Patent Publication Number: US-11036824-B2

Title: Systems and methods for converting discrete wavelets to tensor fields and using neural networks to process tensor fields

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This is a continuation of U.S. application Ser. No. 16/549,557, filed Aug. 23, 2019, which is a division of U.S. application Ser. No. 15/892,407, filed Feb. 8, 2018, both of which are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates generally to the field of neural networks. More specifically, and without limitation, this disclosure relates to systems and methods for using neural networks to process discrete tensor fields. 
     BACKGROUND 
     Extant methods of risk detection rely on rule-based determinations, decision trees, or artificial neural networks. However, each extant method suffers from shortfalls. For example, rule-based determinations tend to have high error rates, which are inconvenient for financial markets. Although decision trees may have lower error rates than rule-based determinations, they often rely on manual verification along one or more branches, as well as increasing complexity and processing resources. Finally, artificial neural networks fail to recognize many patterns and exponentially increase resource drain as the number of hidden neuron layers increases linearly. 
     Moreover, extant rules, trees, and neural networks must be implemented separately. This both reduces processing efficiency and requires further resource drain and algorithmic complexity to handle disparate results from the rules, trees, and networks. 
     Additionally inefficiencies inhere in the storage of discrete data representing transactions. This discrete data is generally stored in a relational database or a graph database. The former relies on resource-costly searches and concatenations while the latter relies on exponentially costly nodal traversals. 
     SUMMARY 
     In view of the foregoing, embodiments of the present disclosure provide systems and methods for constructing and using wavelet databases to predict risk through neural networks. 
     As used herein, “database” refers to a “data space,” which is a tertiary database that uses in-process RAM dictionaries, a shared memory data cache, a multi-process/multi-server object cache, and one or more common databases (e.g., a Structured Query Language (SQL) database) and/or Binary Large Objects (BLOBs). 
     According to an example embodiment of the present disclosure, a system for detecting anomalies within a database comprising discrete wavelets may comprise one or more memories storing instructions and one or more processors configured to execute the instructions. The instructions may include instructions to receive a new wavelet, convert the wavelet to a tensor using an exponential smoothing average, calculate a difference field between the tensor and a field having one or more previous wavelets represented as tensors, perform a weighted summation of the difference field to produce a difference vector, apply one or more models to the difference vector to determine a likelihood of the new wavelet representing an anomaly, and add the new wavelet to the field when the likelihood is below a threshold. 
     In another embodiment, a system for training a deep field network to detect anomalies within a database comprising discrete wavelets may comprise one or more memories storing instructions and one or more processors configured to execute the instructions. The instructions may include instructions to receive a plurality of transactions, convert each transaction to a corresponding wavelet, group the plurality of wavelets and corresponding tensors by coefficients included in the wavelets, train a neural network for each group independently of other groups, and integrate the neural networks into a deep field network. 
     In another embodiment, a system for authorizing a transaction using cascading discrete wavelets may comprise one or more memories storing instructions and one or more processors configured to execute the instructions. The instructions may include instructions to receive a new transaction, convert the new transaction to a wavelet, convert the wavelet to a tensor using an exponential smoothing average, calculate a difference field between the tensor and a field having one or more previous transactions represented as tensors, perform a weighted summation of the difference field to produce a difference vector, apply one or more models to the difference vector to determine a likelihood of the transaction being high risk, and authorize the new transaction when the likelihood is below a threshold. 
     Any of the alternate embodiments for disclosed systems for indexing and restructuring a headshot database for a user may apply to disclosed non-transitory computer-readable media storing instructions for indexing and restructuring a headshot database for a user. 
     It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not restrictive of the disclosed embodiments. 
     Further, by employing the unconventional training disclosed herein, a deep field network may be trained to function with greater efficiency and accuracy than extant neural networks as well as trained to operate on a wavelet database rather than a relational or graph database. In addition, by employing the unconventional deep field network disclosed herein, more accurate and efficient detection of anomalies may be performed than by using extant rule-based systems, decision trees, or neural networks. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which comprise a part of this specification, illustrate several embodiments and, together with the description, serve to explain the principles disclosed herein. In the drawings: 
         FIG. 1  is a diagram of a wavelet, according to an exemplary embodiment of the present disclosure. 
         FIG. 2A  is a block diagram of a filter bank, according to an exemplary embodiment of the present disclosure. 
         FIG. 2B  is a graphical representation of the exemplary filter bank of  FIG. 2A . 
         FIG. 3  is a diagram of a convolutional-accumulator, according to an exemplary embodiment of the present disclosure. 
         FIG. 4  is a graphical representation of exponential smoothing coefficients, according to an exemplary embodiment of the present disclosure. 
         FIG. 5  is a block diagram of tensor extrapolation from wavelets, according to an exemplary embodiment of the present disclosure. 
         FIG. 6  is a graphical representation of a manifold, according to an exemplary embodiment of the present disclosure. 
         FIG. 7  is a graphical representation of an atlas mapping a manifold to a linear space, according to an exemplary embodiment of the present disclosure. 
         FIG. 8  is a diagram of a Galois connection, according to an exemplary embodiment of the present disclosure. 
         FIG. 9  is a diagram of an exemplary artificial neural network. 
         FIG. 10A  is a block diagram of an exemplary system for detecting anomalies within a database comprising discrete wavelets, according to an exemplary embodiment of the present disclosure. 
         FIG. 10B  is a block diagram of another exemplary system for detecting anomalies within a database comprising discrete wavelets, according to an exemplary embodiment of the present disclosure. 
         FIG. 10C  is a block diagram of an exemplary workflow for detecting high risk transactions using a database comprising discrete wavelets, according to an exemplary embodiment of the present disclosure. 
         FIG. 10D  is a block diagram of an exemplary workflow for constructing and using a database comprising discrete wavelets, according to an exemplary embodiment of the present disclosure. 
         FIG. 11  is a diagram of an example of training a deep field network to detect anomalies within a database comprising discrete wavelets, according to an exemplary embodiment of the present disclosure. 
         FIG. 12  is a flowchart of an exemplary method for detecting anomalies within a database comprising discrete wavelets, according to an exemplary embodiment of the present disclosure. 
         FIG. 13  is a flowchart of an exemplary method for training a deep field network to detect anomalies within a database comprising discrete wavelets, according to an exemplary embodiment of the present disclosure. 
         FIG. 14  is a flowchart of an exemplary method for authorizing a transaction using cascading discrete wavelets, according to an exemplary embodiment of the present disclosure. 
         FIG. 15  is a block diagram of an exemplary computing device with which the systems, methods, and apparatuses of the present disclosure may be implemented. 
