined as the bad (e.g., fraudulent) rate of i th  bin for any normalized feature Xj. DR engine  410  calculates M j   i  as follows: 
         M   j   i =(Total number of bad class/labels in the  i   th  bin of feature  Xj +σ)/(Total number of records in the  i   th  bin of feature  Xj +σ)  eq. (12)
 
     where σ is a small positive real number (i.e., 10 −5 ) and M j   i ∈(0,1]. 
     Thus, feature bins with better odds ratios (probability of good over probability of bad) than others will have higher Multiplication Factors. In other words, in those feature bins with high Multiplication Factors, the transactions labelled as bad (e.g., fraudulent transactions) are better separated from the transactions labelled as good (e.g., non-fraudulent transactions). DR engine  410  then proceeds to the next step—feature importance factor. 
     04 Feature Importance Factor (Fif) 
     At this step, DR engine  410  generates a feature importance factor to determine which features are more indicative of a fraudulent transaction. The feature importance factors may be determined, for example, by execution of the equation below: 
         F   j =Σ i=0   k   X   j   i   *M   j   i   eq. (13)
 
     In some examples, the feature importance factors must meet a requirement. For example, the feature importance factors may need to meet a minimum importance factor requirement (i.e., Fj&gt;0.125 for j=1, . . . , n), or they may need to meet a varying importance factor requirement (i.e., F 1 &gt;0, F 2 &gt;0.5, . . . etc.). The requirements may be specified by a user, for example, by using I/O device  203  to input requirements into user interface  205 . In some examples, two or more features are combined, where they must meet one or more of an upper bound requirement and a lower bound requirement. For example, equations (14) and (15) below show two such combinations: 
       0.75&lt; F   1   +F   3   +F   7 &lt;1  eq. (14)
 
       0&lt; F   7   +F   9 &lt;1.5  eq. (15)
 
     where, in addition, the following importance factor requirements must be met: 
       0.15&lt; F   1 &lt;1 
       0.2&lt; F   3 &lt;0.65 
       0&lt; F   7 &lt;1 
       0&lt; F   9 &lt;1 
     For every existing strategy, DR engine  410  may generate one or more linear inequalities that comprise relevant features, such as: 
         I   j   *F   j   |I   j =1 if  F   j  is selected (e.g., equations (14) and (15) are satisfied),  I   j =0 otherwise, for  j= 1, . . . , n   eq. (16)
 
     DR engine  410  may then determine a minimal set of predominant features that still satisfy one or more linear inequalities, such as those exemplified in equations (14) and (15), where I j =1 if F j  is selected, and I j =0 otherwise. If I j  is 0, then that particular feature cannot be used to satisfy the rule. 
     For example, DR engine  410  may solve the Integer Programming model as shown in the equation below: 
       Min Σ j=0   n   I   j   eq. (17)
 
     In this example, to satisfy the one or more inequalities shown in equations (14) and (15), the following equations would need to be satisfied: 
       0.75&lt; I   1   F   1   +I   3   F   3   +I   7   F   7 &lt;1  eq. (18)
 
       0&lt; I   7   F   7   +I   9   F   9 &lt;1.5  eq. (19)
 
