an adaptive neural network-based method for tile replacement in a web map cache

An Adaptive Neural Network-Based Method forTile Replacement in a Web Map Cache

Ricardo Garcıa, Juan Pablo de Castro, Marıa Jesus Verdu,Elena Verdu, Luisa Marıa Regueras, and Pablo Lopez

Higher Technical School of Telecommunications Engineering, University of Valladolid,Valladolid, Spain

{ricgar,juacas,marver,elever,luireg}@tel.uva.es,

[email protected]

http://www.tel.uva.es

Abstract. Most popular web map services, such as Google Maps, servepre-generated image tiles from a server-side cache. However, storageneeds are often prohibitive, forcing administrators to use partial cachescontaining a subset of the total tiles. When the cache runs out of spacefor allocating incoming requests, a cache replacement algorithm mustdetermine which tiles should be replaced. Cache replacement algorithmsare well founded and characterized for general Web documents but spa-tial caches comprises a set of specific characteristics that make themsuitable to further research. This paper proposes a cache replacementpolicy based on neural networks to take intelligent replacement deci-sions. Neural networks are trained using supervised learning with realdata-sets from public web map servers. Hight correct classification ratioshave been achieved for both training data and a completely independentvalidation data set, which indicates good generalization of the neuralnetwork. A benchmark of the performance of this policy against severalclassical cache management policies are given for discussion.

Keywords: Web map service, Tile cache, Replacement policy, Neuralnetworks, benchmark

1 Introduction

The Web Map Service (WMS) standard of the Open Geospatial Consortium(OGC) offers a standardized and flexible way of serving cartographic digitalmaps of spatially referenced data through HTTP requests [?]. However, spatialparameters in requests are not constrained, which forces images to be generatedon the fly each time a request is received, limiting the scalability of these services.

A common approach to improve the scalability of the map server is to improvethe cachability of requests by dividing the map into a discrete set of images,called tiles, and restrict user requests to that set. Several specifications havebeen developed to address how cacheable image tiles are advertised from server-side and how a client requests cached image tiles. The Open Source Geospatial

2 Lecture Notes in Computer Science: Authors’ Instructions

Foundation (OSGeo) developed the WMS Tile Caching (usually known as WMS-C) proposal [?], while the OGC has recently released the Web Map Tile ServiceStandard (WMTS) [?] inspired by the former and other similar initiatives.

The problem that arises when deploying these server-side caches in practicalimplementations is that the storage requirements are often prohibitive for manyorganizations, thus forcing to use partial caches containing just part of the totaltiles. Even if there are enough available resources to store a complete cache ofthe whole map, many tiles will never be requested, so it is not worth it to cachethose “unpopular” tiles because no gain will be obtained.

When the cache runs out of space it is necessary to determine which tilesshould be replaced by the new ones. The cache replacement algorithm proposedin this paper uses a neural network to estimate the probability that a requestof a tile occurs before a certain period of time. Those tiles that are not likely tobe requested shortly are good candidates for replacement (assuming the cost tofetch a tile from the remote server is the same for all tiles).

The rest of the document is organized as follows. Section 2 provides a briefbackground about how the map is tiled in order to offer a tiled web map service.Section 3 presents related work in replacement algorithms. Section 4 describesthe trace files used for training and simulation. In Section 5 the proposed replace-ment algorithm based on neural network is discussed. Results are presented inSection 6, while the conclusions of the paper are gathered together in Section 7.

2 Tiling Space

In order to offer a tiled web map service, the web map server renders the mapacross a fixed set of scales through progressive generalization. Rendered mapimages are then divided into tiles, describing a tile pyramid as depicted in Fig. 1.

For example, Google Maps uses a tiling scheme where level 0 allows repre-senting the whole world in a single tile of 256x256 pixels (where the first 64 andlast 64 lines of the tile are left blank). The next level represents the whole worldin 2x2 tiles of 256x256 pixels and so on in powers of 2. Therefore, the number oftiles n grows exponentially with the resolution level l. Using this tiling scheme,to cover the whole world with a pyramid of 20 levels, around 3.7× 1011 tiles arerequired and several petabytes of disk are used.