     
    
    
     DETAILED DESCRIPTION 
     The disclosed embodiments relate to systems and methods for detecting anomalies within a database comprising discrete wavelets, training a deep field network to detect anomalies within a database comprising discrete wavelets, and authorizing a transaction using cascading discrete wavelets. Embodiments of the present disclosure may be implemented using a general-purpose computer. Alternatively, a special-purpose computer may be built according to embodiments of the present disclosure using suitable logic elements. 
     As used herein, “deep field network” refers to one or more trained algorithms integrated into a prediction schema. In some embodiments, deep field networks may be applied to a multi-nodal manifold converted differential field, e.g., determined based on the difference between a wavelet converted to a tensor and a field of existing (e.g., previous) tensors. 
     Disclosed embodiments allow for efficient and accurate detection of anomalies within a wavelet database. Additionally, embodiments of the present disclosure allow for efficient and accurate authorization of transactions using a wavelet database. Furthermore, embodiments of the present disclosure provide for greater flexibility and accuracy than extant anomaly detection techniques, such as rule-based determinations, decision trees, and neural networks. 
     According to an aspect of the present disclosure, a processor may receive a new wavelet. As used herein, the term “wavelet” refers to any data that may be represented as a brief oscillation. The wavelet need not be received in the form of an oscillation but may be represented in any appropriate form (e.g., an array, a digital signal, or the like). The wavelet may be received from one or more memories (e.g., a volatile memory such as a random access memory (RAM) and/or a non-volatile memory such as a hard disk) and/or across one or more computer networks (e.g., the Internet, a local area network (LAN), or the like). Alternatively, the processor may receive data and convert the data into a wavelet. For example, the processor may receive a transaction having associated properties (such as time, location, merchant, amount, etc.) and may convert the transaction into a wavelet or into an array or other format that represents a wavelet. 
     The processor may convert the wavelet to a tensor. For example, a tensor may represent an array that satisfies one or more mathematical rules (for example, a tensor may be a multi-dimensional array with respect to one or more valid bases of a multi-dimensional space). 
     In some embodiments, the processor may convert the wavelet to a tensor using a moving average. For example, a simple moving average, a cumulative moving average, a weighted moving average, or the like, may be used to convert the wavelet to a tensor. In certain aspects, the processor may convert the wavelet to a tensor using an exponential smoothing average. By using an exponential smoothing average, the natural base e may be incorporated into the smoothing. Because e represents the limit of compound interest, the smoothed wavelet may be easier to identify as anomalous within a financial market. Accordingly, the processor may perform a discrete wavelet transform with an exponential smoothing average accumulator to transform the received wavelet into a tensor. 
     The processor may calculate a difference field between the tensor and a field having one or more previous wavelets represented as tensors. For example, the field may have been previously constructed as explained above. That is, the processor may perform a discrete wavelet transform with an exponential smoothing average accumulator to transform the one or more previous wavelets into tensors. The processor may then obtain the field by mapping the tensors onto a manifold (e.g., a differential manifold). One or more atlases may be used in order to do so. Alternatively, the processor may receive the tensors (e.g., from one or more memories and/or over one or more computer networks) and construct the field therefrom or may receive the field directly (e.g., from one or more memories and/or over one or more computer networks). 
     In some embodiments, the difference field may represent a tensor product of fields (i.e., between a field having only the tensor and the field having the one or more previous wavelets represented as tensors). Accordingly, the difference field may represent a Galois connection between the tensor and the field. 
     The processor may perform a weighted summation of the difference field to produce a difference vector. For example, the coefficient weights may be derived from training of one or more particular models. For example, the processor may apply a variety of models in the weighting, such as models trained for particular identifiers (e.g., particular accounts, particular persons, particular merchants, particular institutions, etc.), particular times (e.g., time of day, time of year, etc.), particular locations (e.g., particular country, particular city, particular postal code, etc.), or the like. 
     Additionally or alternatively, the summation may include a notch filter. Accordingly, particular frequencies may be filtered out during the summation. For example, the processor may apply one or more particular models to determine which particular frequencies to filter out. The one or more filter models may be the same models as the one or more weighting models or may be different models. 
     In some embodiments, an absolute or a squaring function may be applied. Alternatively, the weighted summation may produce a directional difference vector. Accordingly, the difference vector may include a direction of the difference as well as a magnitude of the difference. This additional information may improve accuracy of the anomaly detection. For example, a large difference vector pointing in an expected direction may be less anomalous than a small difference vector pointing in an unexpected direction. 
     The processor may apply one or more models to the difference vector to determine a likelihood of the new wavelet representing an anomaly. For example, the one or more likelihood models may be the same models as the one or more filter models and/or the one or more weighting models or may be different models. In embodiments having direction as well as magnitude, the one or more models may use the magnitude and direction of the difference vector to determine the likelihood. As used herein, “likelihood” may refer to a percentage (e.g., 50%, 60%, 70%, etc.), a set of odds (e.g., 1:3, 1 in 5, etc.), a score (e.g., 1 out of 5, 5.6 out of 10.0, etc.), an indicator (e.g., “not likely,” “likely,” “very likely,” etc.), or the like. 
     Based on the likelihood, the processor may either add the new wavelet to the field or reject the new wavelet. For example, the processor may add the new wavelet to the field when the likelihood is below a threshold. If the processor rejects the new wavelet, the processor may send a notification to such effect. For example, the processor may send a rejection signal or a message indicating the likelihood and/or a reason (e.g., based on the one or more models) for rejection. The processor may send the notification to one or more parties associated with the new wavelet (e.g., a financial institution, an individual, a merchant, or the like) and/or to one or more computer systems from which the new wavelet was received (e.g., a personal computer such as a desktop computer or mobile phone, a point-of-service system, a financial processing server, a credit bureau server, or the like). 
     According to a second aspect of the present disclosure, a processor may receive a plurality of transactions. As used herein, the term “transactions” refers to any data including an indication of an amount of currency or commodity that is transferred between parties. The transactions need not be received in any particular format but may be represented in any appropriate form such as arrays, digital signals, or the like. The transactions may be received from one or more memories (e.g., a volatile memory such as a random access memory (RAM) and/or a non-volatile memory such as a hard disk) and/or across one or more computer networks (e.g., the Internet, a local area network (LAN), or the like). Alternatively, the processor may receive raw data and convert the data into a format representing a transaction. For example, the processor may receive a data with time, location, party identifiers, amount, and the like and may convert this data into a single bundle representing a transaction. 
     The processor may convert each transaction to a corresponding wavelet. For example, as explained above, the processor may receive a transaction having associated properties (such as time, location, merchant, amount, etc.) and may convert the transaction (along with its associated properties) into a wavelet or into an array or other format that represents a wavelet. 
     The processor may group the plurality of wavelets and corresponding tensors by coefficients included in the wavelets. For example, the corresponding tensors may be determined using an exponential smoothing average. That is, the processor may perform a discrete wavelet transform with an exponential smoothing average accumulator to transform the wavelets into corresponding tensors. 
