On the eigenvectors of p-Laplacian Abstract Spectral analysis approaches have been actively studied in machine learning and data mining areas, due to their generality, efficiency, and rich theoretical foundations. As a natural non-linear generalization of Graph Laplacian, p-Laplacian has recently been proposed, which interpolates between a relaxation of normalized cut and the Cheeger cut. However, the relaxation can only be applied to two-class cases. In this paper, we propose full eigenvector analysis of p-Laplacian and obtain a natural global embedding for multi-class clustering problems, instead of using greedy search strategy implemented by previous researchers. An efficient gradient descend optimization approach is introduced to obtain the p-Laplacian embedding space, which is guaranteed to converge to feasible local solutions. Empirical results suggest that the greedy search method often fails in many real-world applications with non-trivial data structures, but our approach consistently gets robust clustering results. Visualizations of experimental results also indicate our embedding space preserves the local smooth manifold structures existing in real-world data. Spectral data analysis is important in machine learning and data mining areas. Unlike other relaxation-based approximation techniques, the solution obtained by p-Laplacian can approximate the global solution arbitrarily tight. Meanwhile, Cheeger cut favors the solutions which are more balanced. This paper is the first one to offer a full eigenvector analysis of p-Laplacian. We proposed an efficient gradient descend approach to solve the full eigenvector problem. Moreover, we provided new analysis of the properties of eigenvectors of p-Laplacian. Empirical studies show that our algorithm is much more robust in real world data sets clustering than the previous greedy search p-Laplacian spectral clustering. Therefore, both theoretical and practical results proposed by this paper introduce a promising direction to machine learning community and related applications.

O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O B O B O O O O O O O O O O O O O O O O O O O O O


The Computational Complexity of Distance Functions of Two-Dimensional Domains We study the computational complexity of the distance function associated with a polynomial-time computable two-dimensional domains, in the context of the Turing machine-based complexity theory of real functions. It is proved that the distance function is not necessarily computable even if a two-dimensional domain is polynomial-time recognizable. On the other hand, if both the domain and its complement are strongly polynomial-time recognizable, then the distance function is polynomial-time computable if and only if P = NP . Assume that S ⊆ R 2 is a bounded two-dimensional domain (i.e., a bounded, connected open set). We let δ S (x) denote the distance between a point x in R 2 and the boundary Γ S of set S. Intuitively, the distance function δ S is computable if the set S itself is computable: We can search for the nearest point y ∈ S and output the distance between x and y. Indeed, Brattka and Weihrauch [1999] showed that for several formulations of computable closed sets in R 2 , the associated distance function is also computable.. When we consider the computational complexity of the distance function δ S with respect to the computational complexity of the set S, the situation is different. For instance, in the context of the Turing machine-based complexity theory, Chou and Ko [1995] showed the following result: If P = NP , then there exists a simply connected domain S ⊆ [0, 1] 2 whose boundary Γ S is a polynomial-time computable Jordan curve (i.e., the image of a polynomial-time computable function f from [0, 1] to [0, 1] 2 , which is one-to-one except that f (0) = f (1)), but its distance function δ S is not polynomial-time computable.. In this note, we continue the investigation of the computational complexity of the distance functions δ S of polynomial-time computable sets S ⊆ [0, 1] 2 . We consdier the following two formulations of polynomial-time computable two-dimensional regions [Chou and Ko, 1995] : A bounded two-dimensional domain S is called polynomial-time recognizable if there is a polynomial-time oracle Turing machine M such that, for any oracles φ 1 , φ 2 representing a point x ∈ R 2 and any input integer n > 0, M φ 1 ,φ 2 (n) correctly determines whether x ∈ S for all points x which have distance at least 2 −n away from the boundary of S. It is called strongly polynomial-time recognizable if, furthermore, M φ 1 ,φ 2 (n) gives correct answers for all x ∈ S (thus, M φ 1 ,φ 2 (n) can make mistakes only for those x not in S but are within the distance of 2 −n of the boundary of S). The general question we ask is the following: What is the time complexity of δ S if S is known to be polynomial-time recognizable, or strongly polynomial-time recognizable? Our main results can be summarized as follows:. (1) A polynomial-time recognizable two-dimensional domain S may have a noncomputable distance function δ S , even if S is simply connected and its boundary is a Jordan curve.. (2) If both a bounded, simply connected two-dimensional domain and its complement are strongly polynomial-time recognizable, then the associated distance function must be polynomial-time computable relative to a set in NP.. (3) If P = NP , then there exists a bounded, simply connected two-dimensional domain S whose boundary is a Jordan curve such that both S and its complement are strongly polynomial-time recognizable, but the associated distance function δ S is not polynomialtime computable.. The above result (1) seems to suggest that the notion of polynomial-time recognizability is too weak compared with other notions of computable two-dimensional sets. Results (2) and (3) agree with earlier results of Chou and Ko [1995] , and indicate that nondeterministic polynomial-time is the inherent complexity of distance functions.. Our basic computational model for real-valued functions and two-dimensional domains is the oracle Turing machine. For the theory of computational complexity of real functions based on this computational model, see Ko [1991 Ko [ , 1998 ] and Chou and Ko [1995] . We include a short summary of the definitions and notation of this theory in Section 2. For the general theory of computable analysis based on the Turing machine model, see, for instance, Pour-El and Richards [1989] and Weihrauch [2000] . The complexity classes defined in this paper are the standard ones of the discrete theory of NP-completeness; see, for instance, Du and Ko [2000] .

O B I O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O B O O O O B O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