3 Related Work

Most important characteristics of Web objects used in Web cache replacementstrategies are: recency (time since the last reference to the object), frequency(number of requests to the object), size of the Web object and cost to fetch theobject from its origin server. Depending on the characteristics used, replacementstrategies can be classified as recency-based, frequency-based, recency/frequency-based, function-based and randomized strategies [?].

Recency-based strategies exploit the temporal locality of reference observedin Web requests. These are usually extensions of the well-known LRU strategy,

Lecture Notes in Computer Science: Authors’ Instructions 3

Fig. 1. Tile pyramid representation.

which removes the least recently referenced object. Pyramidal Selection Scheme(PSS) [?] algorithm uses a pyramidal classification of objects depending upontheir size, and objects in each group are maintained as a separate LRU list.Only the least recently used objects in each group are compared, and the objectselected for replacement is which is maximizing the product of its size and thenumber of accesses since the last time it was requested.

Frequency-based strategies rely on the fact that popularity of Web objectsis related to their frequency values. These strategies are built around the LFUstrategy, which removes the least frequently requested object.

Recency/frequency-based strategies combine recency and frequency informa-tion to take replacement decisions.

Function-based strategies employ a general function of several parameters tomake decisions of which object to evict from the cache. GD-Size [?] strategy usesa function of size, cost and an aging factor. GDSF [?] is an extension of GD-Sizethat also takes account for frequency. Least-Unified Value (LUV) [?] rates anobject based on its past references to estimate the likelihood of a future request,and normalizes the value by the cost of the object per unit size.

Randomized strategies use a non-deterministic approach to randomly selecta candidate object for replacement.

For a further background, a comprehensive survey of web cache replacementstrategies is presented in [?]. According to that work, algorithms like GD-Size,GDSF, LUV and PSS were considered “good enough” for caching needs at thetime it was published in 2003. However, the explosion of web map traffic did nothappen until a few years later.


Despite the vast proliferation of web cache replacement algorithms, there isa reduced number of replacement policies specific to map tile caches that benefitof spatial correlation between requests.

Map tile caching can benefit from spatial locality principle as stated by theTobler’s first law of geography, which states that “Everything is related to ev-erything else, but near things are more related than distant things” [?].

In [?] and [?], a probability-based tile pre-fetching algorithm and a collab-orative cache replacement algorithm for Web geographical information systems(Web GISs) are proposed. The server collects and maintains the transition prob-abilities between adjacent tiles. With these probabilities the server can predictwhich tiles have the highest probability of access in next time than others, basedon the global tile access pattern of all users and the semantics of query. The pro-posed cache replacement algorithm determines which tiles should be replacedbased on the estimated future access probabilities.

In [?,?,?] the web application Hotmap is presented. This application analyzeslog requests from the Microsoft’s Live Search Maps service and visualizes thenumber of requests of each tile accurately on a map. These studies reflect thatseveral features which drive most people’s attention, like shorelines, roads andpopulated places, can be identified. [?] proposes that significant performanceimprovements can be achieved by caching tiles corresponding to those featuresknown to be of interest to Web map users.

The use of neural networks for cache replacement was first introduced byKhalid [?], with the KORA algorithm. KORA uses backpropagation neural net-work for the purpose of guiding the line/block replacement decisions in cache.The algorithm identifies and subsequently discards the dead lines in cache mem-ories. It is based on previous work by Pomerene et al. [?], who suggested the useof a shadow directory in order to look at a longer history when making decisionswith LRU. Later, an improved version of the former, KORA-2, was proposed[?,?]. Other algorithms based on KORA were also proposed [?,?].

A survey on applications of neural networks and evolutionary techniques inweb caching can be found in [?].