     Because each tensor includes coefficients for each base in the set of bases representing a corresponding multi-dimensional space in which the tensor may be represented, the processor may group the tensors (and therefore, the corresponding wavelets) by these coefficients. Because the coefficients depend on the bases selected (which must satisfy one or more mathematical rules in order to form a mathematically consistent multi-dimensional space), the processor may generate a plurality of groups of coefficients and, thus, a plurality of groupings of the tensors (with the corresponding wavelets). For example, the processor may select bases depending on which factors are most heavily weighted in one or more models and then perform a plurality of groupings, each for a particular model (or set of models) having factors corresponding to the bases used to determine the corresponding grouping. 
     The processor may train a neural network for each group independently of other groups. Although “neural network” usually refers to a traditional artificial neural network as depicted, for example, in  FIG. 9 , the processor here may train any model (e.g., the models discussed above with respect to the groupings) that produces a likelihood of a particular tensor being anomalistic within a group. By training each group independently, the processor may develop specialized models that are orders of magnitude greater in number (and, therefore, accuracy) than extant neural networks. For example, the processor may develop thousands (or even millions) of models without requiring exponentially more resources than used to construct a single artificial neural network. 
     The processor may integrate the neural networks into a deep field network. For example, the models may be combined into a larger predictive scheme. In one particular example, the models may be combined such that when a new tensor is convolved (or otherwise combined with the models), the model trained on the group (or groups) having the most similar coefficients will be amplified while other models (e.g., trained on groups with less similar coefficients) will be minimized. 
     According to a third aspect of the present disclosure, a processor may receive a new transaction. For example, as explained above, the term “transaction” refers to any data including an indication of an amount of currency or commodity that is transferred between parties. The transaction need not be received in any particular format but may be represented in any appropriate form such as arrays, digital signals, or the like. The transaction may be received from one or more memories (e.g., a volatile memory such as a random access memory (RAM) and/or a non-volatile memory such as a hard disk) and/or across one or more computer networks (e.g., the Internet, a local area network (LAN), or the like). Alternatively, the processor may receive raw data and convert the data into a format representing a transaction. For example, the processor may receive a data with time, location, party identifiers, amount, and the like and may convert this data into a single bundle representing a transaction. 
     The processor may convert the new transaction to a wavelet. For example, as explained above, the new transaction may have associated properties (such as time, location, merchant, amount, etc.), and the processor may convert the new transaction (along with its associated properties) into a wavelet or into an array or other format that represents a wavelet. 
     The processor may convert the wavelet to a tensor using an exponential smoothing average. For example, as explained above, the processor may perform a discrete wavelet transform with an exponential smoothing average accumulator to transform the wavelet into a corresponding tensor. 
     The processor may calculate a difference field between the tensor and a field having one or more previous transactions represented as tensors. For example, as explained above, the processor may have performed a discrete wavelet transform with an exponential smoothing average accumulator to transform the one or more previous transactions into tensors. The processor may then obtain the field by mapping the tensors onto a manifold (e.g., a differential manifold). One or more atlases may be used to map the tensors onto the manifold. Alternatively, the processor may receive the tensors (e.g., from one or more memories and/or over one or more computer networks) and construct the field therefrom or may receive the field directly (e.g., from one or more memories and/or over one or more computer networks). 
     The processor may perform a weighted summation of the difference field to produce a difference vector. For example, as explained above, the coefficient weights may be derived from training of one or more particular models. For example, the processor may apply a variety of models in the weighting, such as models trained for particular identifiers (e.g., particular accounts, particular persons, particular merchants, particular institutions, etc.), particular times (e.g., time of day, time of year, etc.), particular locations (e.g., particular country, particular city, particular postal code, etc.), or the like. 
     Additionally or alternatively, the summation may include a notch filter. Accordingly, particular frequencies may be filtered out during the summation. For example, the processor may apply one or more particular models to determine which particular frequencies to filter out. The one or more filter models may be the same models as the one or more weighting models or may be different models. 
     The processor may apply one or more models to the difference vector to determine a likelihood of the transaction being high risk. For example, the one or more likelihood models may be the same models as the one or more filter models and/or the one or more weighting models or may be different models. In embodiments having direction as well as magnitude, the one or more models may use the magnitude and direction of the difference vector to determine the likelihood. As used herein, “likelihood” may refer to a percentage (e.g., 50%, 60%, 70%, etc.), a set of odds (e.g., 1:3, 1 in 5, etc.), a score (e.g., 1 out of 5, 5.6 out of 10.0, etc.), an indicator (e.g., “not likely,” “likely,” “very likely,” etc.), or the like. 
     As used herein, “risk” refers to any quantification of the probability of a transaction being lost (e.g., via automatic decline, insolvency of the purchaser, fraudulency, or the like). Accordingly, “high risk” refers to any level of risk that exceeds an acceptable level, whether the acceptable level be predetermined or dynamically determined (e.g., certain purchasers, merchants, regions, times of day, or the like may have differing acceptable levels of risk). 
     Based on the likelihood, the processor may authorize or deny the new transactions. For example, the processor may authorize the new transaction when the likelihood is below a threshold. If the processor rejects the new wavelet, the processor may send a notification to such effect. For example, the processor may send a rejection signal or a message indicating the likelihood and/or a reason (e.g., based on the one or more models) for rejection. The processor may send the notification to one or more parties associated with the new transaction (e.g., a financial institution, an individual, a merchant, or the like) and/or to one or more computer systems from which the new transaction was received (e.g., a personal computer such as a desktop computer or mobile phone, a point-of-service system, a financial processing server, a credit bureau server, or the like). 
     In some embodiments, based on the likelihood, the processor may request manual verification of the new transaction. For example, if the likelihood is above a first threshold but below a second threshold, the processor may send one or more messages to one or more parties associated with the new transaction (e.g., a financial institution, an individual, a merchant, or the like) with a request to send confirmation of the new transaction. In such an example, the processor may send a message to a mobile phone and/or email address of the individual to request that the new transaction be verified (e.g., by sending a “Y,” “yes,” or other affirmative response). Additionally or alternatively, the processor may send a message to a merchant warning that a suspicious transaction has been processed and that the merchant will be denied future transactions if the number of suspicious transactions in a period of time exceeds a threshold. 
     Turning now to  FIG. 1 , there is shown an example of a wavelet. For example, the wavelet is an oscillation with an amplitude rising from zero to a maximum and returning to zero over a finite period of time. As explained above, systems of the present disclosure may encode transactions as wavelets. For example, a transaction may be visualized as a wavelet in which currency and/or commodity is temporarily disturbed by transfer between parties. The wavelet representing the transaction may be indexed by location, time, category of transaction (e.g., furniture, contractor services, grocery, or the like), and/or other indicators. 