DNS performance and the effectiveness of caching This paper presents a detailed analysis of traces of DNS and associated TCP traffic collected on the Internet links of the MIT Laboratory for Computer Science and the Korea Advanced Institute of Science and Technology (KAIST). The first part of the analysis details how clients at these institutions interact with the wide-area DNS system, focusing on performance and prevalence of failures. The second part evaluates the effectiveness of DNS caching.In the most recent MIT trace, 23% of lookups receive no answer; these lookups account for more than half of all traced DNS packets since they are retransmitted multiple times. About 13% of all lookups result in an answer that indicates a failure. Many of these failures appear to be caused by missing inverse (IP-to-name) mappings or NS records that point to non-existent or inappropriate hosts. 27 % of the queries sent to the root name servers result in such failures.The paper presents trace-driven simulations that explore the effect of varying TTLs and varying degrees of cache sharing on DNS cache hit rates. The results show that reducing the TTLs of address (A) records to as low as a few hundred seconds has little adverse effect on hit rates, and that little benefit is obtained from sharing a forwarding DNS cache among more than 10 or 20 clients. These results suggest that the performance of DNS is not as dependent on aggressive caching as is commonly believed, and that the widespread use of dynamic, low-TTL A-record bindings should not degrade DNS performance.166 This paper presented a detailed analysis of traces of DNS and associated TCP traffic collected on the Intervery long TTL values. In turn, a name's popularity among net links of the MIT Laboratory for Computer Science a group of clients that share a cache is to some extent deand the Korea Advanced Institute of Science and Techtermined by the number of clients in the group.. nology. We analyzed the client-perceived performance of To gauge the effect of TTL on DNS cache hit rate, we DNS, including the latency to receive answers, the perforperform simulations using a small modification to the al-mance of the DNS protocol, the prevalence of failures and gorithm described in Section V-B. Instead of using TTL errors, and the interactions with root/gTLD servers. We values taken from the actual DNS responses in the traces, conducted trace-driven simulations to study the effectivethese simulations set all TTL values to specific values. Fig-ness of DNS caching as a function of TTL and degree of ure 13 shows the results, with one graph for each of the cache sharing. three traces. Each graph shows the hit rate as a function A significant fraction of lookups never receive an an- In 1992, Danzig et al. [l] presented measurements of DNS traffic at a root name server. Their main conclusion was that the majority of DNS traffic is caused by bugs and misconfiguration. They considered the effectiveness of DNS name caching and retransmission timeout calculation, and showed how algorithms to increase resilience led to disastrous behavior when servers failed or when certain implementation faults were triggered. Implementation issues were subsequently documented by Kumar et al. [lo] , who note that many of these problems have been fixed in more recent DNS servers. Danzig et al. also found that one third of wide-area DNS traffic that traversed the NSFnet was destined to one of the (at the time) seven root name servers.. In contrast to Danzig et al's work, our work focuses on analyzing client-side performance characteristics. In the process, we calculate the fraction of lookups that caused wide-area DNS packets to be sent, and the fraction that caused a root or gTLD server to be contacted.. In studies of wide-area traffic in general, DNS is often included in the traffic breakdown [2] , [3] . As noted in Section I, the high ratio of DNS to TCP flows in these studies motivated our investigation of DNS performance.. It is likely that DNS behavior is closely linked to Web traffic patterns, since most wide-area traffic is Webrelated and Web connections are usually preceded by DNS lookups. One result of Web traffic studies is that the popularity distribution of Web pages is heavy-tailed [l 11, [12] , [13] . In particular, Breslau et al. conclude that the Zipflike distribution of Web requests causes low Web cache hit rates [14] . We find that the popularity distribution of DNS names is also heavy-tailed, probably as a result of the same underlying user behavior. On the other hand, DNS cache performance might be expected to differ from Web cache performance: DNS caches typically do not incur cache misses because they run out of capacity, and exclusively use TTL-based caching; DNS also caches information about each component of a hierarchical name sepa-rately (NS records); and many Web documents are present under a single DNS name. However, we find that DNS caches are nevertheless similar to Web caches in their overall effectiveness.. A recent study by Shaikh et al. shows the impact of DNS-based server selection on DNS [ 151. This study finds that extremely small TTL values (on the order of seconds) are detrimental to latency, and that clients are often not close in the network topology to the name servers they use, potentially leading to sub-optimal server selection. In contrast, our study evaluates client-perceived latency as a function of the number of referrals, and analyzes the impact of TTL and sharing on cache hit rates. We also study the performance of the DNS protocol and DNS failure modes.. Wills and Shang studied NLANR proxy logs and found that DNS lookup time contributed more than one second to approximately 20% of retrievals for the Web objects on the home page of larger servers. They also found that 20% of DNS requests are not cached locally [16] , which we consider a large percentage for the reasons explained before. Cohen and Kaplan propose proactive caching schemes to alleviate the latency overheads of synchronously requesting expired DNS records [ 171; their analysis is also derived from NLANR proxy log workload. Unfortunately, proxy logs do not capture the actual DNS traffic; thus any analysis must rely on on measurements taken after the data is collected. This will not accurately reflect the network conditions at the time of the request, and the DNS records collected may also be newer. Our data allows us to directly measure the progress of the DNS lookup as it occured. Additionally, our data captures all DNS lookups and their related TCP connections, not just those associated with HTTP requests.

B B O O O O B O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O B O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B B O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O B O O O O O O O O B B O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O


An On-line Handwritten Japanese Text Recognition System Free from Line Direction and Character Orientation Constraints SUMMARY This paper describes an on-line handwritten Japanese text recognition system that is liberated from constraints on line direction and character orientation. The recognition system first separates freely written text into text line elements, second estimates the line direction and character orientation using the time sequence information of pen-tip coordinates, third hypothetically segment it into characters using geometric features and apply character recognition. The final step is to select the most plausible interpretation by evaluating the likelihood composed of character segmentation, character recognition, character pattern structure and context. The method can cope with a mixture of vertical, horizontal and skewed text lines with arbitrary character orientations. It is expected useful for tablet PC's, interactive electronic whiteboards and so on. Due to the increasing size of writing surface on a PDA, and the advent of a tablet PC or an electronic whiteboard, people can write text more freely as on a piece of paper. Thus, the demand to remove writing constraints from on-line handwriting recognition is getting higher. A new type of pen interfaces like E-pen [1] and paper interface by Anoto pen and paper [2] , [3] are also raising this demand even higher.. Text input interface by a stylus pen started form character writing boxes and they are still in use in most of PDA, but research has been made to remove them. Murase et al. made an initial attempt to remove character writing boxes and applied DP-matching to find the best interpretation of a character pattern sequence [4] . Okamoto et al. proposed geometrical rules and features to improve the segmentation hypothesis [5] . Aizawa et al. presented a real-time segmentation of characters by a neural network using geometric features [6] . Fukushima et al. proposed a probabilistic approach and considered the likelihood based on character segmentation, shape (recognition), context, and character size [7] , [8] . Senda et al. published a similar approach to the above method and formulated the problem as a search for the most probable interpretation of character segmentation, recognition and context, but they did not deal with the likelihood of character size [9] , [10] . Recently, Microsoft Tablet PC provides on-line text recognition without character writing boxes. Although many attempts have been made to remove writing constraints, most of them have been assuming only horizontal lines of text. However, people may also write Japanese text vertically or even slantingly. Moreover, they write text with characters rotated when they write text on a whiteboard or write a memo on a piece of paper.. Therefore, we have been trying to relinquish any writing constraint from on-line text input. We proposed a method to recognize mixtures of horizontal, vertical and slanted lines of text with assuming normal character orientation [11] and even attempted to avoid character orientation constraint [12] . This paper is the updated version of the last paper and presents a system to recognize mixed on-line handwriting of arbitrary line directions and character orientations.. Section 2 of this paper defines line direction and character orientation. Section 3 presents the detailed flow of processing. Section 4 presents evaluation and shows examples of recognition and errors. Section 5 concludes this paper. This paper has presented an on-line handwritten Japanese text recognition system that is liberated not only from writing boxes or rules lines but also from constraints on line direction and character orientation. This system first separates freely written text into text line elements, second estimates the line direction and character orientation, third hypothetically segment it into characters, fourth apply character recognition and finally select the most plausible interpretation by evaluating the likelihood.. As far as a preliminary test is made, the method is working for a mixture of vertical, horizontal and skewed lines with arbitrary character orientations.. Although we have fixed the architecture of the system, we need to train each component and the total system.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Learning