[?,?,?,?,?] proposes the use of a backpropagation neural network in a Webproxy cache for taking replacement decisions.

A predictor that learns the patterns of Web pages and predicts the futureaccesses is presented in [?].

[?] discusses the use of neural networks to support the adaptivity of theClass-based Least Recently Used (C-LRU) caching algorithm.

The novelty and significance of this work resides on the target scenario whereit is applied. No similar studies about the application of neural networks to takereplacement decisions in a Web map cache have been found in the literature.

Although the underlying methodology has already been discussed in relatedwork on conventional web caching, web map requests’ distributions and at-tributes are very different from those of traditional web servers. In this context,the size of the requested object is heavily related to its “popularity” so it canbe used to estimate the probability of a future request. Traditional web caching


replacement policies commonly use this parameter only to evaluate the trade offbetween the hits produced on that object and the space required to store it.

4 Training Data

Simulations are driven by trace files from three different tiled web map services,CartoCiudad, IDEE-Base and PNOA, provided by the National Geographic In-stitute (IGN) of Spain. CartoCiudad is the official cartographic database of theSpanish cities and villages with their streets and roads networks topologicallystructured. PNOA serves imagery from the Aerial Ortophotography NationalPlan, which updates every two years Spanish covers by aerial photography, highresolution and accuracy digital ortophotography, and high density and accuracyDigital Terrain Model. IDEE-Base allows viewing the Numeric CartographicBase 1:25,000 and 1:200,000 of the IGN.

Trace files were filtered to contain only valid web map requests, so the neu-ral network is trained with requests that would actually be cached. Each tracecomprises requests received from the 1th to 7th of March in 2010. Between thesedates, a total of 25.922, 94.520, and 186.672 valid map requests were receivedrespectively for CartoCiudad, IDEE-Base and PNOA.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

tiles (%)

requ

ests

(%

)

cartociudadidee−basepnoa

Fig. 2. Percentile of requests for the analyzed services.

It must be noted that the performance gain achieved by the use of a tilecache will vary depending on how the tile requests are distributed over the tilingspace. If those were uniformly distributed, the cache gain would be proportionalto the cache size. However, it has been found that tile requests describe a Paretodistribution, as shown in Figure 2. Tile requests to the CartoCiudad map servicefollow the 20:80 rule, which means that the 20% of tiles receive the 80% of thetotal number of requests. In the case of IDEE-Base, this behaviour is even moreprominent, where the 10% of tiles receive almost a 90% of total requests. PNOArequests are more scattered. This happens because about the 90% of requests


belong to the two higher resolution levels (19 and 20), the ones with largernumber of tiles.

Services that show Pareto distributions are well-suited for caching, becausehigh cache hit ratios can be found by caching a reduced fraction of the totaltiles.

5 Neural Network Cache Replacement

Artificial neural networks (ANNs) are inspired by the observation that biologicallearning systems are composed of very complex webs of interconnected neurons.In the same way, ANNs are built out of a densely interconnected group of units.Each artificial neuron takes a number of real-valued inputs (representing theone or more dendrites) and calculates a linear combination of these inputs, plusa bias term. The sum is then passed through a non-linear function, known asactivation function or transfer function, which outputs a single real-value, asshown in Fig. 3.

w1x1

w2x2

wnxn

Σ ϕ o(x1, x2,… xn)

Inputs Weights Activationfunction

Output

bias

Fig. 3. Artificial neuron.

In this work, a special class of layered feed-forward network known as multi-layer perceptron (MLP) has been used, where units at each layer are connectedto all units from the preceding layer. It has an input layer with three inputs, two-hidden layers each one comprised of 3 hidden nodes, and a single output (Fig. 4).According to the standard convention, it can be labeled as a 3/3/3/1 network.It is known that any function can be approximated to arbitrary accuracy by anetwork with three layers of units [?].

Learning an artificial neuron involves choosing values for the weights so thedesired output is obtained for the given inputs.