       FIG. 2A  depicts an exemplary filter bank used to perform a discrete wavelet transform. For example, as depicted in  FIG. 2A , the cascading filters may decompose a signal into low and high frequencies at each level and may produce corresponding coefficients. The decomposition (and corresponding coefficients) may be output from a convolution at each level that samples particular frequencies. A graphical depiction of frequency range for each level of the filters of  FIG. 2A  is depicted in  FIG. 2B . 
       FIG. 3  depicts an exemplary convolutional-accumulator. The example of  FIG. 3  is systematic because is includes the input data in output W as well as outputting convolution X. Although not depicted, non-systematic convolutional-accumulators may be used in combination with or in lieu of systematic convolutional-accumulators. Furthermore, the example of  FIG. 3  is recursive because the convolutional output may be fed back into the convolutional-accumulator for use in other convolutions. Although not depicted, non-recursive convolutional-accumulators may be used in combination with or in lieu of recursive convolutional-accumulators. 
     Systems of the present disclosure may use cascading convolution-accumulators, similar to the examples depicted in  FIGS. 2 and 3 , to perform discrete wavelet transforms and obtain a tensor from the accumulation. In some embodiments, the accumulation function may be an exponential smoothing average to incorporate the natural base e into the tensor. 
       FIG. 4  depicts exemplary coefficients (depicted as columns in  FIG. 4 ) used to perform exponential smoothing. As depicted in  FIG. 4 , the coefficients may exponentially decrease as the number of observations included in the smoothing linearly increases. Accordingly, as explained above, the natural base e is incorporated into the resulting smoothed tensor, which increases the ease of detecting anomalous tensors in financial markets. 
       FIG. 5  depicts an exemplary transformation from discrete wavelets (S(Δt) as depicted in  FIG. 5 ) to tensors. In particular, the discrete wavelets may undergo convolution (e.g., recursively as depicted in  FIG. 5 ) followed by one or more accumulating (and smoothing) operations (D(S m ) as depicted in  FIG. 5 ). For example, D(S m ) may represent any moving average, such as a simple moving average, a cumulative moving average, a weighted moving average, or the like. In some embodiments, D(S m ) may represent an exponential smoothing average, as explained above with reference to  FIG. 4 . 
       FIG. 6  depicts an exemplary manifold onto which a plurality of tensors are mapped. For example, similarly to the example of  FIG. 6 , systems of the present disclosure may map a set of tensors to a differentiable manifold, which is a topological manifold having a differentiable structure. Additionally, similar to the example of  FIG. 6 , systems of the present disclosure may use a smooth manifold, which is a differentiable manifold having derivatives of all orders that exist across the entire manifold. Additionally, similar to the example of  FIG. 6 , systems of the present disclosure may use an analytic manifold, which is a smooth manifold whose Taylor series is absolutely convergent. Additionally or alternatively, although not shown in  FIG. 6 , systems of the present disclosure may use a complex manifold, which is a manifold in complex space that is holomorphic. 
       FIG. 7  depicts an exemplary atlas mapping a subset of points to points on a manifold (such as that depicted in  FIG. 6 ) by an index set. By selecting an appropriate atlas to perform a mapping, various constraints on the resulting manifold may be obtained. For example, by selecting an appropriate atlas, systems of the present disclosure may ensure the mapping of tensors onto a differentiable manifold (or a smooth manifold, an analytic manifold, a complex manifold, or the like). 
       FIG. 8  depicts an example Galois connection between a base field Q and a group G={f,f 2 ,g,gf,gf 2 }. As depicted in  FIG. 8 , three subgroups of G and three subfields of Q are isomorphic. Systems of the present disclosure may use a Galois connection between a field and a tensor (or group) to calculate difference vectors while ensuring isomorphism between the field and the tensor. 
       FIG. 9  depicts an exemplary artificial neural network as used in extant systems. In neural networks like the example depicted in  FIG. 9 , one or more inputs (e.g., real numbers) are processed by nodes (or neurons) in a hidden layer in order to produce outputs. Although not depicted in  FIG. 9 , the hidden layer may comprise a plurality of layers such that some nodes pass their output(s) to an additional hidden layer rather than directing outputting. Each node (or neuron) typically has a weighting function (often non-linear), and its weights are modified during a learning procedure to reduce a loss function (and therefore increase accuracy). 
     Unlike the Galois connection networks used by systems of the present disclosure, however, neural networks like that depicted in  FIG. 9  frequently fail to recognize particular patterns. In addition, there may be significant numbers of false positives (and, correspondingly, false negatives) in the use of neural networks. Galois connection networks developed according to the present disclosure generally produce higher accuracy and, corresponding, lower false positives and false negatives than traditional neural networks. 
       FIG. 10A  depicts an exemplary system  1000  for detecting anomalies within a database comprising discrete wavelets. System  1000  may be implemented on one or more servers, such as detection server  1501  of  FIG. 15 . The one or more servers may be housed on one or more server farms. 
     As depicted in  FIG. 10A , system  1000  may use wavelets  1001  as input. For example, as explained above, wavelets  1001  may be received by system  1000  (e.g., from one or more memories and/or over one or more computer networks) and/or determined by system  1000  based on data (e.g., one or more transactions) received by system  1000 . 
     As further depicted in  FIG. 10A , system  1000  may convert wavelets  1001  to tensors  1003 . For example, as explained above, system  1000  may perform a discrete wavelet transform (that is, a cascading convolution) with a smoothing accumulator to transform the wavelets  1001  to tensors  1003 . In some embodiments, a simple moving average, a cumulative moving average, a weighted moving average, or the like, may be used for smoothing. In certain aspects, the smoothing may be an exponential smoothing average. By using an exponential smoothing average, the natural base e may be incorporated into the smoothing. 
     As further depicted in  FIG. 10A , system  1000  may convert tensors  1003  to a field  1005 . For example, as explained above, system  1000  may use one or more atlases to map tensors  1003  onto a manifold to form field  1005 . In some embodiments, system  1000  may select the one or more atlases to ensure particular properties of the resulting manifold (e.g., to result in a differential manifold, a smooth manifold, an analytic manifold, a complex manifold, or the like). 
     Field  1005  may be used by system  1000  to detect anomalous wavelets, as explained above. For example, system  1000  may calculate a difference field between a new wavelet and field  1005  and may sum the difference field to form a difference vector. Accordingly, the magnitude and/or direction of the difference vector may be used to determine an anomaly likelihood (e.g., using one or more models, as explained above). 
       FIG. 10B  depicts another exemplary system  1000 ′ for detecting anomalies within a database comprising discrete wavelets. System  1000 ′ may be implemented on one or more servers, such as detection server  1501  of  FIG. 15 . The one or more servers may be housed on one or more server farms. 