Query-Specific

Distance

Functions

for

Large-Scale

Web

Image

Search

Abstract-Current

Google

image

search

adopt

a

hybrid

search

approach

in

which

a

text-based

query

(e.g.,

"Paris

landmarks")

is

used

to

retrieve

a

set

of

relevant

images,

which

are

then

refined

by

the

user

(e.g.,

by

re-ranking

the

retrieved

images

based

on

similarity

to

a

selected

example).

We

conjecture

that

given

such

hybrid

image

search

engines,

learning

per-query

distance

functions

over

image

features

can

improve

the

estimation

of

image

similarity.

We

propose

scalable

solutions

to

learning

query-specific

distance

functions

by

adopting

a

simple

large-margin

learning

framework,

using

the

query-logs

of

text-based

image

search

engine

to

train

distance

functions

used

in

content-based

systems.

We

evaluate

the

feasibility

and

efficacy

of

our

proposed

system

through

comprehensive

human

evaluation,

and

compare

the

results

with

the

state-of-the-art

image

distance

function

used

by

Google

image

search.Index

Terms-Image

search,

image

processing,

content

based

retrieval,

search

engine,

distance

learning.

E

STIMATING

image

distances

is

central

to

all

contentbased

image

retrieval

systems.

Commonly

used

distance

functions

for

image

retrieval

include

Euclidean

distance

and

Earth

Mover

distance

In

some

cases,

distance

functions

are

learned

from

data

Such

methods

have

been

generally

adopted

to

learn

a

single

distance

for

all

images

in

the

training

data..

This

work

studies

the

problem

of

learning

distance

functions

to

be

used

in

a

hybrid

image

retrieval

systems

such

as

the

one

used

by

Google

image

search.

Shown

in

Fig.

such

systems

adopt

a

hybrid

search

approach

in

which

a

text-based

query

(e.g.,

"Paris

landmarks")

is

used

to

retrieve

a

set

of

relevant

images,

which

are

then

refined

by

the

user

(e.g.,

by

re-ranking

the

retrieved

images

based

on

similarity

to

a

selected

example).

Unlike

standard

content-based

image

retrieval

system,

the

goal

is

not

to

retrieve

an

similar

image

from

a

common

set

of

images

from

the

Web,

but

rather

to

re-rank

the

query-specific

search

results

produced

by

a

text

query.

For

this

reason,

the

same

query

image

can

produce

different

similar

images

depending

on

the

context

of

the

text

query

(concrete

example

retrieval

results

can

Google

or

Bing

images

adopt

a

hybrid

search

approach

in

which

a

textbased

query

(e.g.,

"Paris

Landmarks")

is

used

to

retrieve

a

set

of

relevant

images,

which

are

then

refined

by

the

user

(e.g.,

by

re-ranking

the

retrieved

images

based

on

similarity

to

a

selected

example)..

be

seen

using

the

following

two

link-shortener:

goo.gl/gSRVN

and

goo.gl/xtZbN).

Therefore,

we

are

interested

in

learning

query-specific

distance

functions.

Similar

observation

has

made

for

exemplar-specific

distance

functions

The

motivation

for

learning

query-specific

distance

functions

stems

from

our

hypothesis

that

the

appropriate

choice

of

feature

depends

upon

the

query.

For

example,

consider

the

problem

of

identifying

a

photo

of

Eiffel

Tower.

If

the

query

is

"Paris

landmarks"

as

shown

in

Fig.

then

shape

feature

will

be

valuable

as

it

differentiates

Eiffel

tower

more

clearly

from

other

architectural

structures.

On

the

other

hand,

if

the

query

is

"Eiffel

Tower"

as

shown

in

Fig.

then

color

feature

would

be

relatively

more

useful

than

shape.

Since

the

context

(e.g.,

the

query

"Eiffel

Tower")

is

expected

to

already

restrict

the

images

to

the

correct

landmark,

the

measure

of

similarity

should

instead

group

the

images

on

a

less

constrained

dimension,

such

as

time-of-day,

as

the

color

distribution

corresponding

to

time

of

day..

This

work

proposes

a

simple

query-specific

distance

learning

framework:

the

system

groups

training

images

and

meta-data

by

their

associated

text

labels,

the

system

learns

the

optimal

distance

function

from

each

group

of

training

data

using

largemargin

formulation

introduced

by

This

learning

framework

can

be

easily

implemented

using

parallel

computational

MapReduce

framework.

Once

learned,

the

distance

functions

are

indexed

together

with

the

images

annotated

with

the

specific

text-query..

Our

work

is

partially

inspired

by

Frome

et

al.

who

proposed

to

learn

local

distance

function

for

each

image

exemplar.

Such

exemplar-specific

distance

functions,

however,

are

computationally

expensive

for

large-scale

Web

image

retrieval.

Therefore,

based

on

the

observation

that

search

query

frequency

follows

power

law

distribution

we

believe

query-specific

distance

functions

can

be

applied

to

only

the

most

popular

search

queries

and

still

service

large

portion

of

the

overall

search

engine

traffic..

IEEE.

Translations

and

content

mining

are

permitted

for

academic

research

only.

Personal

use

is

also

permitted,

but

republication/

redistribution

requires

IEEE

permission.

See

for

more

information.

This

work

focuses

on

addressing

two

questions

related

to

learning

query-specific

distance

functions

for

large-scale

Web

image

search..

How

can

we

collect

sufficient

amount

of

labelled

training

data

to

learn

distance

function

for

each

query?

Standard

methods

to

collect

training

labels,

such

as

manual

labelling

and

relevance

feedback,

are

costly

as

they

require

active

human

participation,

and

the

resulting

annotations

are

usually

insufficiently

descriptive

of

the

image

contents

Does

learned

query-specific

distance

functions

significantly

improve

the

estimation

of

image

similarity

from

the

perspective

of

human

raters?