Network weights are adjusted through supervised learning using subsets ofthe trace data sets, where the classification output of each request is known.Backpropagation with momentum is the used algorithm for training. The neuralnetwork parameters, such as the learning rate, momentum constant or network


size, have been carefully chosen through experimentation. The parameters thatprovide the best convergence of the neural network are summarized in Table 1.

x1

x2

x3

o(x1, x2, x3)

Input layer

Hiddenlayer 1

Hiddenlayer 2

Output layer

Fig. 4. Proposed two-hidden layer feed-forward artificial neural network.

Table 1. Neural network parameters

Parameter Value

Architecture Feed-forward Multilayer PerceptronHidden layers 2Neurons per hidden layer 3Inputs 3 (recency, frequency, size)Output 1 (probability of a future request)Activation functions Log-sigmoid in hidden layers, Hyperbolic

tangent sigmoid in output layerError function Minimum Square Error (mse)Training algorithm Backpropagation with momentumLearning method Supervised learningWeights update mode Batch modeLearning rate 0.05Momentum constant 0.2

5.1 Neural Network Inputs

The neural network inputs are three properties of tile requests: recency of refer-ence, frequency of reference, and the size of the referenced tile. These propertiesare known to be important in web proxy caching to determine object cachability.

Inputs are normalized so that all values fall into the interval [−1, 1], by usinga simple linear scaling of data as shown in Equation 1, where x and y arerespectively the data values before and after normalization, xmin and xmax arethe minimum and maximum values found in data, and ymax and ymin define


normalized interval so ymin ≤ y ≤ ymax. This can speed up learning for manynetworks.

y = ymin + (ymax − ymin) × x− xmin

xmax − xmin(1)

Recency values for each processed tile request are computed as the amount oftime since the previous request of that tile was made. Recency values calculatedthis way do not address the case when a tile is requested for the first time.Moreover, measured recency values could be too disparate to be reflected in alinear scale.

To address this problem, a sliding window is considered around the timewhen each request is made, as done in [?].

With the use of this sliding window, recency values are computed as shownin Equation 2.

recency =

{max(SWL,∆Ti) if object i was requested before

SWL otherwise(2)

where ∆Ti is the time since that tile was last requested and SWL is thesliding window length.

Recency values calculated that way can already be normalized as statedbefore in Equation 1.

Frequency values are computed as follows. For a given request, if a previousrequest of the same tile was received inside the window, its frequency valueis incremented by 1. Otherwise, frequency value is divided by the number ofwindows it is away from. This is reflected in Equation 3.

frequency =

frequency + 1 if ∆Ti ≤ SWL

MAX

[frequency

∆TiSWL

, 1

]otherwise

(3)

Size input is directly extracted from server logs. As opposite to conventionalWeb proxies where requested object sizes can be very heterogeneous, in a webmap all objects are image tiles with the same dimensions (typically 256x256pixels). Those images are usually rendered in efficient formats such as PNG,GIF or JPEG that rarely reach 100 kilobytes in size.

As discussed in [?], due to greater variation in colors and patterns, the popu-lar areas, stored as compressed image files, use a larger proportion of disk spacethan the relatively empty non-cached tiles. To illustrate this, Table 2 comparesthe storage size of a “popular” tile corresponding to a city centre and an “un-popular” tile in the middle of the sea for the analyzed services.

Because of the dependency between the file size and the “popularity” of tiles,tile size can be a very valuable input of the neural network to correctly classifythe cachability of requests.


Table 2. Size on disk for a tile belonging to a city centre and to a sea region, for thedifferent services.

CartoCiudad PNOA IDEE-Base

city centre 101,08 KB 29,95 KB 12,56 KBsea region 3,57 KB 5,49 KB 1,73 KB

5.2 Neural network target

During the training process, a training record corresponding to the request of aparticular tile is associated with a boolean target (0 or 1) which indicates whetherthe same tile is requested again or not in window, as shown in Equation 4.

target =

{1 if the tile is requested again in window0 otherwise

(4)

Once trained, the neural network output will be a real value in the range[0,1] that must be interpreted as the probability of receiving a successive requestof the same tile within the time window.