     Similar to system  1000  of  FIG. 10A , system  1000 ′ receives wavelets  1001 , converts wavelets  1001  to tensors  1003 , and maps tensors  1003  to field  1005 . In addition, as depicted in  FIG. 10B , system  1000 ′ determines wavelets  1001  based on received input comprising JavaScript Object Notation (JSON) data. Additional or alternative data serialization formats, such as Extensible Markup Language (XML), YAML Ain&#39;t Markup Language (YAML), or the like. Data serialization formats allow for rapid and lightweight transmission of data (e.g., transactions) to system  1000 ′. In addition, data serialization formats may allow for direct use of the received data (e.g., for conversion to wavelets or even for direct processing by a discrete wavelet transform) without having to reconstruct a data structure or object therefrom. Furthermore, many extant database structures (such as MongoDB, Oracle NoSQL Database, or the like) support native exportation directly to a data serialization format such as JSON. Accordingly, accepting data serialization formats may allow for faster and more native integration with existing transaction databases. 
       FIG. 10C  depicts an exemplary workflow  1050  of detecting a high risk transaction using a database comprising discrete wavelets. For example, workflow  1050  may represent one exemplary usage of system  1000  of  FIG. 10A  and/or system  1000 ′ of  FIG. 10B . 
     At step  1051 , system  1000  receives a new transaction. For example, as explained above, system  1000  may receive a wavelet representing a transaction, may receive a data serialization format for use as though it were a wavelet, and/or raw data for conversion to a wavelet and/or a data serialization format. 
     At steps  1053   a  and  1053   b , system  1000  may extract a first indicator and a second indicator from the new transaction. For example, the first indicator may comprise an identifier of a financial account, an identifier of a merchant, a location of the new transaction, a time of the new transaction, an Internet Protocol (IP) address or other identifier of a payment device (e.g., a mobile phone) and/or of a point-of-service system (e.g., a register), or the like. Similarly, the second indicator may comprise an identifier of a financial account, an identifier of a merchant, a location of the new transaction, a time of the new transaction, an IP address or other identifier of a payment device (e.g., a mobile phone) and/or of a point-of-service system (e.g., a register), or the like. 
     In addition, at step  1055 , system  1000  may convert the new transaction to a tensor, as explained above. For example, system  1000  may perform a discrete wavelet transform (that is, a cascading convolution) with a smoothing accumulator to transform the new transaction to a tensor. In some embodiments, a simple moving average, a cumulative moving average, a weighted moving average, or the like, may be used for smoothing. In certain aspects, the smoothing may be an exponential smoothing average. By using an exponential smoothing average, the natural base e may be incorporated into the smoothing. 
     At steps  1057   a  and  1057   b , system  1000  may use the first indicator and the second indicator to generate wavelets from the new transaction indexed by and/or incorporating the properties of the first indicator and the second indicator. In some embodiments, these wavelets may be further converted to tensors, as explained above. 
     In addition, at step  1059 , system  1000  may determine a difference between the new transaction tensor and an existing tensor database (e.g., a tensor field representing previous transaction tensors mapped to a manifold). For example, as explained above, system  1000  may determine a difference field between the new transaction tensor and the existing tensor database and sum the difference field into a difference vector. 
     At steps  1061   a  and  1061   b , system  1000  may use the wavelets indexed by and/or incorporated into the first indicator and the second indicator to find matching wavelets in the existing tensor database. For example, system  1000  may determine whether the matching wavelets are in an expected location in the database (e.g., in the field) in order to assist with authorizing the new transaction. 
     In addition, at step  1063 , system  1000  may apply a model (or a plurality of models) to the difference between the new transaction tensor and an existing tensor database. For example, as explained above, system  1000  may apply the model to determine a likelihood of the new transaction being anomalous (and/or high risk). In some embodiments, as depicted in  FIG. 10C , system  1000  may include the first indicator and the second indicator as inputs to the model. For example, the first indicator and/or the second indicator may server to select the model (or plurality of models) to apply. In such an example, the selection of the model (or plurality of models) may depend on a particular financial account, a particular merchant, a particular location of the new transaction, a particular time of the new transaction, a particular IP address of a payment device (e.g., a mobile phone) and/or of a point-of-service system (e.g., a register), or any combination thereof. 
     By using workflow  1050 , systems of the present disclosure may incorporate traditional rule-based authentication techniques (e.g., using the first indicator and the second indicator) with the deep field networks disclosed herein. Accordingly, systems of the present disclosure may be used to combine extant transactions authorizations with novel determinations of fraudulency likelihood. 
     Although  FIG. 10C  depicts using a first indicator and a second indicator, workflow  1050  of  FIG. 10C  may incorporate any number of indicators, such as one, two, three, four, five, or the like. In alternative embodiments not depicted, workflow  1050  of  FIG. 10C  may use the model (or plurality of models) without any additional indicators. 
       FIG. 10D  depicts an exemplary workflow  1080  of constructing and using a database comprising discrete wavelets. For example, workflow  1080  may represent an additional or alternative example usage of system  1000  of  FIG. 10A  and/or system  1000 ′ of  FIG. 10B . 
     As depicted in  FIG. 10D , one or more sources of transactions for systems of the present disclosure may include one or more data lakes comprising a distributed file system (such as Apache Hadoop or the like), one or more data lakes comprising images (such as Microsoft Azure Data Lake or the like), one or more real-time online transaction processing systems (RT-OLTPS) (such as PayPal or the like), one or more data oceans (such as JSON objects exchanged using a Representational State Transfer (REST) protocol, XML objects exchanged using a Simple Object Access Protocol (SOAP), or the like). Accordingly, system  1000  may receive historical transactions, transactions awaiting authorization, or a combination thereof. Although depicted as using JSON objects, other data serialization formats such as XML, YAML, or the like, may be used in lieu of or in combination with JSON objects. 
     As further depicted in  FIG. 10D , Deep Decision may represent a system according to the present disclosure (e.g., system  1000  of  FIG. 10A  and/or system  1000 ′ of  FIG. 10B ). Accordingly, Deep Decision may use received transactions for training one or more models (e.g., according to method  1300  of  FIG. 13 , described below), for developing a tensor field representing historical transactions (e.g., as described above), and/or for authorizing new, incoming transactions (e.g., according to method  1400  of  FIG. 14 , described below). Outputs from Deep Decision, which may include, for example, one or more trained models, one or more fields, and/or one or more authorizations, may be stored in one or more caches, as depicted in  FIG. 10D . Additionally or alternatively, outputs may be send to other systems, such as a personal computer such as a desktop computer or mobile phone, a point-of-service system, a financial processing server, a credit bureau server, or the like. 
       FIG. 11  depicts an example of training a deep field network to detect anomalies within a database comprising discrete wavelets. Example  1100  may represent a training sequence implemented on, for example, system  1000  of  FIG. 10A  and/or system  1000 ′ of  FIG. 10B . 