Note

that

due

to

the

added

degrees

of

freedom,

using

query-specific

function

will,

in

many

situations

(especially

when

training

and

testing

data

are

drawn

from

the

same

underlying

distribution),

produce

more

accurate

image

comparisons

than

query-independent

distances.

Therefore,

any

analysis

needs

to

be

conducted

in

a

way

such

that

evaluation

method

are

not

directly

tied

to

how

training

data

is

produced.

This

work

makes

the

two

contributions.

First,

we

demonstrate

that

user

click-patterns

made

on

text-based

search

engine

(e.g.,

Google

image

search)

can

be

used

to

train

content-based

image

distance

functions.

As

text-based

search

engines

attract

large

user

traffic,

such

"transfer"

of

labelled

data

to

train

contentbased

retrieval

system

makes

it

possible

to

apply

supervised

metric

learning

techniques

such

as

to

large

number

of

Web

queries

and

images.

Although

learning

from

click-data

has

been

explored

previously

there

is

very

little

work

on

learning

image

distances

from

an

open

and

unconstrained

text-based

system,

on

which

users

do

not

have

a

predefined

guideline

on

tasks

to

accomplish.

For

example,

the

images

clicked

by

a

casual

surfer

may

not

exhibit

any

semantic

or

visual

relations

at

all.

This

work

conducted

a

detailed

study

in

order

to

verify

that,

by

aggregating

the

query

sessions

made

by

large

number

of

Web

users,

the

averaged

click-patterns

largely

reflect

the

results

of

perceptual

similarity

test..

The

second

contribution

of

this

work

is

a

comprehensive

study

on

the

feasibility

and

effectiveness

of

query-specific

distance

functions

for

Web

image

search.

This

work

applies

distance

learning

technique

introduced

in

to

learn

query-specific

distance

function

from

click-data

derived

from

text-based

search

engines.

Our

method

is

more

scalable

than

previously

proposed

exemplar-specific

distance

functions

when

applied

to

large-scale

Web

search.

Our

work

also

demonstrated

that

learning

query-specific

image

distances

produces

more

accurate

measurement

of

image

similarity

than

the

state-of-the-art

Google

similar

image

search

system.

Specifically,

we

conducted

two

types

of

experiments:

perceptual

experiments

that

compare

estimated

image

similarity

with

those

derived

from

judgement

of

human

raters,

target-search

experiments

that

measure

users'

efficiency

in

finding

the

relevant

images

using

various

distance

functions.

Our

results

demonstrate

that

query-specific

distance

functions

outperform

the

distance

function

used

Google

image

search.

The

difference

in

accuracy

is

especially

significant

given

polysemy

queries.

The

rest

of

the

paper

is

divided

into

six

sections.

Section

II

introduces

related

works

in

learning

distance

functions

for

Web

image

retrieval.

Section

III

proposes

methods

to

derive

measurement

of

image

similarity

from

text-based

image-search

query

logs,

and

then

use

this

information

as

training

data.

Section

IV

introduces

methods

to

learn

query-specific

distance

functions.

Sections

V

and

VI

present

evaluation

results

with

perceptual

similarity

and

target-search

experiments

respectively.

Section

VII

presents

the

conclusions

and

future

work.

This

work

studies

the

feasibility

and

efficacy

of

learning

query-specific

distance

functions

for

large-scale

Web

image

search.

We

demonstrate

that

co-click

statistics

derived

from

text-based

search

engine

query

logs

can

be

used

to

predict

how

a

person

will

compare

images

based

on

perceptual

similarity,

one

can

learn

query-specific

distances

from

such

sources

of

information,

and

the

learned

distances

produce

more

accurate

comparisons

of

images

and

reduce

search

abandonment-rate

compare

to

the

query-independent

image

distance

function

used

by

current

Google

image

search..

There

are

two

potential

ways

to

improve

the

learning

approaches

proposed

in

this

work.

First,

one

way

to

improve

query-specific

distance

functions

is

to

allow

related

text-queries

to

"share"

the

learned

distance

functions.

For

example,

one

can

first

group

the

text

queries

into

synsets,

and

learn

synset-specific

distance

functions

for

each

synset.

One

can

derive

synsets

from

an

expert-knowledge

database

such

as

WordNet

or

from

the

text

and

images

associated

such

queries

By

allowing

training

data

to

be

shared

among

related

queries,

synset-specific

distances

can

be

computed

for

less

commonly

used

queries.

Sharing

distance

functions

also

reduces

the

number

of

distance

functions

that

need

to

be

cached

by

the

retrieval

system.

Second,

since

our

results

have

shown

that

query-specific

distance

functions

can

improve

ranking

accuracy

in

certain

query

categories

(e.g.,

polysemy)

more

than

others

(e.g.,

animal),

the

ability

to

automatically

select

queries

or

query

categories

that

are

suitable

for

such

distance

functions

would

be

beneficial.

One

possible

approach

is

to

measure

the

disagreement

between

the

co-click

statistics

and

the

visual

similarity

produced

by

using

un-weighted

Euclidean

distance,

and

use

such

disagreement

as

an

indication

of

whether

query-specific

distance

can

be

useful.

Our

work

is

mainly

related

to

two

areas

of

research.

The

first

area

is

related

to

distance

learning

research

in

machine

learning,

and

the

second

is

related

to

exploring

log

data

as

relevance

feedback

in

Web

search.

This

work

briefly

reviews

some

representative

works

in

both

areas.

O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B I I B I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Forecasting and simulating mortality tables In this paper we suggest solutions to the actuaries, facing the problem of estimating future mortality tables, especially in cases where there is a lack of relevant data and where the tendencies are not easy to estimate directly. We propose the utilization of external sources of information in the form of other, published mortality tables and use formal statistical tests to decide among these possible candidates. The procedure can also be applied for checking e.g. the goodness of mortality selection factors. We suggest the use of parametric families in modelling; for example the simple 2-parameter Azbel model. We conclude the paper by a simulation study which allows for the quantification of the possible risks related to unforeseen changes in the mortality tables in the future. To calibrate the variances of these models, initial estimates are needed, which we get by the Lee-Carter method. An actuary regularly faces the problem of calculating annuities or insurance premiums, for which the exact values depend on future changes in mortality tables. As this is not known at the moment of the calculations, one usually uses the latest available tables for the given (or an analogous) population.. This problem is especially challenging in the new EU member states, which have recently experienced quick changes in mortality patterns and one may expect the changes to continue. As the level of the health care as well as the healthconsciousness lag behind the current western European or American situation, it is logical to assume a development analogous to what was observed in these countries. The application of this method can be summarized as follows:. 1. Find a historical mortality table that resembles well the current table of the population 2. The future development of the mortality table is supposed to be analogous to the development of the historical table, which is available (at least for a certain time period) 3. Several possible scenarios may be simulated alongside the evolution of the main table of point 2, allowing for the investigation of longer series as well as the estimation of the variance of the parameter under investigation (annuity, premium etc.). The suggested methods can be applied in two main situations. In the first case there is enough data for the important age groups. Then the suggested method of analogy can be a relatively simple procedure for checking the classical demographic or more modern forecast methods such as the Lee-Carter method [1] . Such a situation is typical in the case of population mortality.. Another -probably more important -area of application is the case when we have only a short period of observations and these do not cover the whole range of ages. In Hungary (and several other countries in Central Europe) this is true for insurance companies providing life insurance or annuities. The private insurance companies started their operation in the early 1990s and they have sold hardly any annuities since then. Pension funds have large membership, but the financial services itself will start only in the next couple of years. So there is no mortality data of the over 60s available for the insurance companies. The proposed method of analogy helps us to model the mortality of future annuitants without any previous local experience.. The paper is organized as follows. In Section 2 we investigate the similarity measures for mortality tables. Then we propose a new method for hypothesis testing based on these measures in Section 3. Section 4 deals with fitting parametric models, while in Section 5 we investigate forecasting and simulation.