A request is classified as cacheable if the output of the neural network isabove 0.5. Otherwise, it is classified as non cacheable.

5.3 Training

The neural network is trained through supervised learning using the data setsfrom the extracted trace files. The trace data is subdivided into training, valida-tion, and test sets, with the 75%, 15% and 15% of the total requests, respectivelly.The first one is used for training the neural network. The second one is used tovalidate that the network is generalizing correctly and to identify overfitting. Thefinal one is used as a completely independent test of network generalization.

Each training record consists of an input vector of recency, frequency andsize values, and the known target. The weights are adjusted using the backprop-agation algorithm, which employs the gradient descent to attempt to minimizethe squared error between the network output values and the target values forthese outputs [?]. The network is trained in batch mode, in which weights andbiases are only updated after all the inputs and targets are presented.

The pocket algorithm is used, which saves the best weights found in thevalidation set.

6 Results

Neural network performance is measured by the correct classification ratio (CCR),which computes the percentage of correctly classified requests versus the totalnumber of processed requests.

Figures 5, 6 and 7 show the CCRs obtained during training, validation andtest phases for the different services. As can be seen, the neural network is able


0 100 200 300 400 50040

50

60

70

80

90

Epochs

Cor

rect

Cla

ssifi

catio

n R

atio

(%

)

Best Validation CCR is 70.20% at epoch 146.

TrainValidationTest

Fig. 5. Correct classification ratios for CartoCiudad.

0 100 200 300 400 50040

50

60

70

80

90

Epochs

Cor

rect

Cla

ssifi

catio

n R

atio

(%

)


TrainValidationTest

Fig. 6. Correct classification ratios for IDEE-Base.

to correctly classify the cachability of requests, with CCR values over the testingdata set ranging between 72% and 97%, as shown in Table 3.

The network is stabilized to an acceptable CCR within 100 to 500 epochs.

7 Conclusions

Serving pre-generated map image tiles from a server-side cache has become apopular way of distributing map imagery on the Web. However, storage needs


0 100 200 300 400 50090

92

94

96

98

100

Epochs

Cor

rect

Cla

ssifi

catio

n R

atio

(%

)


TrainValidationTest

Fig. 7. Correct classification ratios for PNOA.

Table 3. Correct classification ratios (%) during training, validation and testing forthe different services.

CartoCiudad PNOA IDEE-Base

training 76.5952 96.5355 75.6529validation 70.2000 97.1985 77.5333test 72.7422 97.4026 82.7867

are often prohibitive which forces the use of partial caches. In this work, a cachereplacement policy based on neural networks has been proposed. The network is afeed-forward multilayer perceptron with two-hidden layers. Inputs to the neuralnetwork are recency, frequency and size of the requested tiles, and it outputsa real value in the range [0,1] which can be interpreted as the probability ofreceiving a future request of the same object before a certain period of time.It has been trained with backpropagation through supervised learning usingreal-world trace requests from different map server logs. Trace data sets havebeen divided into three groups; one for training the neural network, anotherone for validating network generalization and a completely independent datasetused for testing. The results show that the proposed neural network is able toaccurately classify cachability of requests in several scenarios from the real worldwith different workloads and request distributions.

Acknowledgments. This work has been partially supported by the SpanishMinistry of Science and Innovation through the project “Espana Virtual” (ref.CENIT 2008-1030), National Centre for Geographic Information (CNIG) andthe National Geographic Institute of Spain (IGN).


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an adaptive neural network-based method for tile replacement in a web map cache

Documents

tile cache

cache replacementpolicy

popular web map services

web map cachericardo

public web map servers

total tiles

unpopular tiles

cacheable image tiles