     As depicted in  FIG. 11 , transactions may be represented as one or more wavelets. Although depicted as two wavelets in  FIG. 11 , a transaction may be represented with any number of wavelets (e.g., one, two, three, four, five, or the like). Additionally, although depicted as each having two wavelets in  FIG. 11 , different transactions may be represented by different numbers of wavelets. For example, a first transaction may be represented by a single wavelet, and a second transaction may be represented by three wavelets. 
     Furthermore, as depicted in  FIG. 11 , the wavelets may be converted to tensors that have coefficients along selected bases. Although the example of  FIG. 11  includes three bases, any number of bases (e.g., one, two, three, four, five, or the like) may be used. In addition, the wavelets may be converted to a plurality of tensors, each having different coefficients along different bases. 
     As further depicted in  FIG. 11 , the tensors may be grouped based on corresponding coefficients. In the example of  FIG. 11 , the tensors representing the first transaction are placed in a first group while the tensors representing the second transaction are placed in a second group. Although depicted as grouped together in  FIG. 11 , tensors representing the same transaction may be placed in different groups based on having different coefficients (e.g., by having different bases). The groups depicted in  FIG. 11  may be used to perform training of one or more models for each group (e.g., as discussed with respect to method  1300  of  FIG. 13 ). 
       FIG. 12  is a flowchart of exemplary method  1200  for detecting anomalies within a database comprising discrete wavelets. Method  1200  may be implemented using a general-purpose computer including at least one processor, e.g., detection server  1501  of  FIG. 15 . Alternatively, a special-purpose computer may be built for implementing method  1200  using suitable logic elements. 
     At step  1201 , a processor may receive a new wavelet. Although the processor may receive the wavelet in the form of a wavelet, the wavelet need not be received in the form of an oscillation but may be represented in any appropriate form (e.g., an array, a digital signal, or the like). The wavelet may be received from one or more memories and/or across one or more computer networks. 
     Alternatively, the processor may receive data and convert the data into a wavelet. For example, the processor may receive a transaction having associated properties (such as time, location, merchant, amount, etc.) and may convert the transaction into a wavelet or into an array or other format that represents a wavelet. The data may be received in and/or converted to one or more data serialization formats, such as JSON, XML, YAML, etc. 
     At step  1203 , the processor may convert the wavelet to a tensor. For example, as explained above, the processor may convert the wavelet to a tensor based using a moving average, such as a simple moving average, a cumulative moving average, a weighted moving average, an exponential moving average, or the like. Accordingly, the processor may perform a cascading convolution (e.g., with one or more filter banks) followed by an accumulation (e.g., using the moving average for smoothing) to transform the received wavelet into a tensor. 
     At step  1205 , the processor may calculate a difference field between the tensor and a field having one or more previous wavelets represented as tensors. For example, the processor may have previously calculated the field using wavelets received in the past. Similarly to step  1203 , the processor may perform cascading convolution (e.g., with one or more filter banks) followed by an accumulation (e.g., using the moving average for smoothing) to transform the previous wavelets into tensors and obtain the field by mapping the tensors onto a manifold (e.g., a differential manifold or the like) using one or more atlases. 
     Alternatively, the processor may receive the tensors representing the previous wavelets (e.g., from one or more memories and/or over one or more computer networks) and construct the field therefrom. Alternatively, the processor may receive the field directly (e.g., from one or more memories and/or over one or more computer networks). 
     At step  1207 , the processor may perform a weighted summation of the difference field to produce a difference vector. For example, the coefficient weights may be derived from training of one or more particular models. The one or more models may be trained for particular identifiers (e.g., particular accounts, particular persons, particular merchants, particular institutions, etc.), particular times (e.g., time of day, time of year, etc.), particular locations (e.g., particular country, particular city, particular postal code, etc.), or the like. Additionally or alternatively, as explained above, the summation may include a notch filter. 
     At step  1209 , the processor may apply one or more models to the difference vector to determine a likelihood of the new wavelet representing an anomaly. As explained above, the likelihood may be output from one or more particular models. The one or more models may be trained for particular identifiers (e.g., particular accounts, particular persons, particular merchants, particular institutions, etc.), particular times (e.g., time of day, time of year, etc.), particular locations (e.g., particular country, particular city, particular postal code, etc.), or the like. 
     At step  1211 , the processor may add the new wavelet to the field when the likelihood is below (or equal to) a threshold. Accordingly, the processor may accept the new wavelet as a valid historical datapoint to be used in future anomaly detection. 
     Method  1200  may include additional steps. For example, method  1200  may include sending a rejection signal or a message indicating the likelihood and/or a reason (e.g., based on the one or more models) for rejection when the likelihood is above (or equal to) the threshold. The processor may send the notification to one or more parties associated with the new wavelet (e.g., a financial institution, an individual, a merchant, or the like) and/or to one or more computer systems from which the new wavelet was received (e.g., a personal computer such as a desktop computer or mobile phone, a point-of-service system, a financial processing server, a credit bureau server, or the like). Similarly, method  1200  may include sending an acceptance signal or a message indicating the likelihood and/or a reason (e.g., based on the one or more models) for acceptance when the likelihood is below (or equal to) the threshold. The notification may be sent similarly to the rejection signal or message. 
       FIG. 13  is a flowchart of exemplary method  1300  for training a deep field network to detect anomalies within a database comprising discrete wavelets. Method  1300  may be implemented using a general-purpose computer including at least one processor, e.g., detection server  1501  of  FIG. 15 . Alternatively, a special-purpose computer may be built for implementing method  1300  using suitable logic elements. 
     At step  1301 , a processor may receive a plurality of transactions. The transactions need not be received in any particular format but may be represented in any appropriate form such as arrays, digital signals, or the like. The transactions may be received from one or more memories and/or across one or more computer networks. Alternatively, the processor may receive raw data and convert the data into a format representing a transaction. For example, the processor may receive a data with time, location, party identifiers, amount, and the like and may convert this data into a single bundle representing a transaction. 
     At step  1303 , the processor may convert each transaction to a corresponding wavelet. For example, as explained above, the processor may receive a transaction having associated properties (such as time, location, merchant, amount, etc.) and may convert the transaction (along with its associated properties) into a wavelet or into an array or other format that represents a wavelet. Additionally or alternatively, the processor may convert raw data representing a transaction to one or more data serialization formats, such as JSON, XML, YAML, etc., that may be operated on as though it were a wavelet. 
     At step  1305 , the processor may group the plurality of wavelets and corresponding tensors by coefficients included in the wavelets. For example, as explained above, the corresponding tensors may be determined using one or more convolutional-accumulators. Because each tensor includes coefficients for each base in the set of bases representing a corresponding multi-dimensional space in which the tensor may be represented, the processor may group the tensors (and therefore, the corresponding wavelets) by these coefficients. In some embodiments, the processor may generate a plurality of groups of coefficients and, thus, a plurality of groupings of the tensors (with the corresponding wavelets). For example, the processor may select bases depending on which factors are most heavily weighted in one or more models being trained and then perform a plurality of groupings, each for a particular model (or set of models) having factors corresponding to the bases used to determine the corresponding grouping. 