B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B O B


First-Order System Least Squares and the Energetic Variational Approach for Two-Phase Flow This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen-Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques. Complex fluids involve multi-physics and multi-scale phenomena that require advanced techniques in scientific computing in order to be solved efficiently. The goal of this paper is to present numerical techniques that have been well tested and shown to give accurate solutions with a reasonable amount of computational cost, while also preserving the global energy of the system. While the systems can be described with partial differential equations (PDEs), in this case a time-dependent and nonlinear system of equations, an underlying energy law also describes the physics. It is from these laws that the PDE is derived. Therefore, approximate solutions to complex fluid problems should adequately approximate this energy law.. Here, we look at one type of complex fluid problem, two-phase flow. The conventional sharp interface description of the mixture of two Newtonian fluids with density, ρ i , and viscosity, µ i , assumes the mixture occupies the overall domain, Ω = Ω 1 ∪ Ω 2 , as in figure 1 . The interface between two materials is the free moving interface, Γ t . The overall system includes the Navier-Stokes equation in each Ω i , where i = 1 or 2:. Here, u i , p i , ρ i , and µ i are the velocities, pressures, densities, and viscosities of each fluid, respectively. Two types of boundary conditions are possible. Kinematic boundary conditions yield u i ·n = V n , where n is the "directional" normal of Γ t and V n is the normal speed of Γ t . Traction free boundary conditions (also known as force balance conditions) satisfy [τ i ] · n = surface force on Γ t , where [τ i ] is the jump of the stress tensor,. Remark Assume u 2 | ∂Ω = 0. With the traction free boundary condition, this implies Γ t ∩ ∂Ω = ∅.. In case the surface force is attributed to the surface tension, i.e., F surface = kHn, where H is the mean curvature of Γ t and k is the surface tension parameter, then the whole system possesses the underlying energy law,. In this paper, we take a different approach, called the diffusive interface method (phase-field method). The label function, φ(x, t), is introduced such that φ(x, t) = +1 in fluid 1, −1 in fluid 2.. The interaction between the two materials is reflected through the "mixing" energy, or the Ginzburg-Landau type of energy:. where Ω 1 2 |∇φ| 2 dx represents the tendency of the mixture to be homogeneous. In other words, it is the "phillic" interaction. In addition, Ω 1 4 2 φ 2 − 1 2 dx represents the "phobic" interaction, or the tendency of the mixture to be separated. The parameter reflects the competition between the two opposite tendencies. Due to the nature of this empirical energy, it is present in many theories in physics, such as superconductivity [1, 2] and phase transitions [3, 4] . It can be shown that φ → ±1 almost everywhere as → 0, thus representing the separation of the two immiscible materials. Moreover, the thermodynamics and patterns of the interface, Γ t , can be captured by the level sets of φ, for instance, {x|φ(x, t) = 0}. In addition, the energy Ω W (φ) → c 0 Area(Γ t ), which is equivalent to the surface tension case in the sharp interface formulation [5] . It is worth pointing out that, while one can view the diffusive interface formula as being the regularizing approximation of the sharp interface formulation, it is more physical to view the sharp interface formulation as being the ideal approximation of the diffusive interface method. Therefore, it can be understood that the phase field description really captures the microscopic interaction of the mixtures.. In the examples presented here, we consider problems where we have one or more bubbles of one phase interacting in a region of a fluid of the other phase. From this system, the continuous energy laws are derived as is the continuous system of PDEs. We then show that these laws are adequately preserved numerically.. To solve the system, we use the first-order system least-squares (FOSLS) finite element approach. This method has been well-tested on many different types of PDEs and, specifically, on several complex fluid systems [6, 7, 8, 9, 10] , including those of magnetohydrodynamics (MHD) [11, 12] . We show that use of the FOSLS method allows both an accurate solution of the system and preservation of the energy laws. Moreover, because we are using this method, we have the advantage of being able to use other numerical techniques, such as nested iteration and adaptive local refinement, which greatly improve the efficiency of solving these problems. This paper is structured as follows. In Section 2, we describe the two-phase model and present the equations to be solved. In section 3, we discuss the FOSLS formulation that is used and show how it presents a well-posed discrete problem. Section 4 introduces the energy laws and discusses what quantities are preserved with the numerical schemes being used. Numerical results for certain bubble test problems and an MHD simulation are presented in section 5, where it is shown that this approach is accomplishing the intended goal. Finally, a discussion of the results and summary is given in section 6. This paper shows that using the Newton-FOSLS finite-element formulation, along with nested iteration, algebraic multigrid, and adaptive local refinement, accurately resolves two-phase flow simulations while still preserving the energetics of the system. The numerical algorithms used were designed in a general setting and have the advantage of reducing the amount of computational cost. For the two-phase flow problems, it is possible to resolve the physics in the equivalent of less than 50 fine-grid relaxation sweeps for each time step. This is accomplished by reducing the amount of work done on highly resolved grids and by reducing the number of elements needed to solve the problem via adaptive local refinement. As a result, complicated systems of PDEs can be solved very efficiently without losing the ability to measure certain physical quantities. This paper shows that, when applied to two-phase flow simulations, all the advantages of using implicit finite element methods are obtained, and the FOSLS methodology is capable of capturing the important aspects of the model, such as the energy laws.. Despite the success of the above algorithms in capturing the correct energy laws efficiently, there has been one bottleneck. In all the simulations, classical algebraic multigrid (AMG) was used to solve the discrete linear systems. Classical AMG was designed for scalar elliptic problems and M-matrices. As can be seen in figure 8 , the average convergence factors for AMG over each time step can be quite poor when it is used on systems for which it was not designed. While it is always bounded away from 1, one can see that the worse the AMG convergence factor gets, the more computational work is needed to solve the problem. Therefore, future work will involve investigating various multigrid methods that will be more well-suited to the test problems described above. Algebraic methods that are designed more specifically for systems of PDEs will be studied as well as geometric multigrid. All the domains have been well structured and, therefore, it is possible to use more of the geometric information to create a better solver. If it is possible to improve the linear solver using these methods, then the amount of work can be reduced even further.