     where I j ∈{0,1}. 
     Once the minimal set of predominant features are determined, DR engine  410  may generate a new strategy S′ identified and characterized by modified strategy data  316  that either complements or replaces the existing strategy S. The new strategy S′ may have different threshold values, a streamlined structure, and/or new features compared to the original strategy S. As such, strategy S′ expands the action space defined by the original strategy to detect additional fraudulent activities. 
       FIG.  5    is a flowchart of an example method  500  that can be carried out by the fraud detection system  100  of  FIG.  1   . Beginning at step  502 , a computing device, such as fraud detection computing device  102 , receives return attempt data, such as return attempt data  324 , identifying and characterizing the return of item. The return attempt data may be received, for example, from store  109 . At step  504 , the computing device obtains modified strategy data, such as modified strategy data  316  from database  116 , identifying and characterizing at least one rule of a modified strategy. Proceeding to step  506 , the return attempt data is parsed to determine feature data that is relevant to the modified strategy. For example, the return attempt data is parsed to extract feature data that may be used by any rule of the modified strategy. At step  508 , the modified strategy is executed based on the parsed data and the at least one rule of the modified strategy. Based on the execution of the modified strategy, at step  510  a determination is made as to whether the return of the item is fraudulent. At step  512 , return attempt data identifying whether the return is fraudulent is transmitted. For example, the return attempt data may be transmitted to store  109 . 
       FIG.  6    is a flowchart of another example method  600  that can be carried out by the fraud detection system  100  of  FIG.  1   . At step  602 , a computing device, such as fraud detection computing device  102 , obtains training data identifying and characterizing a plurality of transactions. For example, fraud detection computing device  102  may obtain training data  420  from database  116 . At step  604 , a classifier is trained based on the training data. The classifier may be may be based on a supervised learning algorithm such as Logic Regression, Support Vector Machines, Random Forest, Gradient Boosting Machines, or any other suitable learning algorithm, for example. At step  606 , an initial strategy is generated based on one or more of the outputs of the trained classifier and the training data. For example, the initial strategy may be generated by initial strategy engine  404  and may include one or more rules, where each rule may require the output of the classifier, or a feature of a transaction (as identified by the training data), to be beyond (e.g., greater than, less than, etc.) a threshold. 
     Proceeding to step  608 , an intermediate strategy is generated based on applying at least one discrete stochastic gradient descent (DSGD) algorithm to the output of the trained classifier and the initial strategy. For example, DSGD engine  408  may apply on one or more discrete stochastic gradient descent algorithms to strategy data  416 . At step  610 , a new strategy is generated based on applying at least one dimensionality reduction (DR) algorithm to the output of the trained classifier and the intermediate strategy. For example, DR engine  410  may apply one or more dimensionality reduction algorithms to a strategy generated by DSGD engine  408  to provide modified strategy data  316 . 
     At step  612 , a determination is made as to whether all fraudulent transactions of the transaction data were identified as fraud by the new strategy. For example, each transaction of the training data may be identified as fraudulent or not. Fraud detection computing device  102  may compare the fraud identification of each transaction to a fraud determination based on the new strategy. If any transactions that should have been determined to be fraud are not identified as such by the new strategy, the method proceeds back to step  602 , where the classifier is re-trained. Otherwise, the method ends. 
     Although the methods described above are with reference to the illustrated flowcharts, it will be appreciated that many other ways of performing the acts associated with the methods can be used. For example, the order of some operations may be changed, and some of the operations described may be optional. 
     In addition, the methods and system described herein can be at least partially embodied in the form of computer-implemented processes and apparatus for practicing those processes. The disclosed methods may also be at least partially embodied in the form of tangible, non-transitory machine-readable storage media encoded with computer program code. For example, the steps of the methods can be embodied in hardware, in executable instructions executed by a processor (e.g., software), or a combination of the two. The media may include, for example, RAMs, ROMs, CD-ROMs, DVD-ROMs, BD-ROMs, hard disk drives, flash memories, or any other non-transitory machine-readable storage medium. When the computer program code is loaded into and executed by a computer, the computer becomes an apparatus for practicing the method. The methods may also be at least partially embodied in the form of a computer into which computer program code is loaded or executed, such that, the computer becomes a special purpose computer for practicing the methods. When implemented on a general-purpose processor, the computer program code segments configure the processor to create specific logic circuits. The methods may alternatively be at least partially embodied in application specific integrated circuits for performing the methods. 
     The foregoing is provided for purposes of illustrating, explaining, and describing embodiments of these disclosures. Modifications and adaptations to these embodiments will be apparent to those skilled in the art and may be made without departing from the scope or spirit of these disclosures.