     At step  1307 , the processor may train a neural network for each group independently of other groups. Although “neural network” usually refers to a traditional artificial neural network as depicted, for example, in  FIG. 9 , the processor at step  1307  may train any model (e.g., the models discussed above with respect to the groupings) that produces a likelihood of a particular tensor being anomalistic within a group. As used herein, the term “train” refers to the adjustment of one or more parameters of the model (such as coefficients, weights, constants, or the like) to increase accuracy of the model (e.g., to match known properties of the tensors in the each group). 
     At step  1309 , processor may integrate the neural networks into a deep field network. For example, the models may be combined into a larger predictive scheme. In one particular example, the models may be combined such that when a new tensor is convolved (or otherwise combined with the models), the model trained on the group (or groups) having the most similar coefficients will be amplified while other models (e.g., trained on groups with less similar coefficients) will be minimized. 
     Method  1300  may include additional steps. For example, the deep field network produced by step  1309  may be stored (or transmitted for remote storage) for use in future analysis. In addition, the processor may index the stored deep field network such as different models within the network may be extracted using one or more indices indicating the properties and/or coefficients on which the model was trained (and to which the model is sensitive). 
       FIG. 14  is a flowchart of exemplary method  1400  for authorizing a transaction using cascading discrete wavelets. Method  1400  may be implemented using a general-purpose computer including at least one processor, e.g., detection server  1501  of  FIG. 15 . Alternatively, a special-purpose computer may be built for implementing method  1400  using suitable logic elements. 
     At step  1401 , a processor may receive a new transaction. The new transaction need not be received in any particular format but may be represented in any appropriate form such as arrays, digital signals, or the like. The new transaction may be received from one or more memories and/or across one or more computer networks. Alternatively, the processor may receive raw data and convert the data into a format representing a transaction. For example, the processor may receive a data with time, location, party identifiers, amount, and the like and may convert this data into a single bundle representing a transaction. 
     At step  1403 , the processor may convert the new transaction to a wavelet. For example, as explained above, the processor may convert new the transaction (along with its associated properties) into a wavelet or into an array or other format that represents a wavelet. Additionally or alternatively, the processor may convert raw data representing the new transaction to one or more data serialization formats, such as JSON, XML, YAML, etc., that may be operated on as though it were a wavelet. 
     At step  1405 , the processor may convert the wavelet to a tensor using an exponential smoothing average. For example, as explained above, the corresponding tensors may be determined using one or more convolutional-accumulators. 
     At step  1407 , the processor may calculate a difference field between the tensor and a field having one or more previous transactions represented as tensors. For example, the processor may have previously calculated the field using transactions received in the past. Similarly to step  1405 , the processor may perform cascading convolution (e.g., with one or more filter banks) followed by an accumulation (e.g., using the moving average for smoothing) to transform the previous transactions into tensors and obtain the field by mapping the tensors onto a manifold (e.g., a differential manifold or the like) using one or more atlases. 
     Alternatively, the processor may receive the tensors representing the previous transactions (e.g., from one or more memories and/or over one or more computer networks) and construct the field therefrom. Alternatively, the processor may receive the field directly (e.g., from one or more memories and/or over one or more computer networks). 
     At step  1409 , the processor may perform a weighted summation of the difference field to produce a difference vector. For example, the coefficient weights may be derived from training of one or more particular models. The one or more models may be trained for particular identifiers of transactions (e.g., particular financial accounts, particular persons, particular merchants, particular financial institutions, etc.), particular transaction times (e.g., time of day, time of year, etc.), particular transaction locations (e.g., particular country, particular city, particular postal code, etc.), or the like. Additionally or alternatively, as explained above, the summation may include a notch filter. 
     At step  1411 , the processor may apply one or more models to the difference vector to determine a likelihood of the transaction being high risk. As explained above, the likelihood may be output from one or more particular models. The one or more models may be trained for particular identifiers of transactions (e.g., particular financial accounts, particular persons, particular merchants, particular financial institutions, etc.), particular transaction times (e.g., time of day, time of year, etc.), particular transaction locations (e.g., particular country, particular city, particular postal code, etc.), or the like. 
     At step  1413 , the processor may authorize the new transaction when the likelihood is below a threshold. Accordingly, the processor may accept the new wavelet as a valid historical datapoint to be used in future anomaly detection. 
     Additionally or alternatively, the processor may use the likelihood determined at step  1412  to perform other functions. For example, if the new transaction is enrollment of a new account (such as a brokerage account, a credit card account, or the like), the processor may use the likelihood determined at step  1412  to set one or more parameters for the account. In such an example, the likelihood may be used to determine an interest rate for the account, a margin requirement for the account, an options trading level for the account, or the like. In another example, if the new transaction is a brokerage trade, the processor may use the likelihood determined at step  1412  for initializing settlement of the trade. In yet another example, if the new transaction is a portfolio rebalancing, the processor may use the likelihood determined at step  1412  for approving the rebalancing, adjusting the rebalancing, or the like. 
     Method  1400  may include additional steps. For example, method  1400  may incorporate traditional authorization in combination with step  1413 . In one example, method  1400  may include identifying one or more indicators from the new transaction and authorizing the new transaction when the one or more indicators match expected values. Additionally or alternatively, method  1400  may include identifying one or more indicators from the new transaction, using the one or more indicators to identify matching wavelets, and authorizing the new transaction when the matching wavelets are in expected locations in the field. Additionally or alternatively, method  1400  may include identifying one or more indicators from the new transaction and using the one or more indicators as inputs to the model(s) for determining the likelihood. 
     In another example, method  1400  may include requesting manual verification of the new transaction when the likelihood is above a first threshold but below a second threshold. For example, the processor may send one or more messages to one or more parties associated with the new transaction (e.g., a financial institution, an individual, a merchant, or the like) with a request to send confirmation of the new transaction. In such an example, the processor may send a message to a mobile phone and/or email address of the individual to request that the new transaction be verified (e.g., by sending a “Y,” “yes,” or other affirmative response). Additionally or alternatively, the processor may send a message to a merchant warning that a suspicious transaction has been processed and that the merchant will be denied future transactions if the number of suspicious transactions in a period of time exceeds a threshold. 
     Additionally or alternatively, method  1400  may include sending a rejection signal or a message indicating the likelihood and/or a reason (e.g., based on the one or more models) for rejection when the likelihood is above (or equal to) the threshold. The processor may send the notification to one or more parties associated with the new transaction (e.g., a financial institution, an individual, a merchant, or the like) and/or to one or more computer systems from which the new transaction was received (e.g., a personal computer such as a desktop computer or mobile phone, a point-of-service system, a financial processing server, a credit bureau server, or the like). Similarly, method  1400  may include sending an acceptance signal or a message indicating the likelihood and/or a reason (e.g., based on the one or more models) for acceptance when the likelihood is below (or equal to) the threshold. The notification may be sent similarly to the rejection signal or message. 