B I I I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B I O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Impact of Landmark Parametrization on Monocular EKF-SLAM with Points and Lines Abstract This paper explores the impact that landmark parametrization has in the performance of monocular, EKFbased, 6-DOF simultaneous localization and mapping (SLAM) in the context of undelayed landmark initialization.Undelayed initialization in monocular SLAM challenges EKF because of the combination of non-linearity with the large uncertainty associated with the unmeasured degrees of freedom. In the EKF context, the goal of a good landmark parametrization is to improve the model's linearity as much This work compares the performances of eight different landmark parametrizations: three for points and five for straight lines. It highlights and justifies the keys for satisfactory operation: the use of parameters behaving proportionally to inverse-distance, and landmark anchoring. A unified EKF-SLAM framework is formulated as a benchmark for points and lines that is independent of the parametrization used. The paper also defines a generalized linearity index suited for the EKF, and uses it to compute and compare the degrees of linearity of each parametrization. Finally, all eight parametrizations are benchmarked employing analytical tools (the linearity index) and statistical tools (based on Monte Carlo error and consistency analyses), with simulations and real imagery data, using the standard and the robocentric EKF-SLAM formulations. Simultaneous localization and mapping (SLAM) is the problem of concurrently estimating in real time the structure of the surrounding world (the map), perceived by moving exteroceptive sensors, while simultaneously getting localized in it. The seminal solution to the problem by Smith and Cheeseman (1987) employs an extended Kalman filter (EKF) as the central estimator, and has been used extensively. In EKF-SLAM, the map is a large vector stacking sensors and landmark states, and it is modeled by a Gaussian variable. This map, usually called the stochastic map, is maintained by the EKF through the processes of prediction (the sensors move) and correction (the sensors observe the landmarks in the environment that had been previously mapped).. In order to achieve true exploration, the EKF machinery is enriched with an extra step of landmark initialization, where newly discovered landmarks are added to the map. Landmark initialization is performed by inverting the observation function and using it and its Jacobians to compute, from the sensor pose and the measurements, the observed landmark state and its necessary co-and cross-variances with the rest of the map. These relations are then appended to the state vector and the covariances matrix.. Monocular SLAM refers to the case where the exteroceptive sensing means are limited to a single projective camera. Monocular SLAM gained popularity back in 2003 thanks to the first full real-time implementation by Davison (2003) , based on Smith and Cheeseman's EKF solution. Davison's technique elegantly solved a great number of problems, but there still remained one that occupied researchers on visual SLAM for some years (Chiuso et al. 2002; Bailey 2003; Kwok and Dissanayake 2003; Lemaire et al. 2005) : the problem of landmark initialization.. Landmark initialization in monocular SLAM is difficult because, due to the projective nature of the sensor, this cannot provide the distance to the perceived landmarks: the measurements are rank-deficient and the observation functions are not invertible. This means that a full 3D estimate of the landmarks just discovered is not available for mapping, because the uncertainty in the unobserved degrees of freedom (DOF) is infinite and, being the measurement equations non-linear, EKF cannot deal with it. Early approaches (Davison 2003; Bailey 2003; Lemaire et al. 2005 ) took advantage of the sensor motion to achieve fully 3D estimates before actually initializing the landmarks. This family of methods introduces a delay until the sensor motion has gained enough parallax for triangulation, during which the landmarks, not yet mapped, cannot provide any information for localization.. Monocular EKF-SLAM reached maturity with the advent of undelayed landmark initialization techniques (ULI, explained in more detail in the next section), a need of partial initialization firstly stated by Solà et al. (2005) . The key to ULI is to substitute the unmeasured DOF by a Gaussian prior: the objective then is to find a way to allow this prior to possess an infinite uncertainty while still being manageable by the EKF. Solà et al. describe a preliminary solution based on an exponentially distributed multi-hypotheses depth parametrization, which was inspired on a previous work by Kwok and Dissanayake (2004) . The problem was successfully solved for the first time with the inverse-depth landmark parametrization (IDP) by Montiel et al. (2006) , which has become very popular. More recently, Marzorati et al. (2008) and Haner and Heyden (2010) have presented new parametrizations for which the authors claim better performances than IDP. Solà (2010) presents a comparative study of three parametrizations for point landmarks.. A smaller number of works incorporate line landmarks or segments to the EKF-SLAM framework. Gee and Mayol (2006) , Smith et al. (2006) and Lemaire and Lacroix (2007) use delayed techniques for initialization. Solà et al. (2009b) reports the only ULI solution for infinite lines we are aware of, which uses the Plücker line. Edgelets (very short line fragments associated to a 3D point) were introduced by Eade and Drummond (2006a) , also in an undelayed manner, using IDP as the supporting point type.. Overall, the methods here cited have many points in common. Unfortunately, their differences lie in many parts of the algorithm other than landmark parametrization, in the evaluation methods and/or in the heterogeneity of the experimental setups. This makes it difficult to tell which aspects of the proposed solutions are at the base of the observed differences in performance. In this work, we fix the algorithmic and experimental aspects of the problem and center our attention to the effect that landmark parametrization has, by its own right, on monocular EKF-SLAM performance. For this, the paper retakes the problem from a unified perspective that considers points and lines alike (edgelets are not covered), and presents and analyzes a compendium of eight different parametrizations, three for points and five for lines, among which three are innovative to the best of our knowledge. This paper was initially conceived as a compendium of landmark parametrizations for monocular SLAM. Our very first aim was to show that all these methods are very intimately related, as we have exposed amply. As the work evolved, we realized that the material and insights provided should also be a good basis for establishing good practices for approaching a more general problem, that is, the problem of accurately estimating high-dimensional dynamic systems of non-linear nature and huge uncertainty levels with the use of relatively simple analytic tools such as the EKF.. We summarize here the main concepts and results presented in this work:. 1. Undelayed landmark initialization (ULI) is fundamental in the sense that it is the way we can make use of all the geometrical information provided by the landmarks: from the first observation, up to the infinity range, and independently of the sensor trajectory. 2. Implementing ULI within EKF is difficult because of the combination of non-linearity and unbounded uncertainty regions.. -Linearity and Gaussiannity are the two keys to satisfactory EKF operation. Astute transformations and redundancy in the parametric descriptions of the system produce analytic expressions and probability densities that are well adapted to the estimator in use. -Inverse-distance behavior of the unmeasurable parameters is the key that makes undelayed initialization of landmarks possible when they are perceived from projective sensors. -Once ULI is achieved, landmark anchoring has shown to be the major actor in further improving linearity to reach satisfactory levels. -Manipulations on the measurable parameters, such as the use of rectangular or polar coordinates for the director vectors, have shown to produce no remarkable effects. This is because, being these parameters measured with good accuracy, their degree of uncertainty is small and the functions in which they appear are regarded by EKF as being linear. -Therefore, AMPP and AMPPL parametrizations are preferred over AHP and AHPL because of their lower computation cost for an equivalent performance.. 3. Because of the higher representativeness of anchored point-supported lines over unanchored and Plücker-based lines, and because of the absence of constraints to be guaranteed, the anchored point-supported lines constitute the preferred choice for undelayed monocular EKF-SLAM. Therefore, AMPPL is the preferred parametrization for infinite straight lines. 4. A great number of parametrizations can be regarded as a sequence of small modifications of ones with respect to the others (Fig. 8) . We have traversed a family of eight parametrizations and established quasi-trivial links between them. We have shown that estimating points and lines is fundamentally the same problem and admits fundamentally the same solutions. Estimating other parametric entities such as conic sections, splines or planes should also be feasible as long as we can take good advantage of the principles exposed here. 5. Measuring non-linearity for high-dimensional MIMO functions is an interesting but difficult task, especially if we want the measure to be useful for comparing parametrizations of different dimensionality.. -We defined a linearity index that incorporates the local knowledge of the uncertainty region, which is well suited for EKF usage. -The index is expressed in the measurement space, which is common to all parametrizations and allows us to compare them with each other.. 6. Visual inspection, linearity analysis, RMS errors and average NEES consistency, all give a coherent picture of the performance of each parametrization. 7. Using more evolved algorithms such as robocentric EKF-SLAM has not altered the relative performances of the parametrizations. This is because the superiority of some parameterizations over others comes from the severe linearity constraints that the EKF imposes, and hence the conclusions drawn in this paper could be extended to any EKF-based visual SLAM algorithm. It would be interesting to see if this also applies to iterative optimizers such as SBA, and in such case if the improvements (e.g. fewer optimizer iterations) are sufficient to compensate for the extra amount of computational power (e.g. more operations per iteration) that would be required. its projective behavior). Each endpoint p i is specified by an abscissa t i such that. -In point-supported lines (Fig. 30(b) ) the endpoints are defined with respect to the support points q i = p 0 + m i /ρ i . The origin is at q 1 and the unit length is defined by q 2 − q 1 , leading to the endpoints. The initial abscissas are defined trivially with (t 1 , t 2 ) = (0, 1).. Before updating, we need to back-project the currently observed endpoints onto the 3D line. This is done by triangulating the 3D line with the optical rays of the two currently observed 2D endpoints. To avoid aberrant results it is advised to update each abscissa only if the triangulation angle between the ray and the line is greater than a certain value (we use 15 • ). The result is a couple of candidate abscissas (t 1 , t 2 ) that are assigned to (t 1 , t 2 ) depending on the following rules: -During convergence the abscissas are either not updated ( Fig. 31(a) , used for AHPL and AMPPL), thus reflecting the initial observation, or systematically updated (Fig. 31(b) , used for PL, APL and HPL), simply reflecting the last observation. -Once the line has converged, an extending-only policy is applied (Fig. 31(c) ): the abscissa is updated only if this lengthens the 3D segment. It is to note that a converged line is ready for reparametrization to any minimal (or at least more economical) form.

O O B I O O O O O O O O O O O O O O B I O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A high fidelity ATM traffic and network simulator The design of an ATM Traffic and Network (ATM-TN) simulator which characterizes cell level network behavior is presented. The ATM-TN simulator can be used to charxterize arbitrary ATM networks with dynamic multimedia traffic loads. Call set up and tear down via ATh4 s i m n g is implemented in addition to the various types of cell traffic streams generated by voice, video and data. The simulator is built on a simple, efficient simulation language called SimKit which is capable of support& both fast sequential and parallel execution. Parallel execution is supported using WarpKit, an optimistically synchronized kemel that is aimed at shared memory multiprocessor platforms such as the Silicon Graphics Powerchallenge and Sun Sparc 1000 series machines.The paper outlines general requirements for ATM W i c and network simulation, presents an ATM-TN simulator architecture, describes its major components and discusses the major issues associated with cell level ATM modeling and simulation. Asynchronous Transfer Mode (ATM) networks a~e rapidly emerging as the next generation communications standard. ATM offers substantial functional advances in communication services including high speed data transfer, and interactive voice and video. ATM multimedia technology is being adopted across a wide spectrum of network configurations including local a m networks ( L A N s ) , metropolitan area networks (MANS), and wide area networks (WANs).

O O O O B O B O O B O O O B O B O O O O O O B B O O O O O O O O O O O O O O B B B O O O O O O O O O O O O O O O O O O O O O B O O B O O O B B O B O O O O O O O O B B O O O O O O O O O O O B O B O O O O O O O O O O O O O B I O O O O O O B O O O O O O O B O B B O O O O O O B B O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O B O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O