     The disclosed systems and methods may be implemented on one or more computing devices. Such a computing device may be implemented in various forms including, but not limited to, a client, a server, a network device, a mobile device, a laptop computer, a desktop computer, a workstation computer, a personal digital assistant, a blade server, a mainframe computer, and other types of computers. The computing device described below and its components, including their connections, relationships, and functions, is meant to be an example only, and not meant to limit implementations of the systems and methods described in this specification. Other computing devices suitable for implementing the disclosed systems and methods may have different components, including components with different connections, relationships, and functions. 
     As explained above,  FIG. 15  is a block diagram that illustrates an exemplary detection server  1501  suitable for implementing the disclosed systems and methods. Detection server  1501  may reside on a single server farm or may be distributed across a plurality of server farms. 
     As depicted in  FIG. 15 , detection server  1501  may include at least one processor (e.g., processor  1503 ), at least one memory (e.g., memory  1505 ), and at least one network interface controller (NIC) (e.g., NIC  1507 ). 
     Processor  1503  may comprise a central processing unit (CPU), a graphics processing unit (GPU), or other similar circuitry capable of performing one or more operations on a data stream. Processor  1503  may be configured to execute instructions that may, for example, be stored on memory  1505 . 
     Memory  1505  may be volatile memory (such as RAM or the like) or non-volatile memory (such as flash memory, a hard disk drive, or the like). As explained above, memory  1505  may store instructions for execution by processor  903 . 
     NIC  1507  may be configured to facilitate communication with detection server  1501  over at least one computing network (e.g., network  1509 ). Communication functions may thus be facilitated through one or more NICs, which may be wireless and/or wired and may include an Ethernet port, radio frequency receivers and transmitters, and/or optical (e.g., infrared) receivers and transmitters. The specific design and implementation of the one or more NICs depend on the computing network  1509  over which detection server  1501  is intended to operate. For example, in some embodiments, detection server  1501  may include one or more wireless and/or wired NICs designed to operate over a GSM network, a GPRS network, an EDGE network, a Wi-Fi or WiMax network, and a Bluetooth® network. Alternatively or concurrently, detection server  1501  may include one or more wireless and/or wired NICs designed to operate over a TCP/IP network. 
     Processor  1503 , memory  1505 , and/or NIC  1507  may comprise separate components or may be integrated in one or more integrated circuits. The various components in detection server  1501  may be coupled by one or more communication buses or signal lines (not shown). 
     As further depicted in  FIG. 15 , detection server  1501  may include a merchant interface  1511  configured to communicate with one or more merchant servers (e.g., merchant server  1513 ). Although depicted as separate in  FIG. 15 , merchant interface  1511  may, in whole or in part, be integrated with NIC  1507 . 
     As depicted in  FIG. 15 , detection server  1501  may include and/or be operably connected to a database  1515  and/or a storage device  1517 . Database  1515  may represent a wavelet database or other digital database, which may be stored, in whole or in part, on detection server  1501  and/or, in whole or in part, on a separate server (e.g., one or more remote cloud storage servers). Storage device  1517  may be volatile (such as RAM or the like) or non-volatile (such as flash memory, a hard disk drive, or the like). 
     I/O module  1519  may enable communications between processor  1503  and memory  1505 , database  1515 , and/or storage device  1517 . 
     As depicted in  FIG. 15 , memory  1505  may store one or more programs  1521 . For example, programs  1521  may include one or more server applications  1523 , such as applications that facilitate graphic user interface processing, facilitate communications sessions using NIC  1507 , facilitate exchanges with merchant server  1513 , or the like. By way of further example, programs  1521  may include an operating system  1525 , such as DRAWIN, RTXC, LINUX, iOS, UNIX, OS X, WINDOWS, or an embedded operating system such as VXWorkS. Operating system  1525  may include instructions for handling basic system services and for performing hardware dependent tasks. In some implementations, operating system  1525  may comprise a kernel (e.g., UNIX kernel). Memory  1505  may further store data  1527 , which may be computed results from one or more programs  1521 , data received from NIC  1507 , data retrieved from database  1515  and/or storage device  1517 , and/or the like. 
     Each of the above identified instructions and applications may correspond to a set of instructions for performing one or more functions described above. These instructions need not be implemented as separate software programs, procedures, or modules. Memory  1505  may include additional instructions or fewer instructions. Furthermore, various functions of detection server  1501  may be implemented in hardware and/or in software, including in one or more signal processing and/or application specific integrated circuits. 
     The foregoing description has been presented for purposes of illustration. It is not exhaustive and is not limited to precise forms or embodiments disclosed. Modifications and adaptations of the embodiments will be apparent from consideration of the specification and practice of the disclosed embodiments. For example, the described implementations include hardware and software, but systems and methods consistent with the present disclosure can be implemented with hardware alone. In addition, while certain components have been described as being coupled to one another, such components may be integrated with one another or distributed in any suitable fashion. 
     Moreover, while illustrative embodiments have been described herein, the scope includes any and all embodiments having equivalent elements, modifications, omissions, combinations (e.g., of aspects across various embodiments), adaptations and/or alterations based on the present disclosure. The elements in the claims are to be interpreted broadly based on the language employed in the claims and not limited to examples described in the present specification or during the prosecution of the application, which examples are to be construed as nonexclusive. 
     Instructions or operational steps stored by a computer-readable medium may be in the form of computer programs, program modules, or codes. As described herein, computer programs, program modules, and code based on the written description of this specification, such as those used by the processor, are readily within the purview of a software developer. The computer programs, program modules, or code can be created using a variety of programming techniques. For example, they can be designed in or by means of Java, C, C++, assembly language, or any such programming languages. One or more of such programs, modules, or code can be integrated into a device system or existing communications software. The programs, modules, or code can also be implemented or replicated as firmware or circuit logic. 
     The features and advantages of the disclosure are apparent from the detailed specification, and thus, it is intended that the appended claims cover all systems and methods falling within the true spirit and scope of the disclosure. As used herein, the indefinite articles “a” and “an” mean “one or more.” Similarly, the use of a plural term does not necessarily denote a plurality unless it is unambiguous in the given context. Words such as “and” or “or” mean “and/or” unless specifically directed otherwise. Further, since numerous modifications and variations will readily occur from studying the present disclosure, it is not desired to limit the disclosure to the exact construction and operation illustrated and described, and accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope of the disclosure. 
     Other embodiments will be apparent from consideration of the specification and practice of the embodiments disclosed herein. It is intended that the specification and examples be considered as example only, with a true scope and spirit of the disclosed embodiments being indicated by the following claims.