Approximating the Bottleneck Plane Perfect Matching of a Point Set A bottleneck plane perfect matching of a set of n points in R 2 is defined to be a perfect non-crossing matching that minimizes the length of the longest edge; the length of this longest edge is known as bottleneck. The problem of computing a bottleneck plane perfect matching has been proved to be NP-hard. We present an algorithm that computes a bottleneck plane matching of size at least n 5 in O(n log 2 n)-time. Then we extend our idea toward an O(n log n)-time approximation algorithm which computes a plane matching of size at least 2n 5 whose edges have length at most √ 2 + √ 3 times the bottleneck. We study the problem of computing a bottleneck non-crossing matching of points in the plane. For a given set P of n points in the plane, where n is even, let K(P ) denote the complete Euclidean graph with vertex set P . The bottleneck plane matching problem is to find a perfect non-crossing matching of K(P ) that minimizes the length of the longest edge. We denote such a matching by M * . The bottleneck, λ * , is the length of the longest edge in M * . The problem of computing M * which has applications in VLSI layout design and operations research, has been proved to be NP-hard [1] . Figure 1 in [1] and [2] shows that the longest edge in the minimum weight matching (which is planar) can be unbounded with respect to λ * . On the other hand the weight of the bottleneck matching can be unbounded with respect to the weight of the minimum weight matching, see Figure 1 . [1] O(n 1.5 √ log n) 2 √ 10λ * n/2 Section 4.1 O(n log 2 n) λ * n/5 Section 4.2 O(n log n) ( √ 2 + √ 3)λ * 2n/5 We considered the NP-hard problem of computing a bottleneck plane perfect matching of a point set. Abu-Affash et al. [1] presented a 2 √ 10-approximation for this problem. We used the maximum plane matching problem in unit disk graphs (UDG) as a tool for approximating a bottleneck plane perfect matching. In Section 3.1 we presented an algorithm which computes a plane matching of size n 6 in UDG, but it is still open to show if this algorithm terminates in polynomial number of steps or not. We also presented a It is desirable to compute a perfect matching of a point set in the plane, which is optimal with respect to some criterion such as: (a) minimum-cost matching which minimizes the sum of the lengths of all edges; also known as minimum-weight matching or min-sum matching, and (b) bottleneck matching which minimizes the length of the longest edge; also known as minmax matching [6] . For the minimum-cost matching, Vaidya [8] presented an O(n 2.5 log 4 n) time algorithm, which was improved to O(n 1.5 log 5 n) by Varadarajan [9] . As for bottleneck matching, Chang et al. [3] proved that such kind of matching is a subset of 17-RNG (relative neighborhood graph). They presented an algorithm, running in O(n 1.5 √ log n)-time to compute a bottleneck matching of maximum cardinality. The matching computed by their algorithm may be crossing. Efrat and Katz [6] extended the result of Chang et al. [3] to higher dimensions. They proved that a bottleneck matching in any constant dimension can be computed in O(n 1.5 √ log n)-time under the L ∞ -norm.. Note that a plane perfect matching of a point set can be computed in O(n log n)-time, e.g., by matching the two leftmost points recursively.. Abu-Affash et al. [1] showed that the bottleneck plane perfect matching problem is NP-hard and presented an algorithm that computes a plane perfect matching whose edges have length at most 2 √ 10 times the bottleneck, i.e., 2 √ 10λ * . They also showed that this problem does not admit a PTAS (Polynomial Time Approximation Scheme), unless P=NP. Carlsson et al. [2] showed that the bottleneck plane perfect matching problem for a Euclidean bipartite complete graph is also NP-hard.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A memetic algorithm with adaptive hill climbing strategy for dynamic optimization problems Abstract Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This paper investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbing method is proposed as the local search technique in the framework of memetic algorithms, which combines the features of greedy crossover-based hill climbing and steepest mutation-based hill climbing. In order to address the convergence problem, two diversity maintaining methods, called adaptive dual mapping and triggered random immigrants respectively, are also introduced into the proposed memetic algorithm for dynamic optimization problems. Based on a series of dynamic problems generated from several stationary benchmark problems, experiments are carried out to investigate the performance of the proposed memetic algorithm in comparison with some peer evolutionary algorithms. The experimental results show the efficiency of the proposed memetic algorithm in dynamic environments. Many real-world optimization problems are dynamic optimization problems (DOPs), where the function landscapes may change over time and, thus, the optimum of these problems may also change over time. DOPs require powerful heuristics that account for the uncertainty present in the real world. Since evolutionary algorithms (EAs) draw their inspiration from the principles of natural evolution, which is a stochastic and dynamic process, they also seem to be suitable for DOPs. However, traditional EAs face a serious challenge for DOPs because they cannot adapt well to the changing environment once converged.. In order to address DOPs, many approaches have been developed [41] and can be grouped into four categories: 1) increasing population diversity after a change is detected, such as the adaptive mutation methods [4, 33] ; 2) maintaining population diversity throughout the run, such as the immigrants approaches [11, 39, 40] ; 3) memory approaches, including implicit [10, 32] and explicit memory [2, 35, 38, 43] methods; 4) multi-population [3, 24] and speciation approaches [27] . A comprehensive survey on EAs applied to dynamic environments can be found in [14] .. In recent years, there has been an increasing concern from the evolution computation community on a class of hybrid EAs, called memetic algorithms (MAs), which hybridize local search (LS) methods with EAs to refine the solution quality. So far, MAs have been widely used for solving many optimization problems, such as scheduling problems [13, 19, 20] , combinatorial optimization problems [8, 30, 31] , multi-objective problems [9, 12, 18] and other applications [44, 45] . However, these problems for which MAs have been applied are mainly stationary problems. MAs have rarely been applied for DOPs [6, 7, 36] . During the running course of general MAs, they may always exhibit very strong exploitation capacity due to executing efficient local refinement on individuals, but they may lose the exploration capacity as a result of the population converging to one optimum, which needs to be avoided in dynamic environments. Therefore, it becomes an interesting research issue to examine the performance of MAs, which are enhanced by suitable diversity methods, for DOPs.. In this paper, we investigate the application of a MA with an adaptive hill climbing strategy, which combines the features of crossover-based hill climbing and mutation-based hill climbing in both cooperative and Procedure General GA-based MA: begin parameterize(pop size, pc, pm); t := 0; initializePopulation(P (0)); evaluatePopulation(P (0)); elite := selectForLocalSearch(P (0)); localSearch(elite); repeat P ′ (t) := selectForReproduction(P (t)); P ′′ (t) := crossover(P ′ (t)); mutate(P ′′ (t)); evaluatePopulation(P ′′ (t)); P (t + 1) := selectForSurvival(P (t),P ′′ (t)); elite := selectForLocalSearch(P (t + 1)); localSearch(elite); t := t + 1; until a stop condition is met end; competitive fashions, to address DOPs. In order to address the convergence problem, two diversity maintaining approaches, an adaptive dual mapping and a triggered random immigrants scheme, are introduced into the proposed MA to improve its performance in dynamic environments. The effect of introducing these two diversity maintaining approaches into our MA for DOPs is experimentally investigated.. The rest of this paper is organized as follows. Section 2 describes the proposed MA with two hill climbing strategies investigated in this paper. Section 3 introduces a series of DOPs generated by a dynamic problem generator from the stationary test suite. Section 4 reports the experimental results and relevant analysis. Finally, Section 5 concludes this paper with some discussions on relevant future work. In this paper, the application of memetic algorithms with an adaptive hill climbing (AHC) strategy for dynamic optimization problems is investigated. In the proposed memetic algorithm, two local search methods, the greedy crossover-based hill climbing (GCHC) and the steepest mutation-based hill climbing (SMHC), are used to refine the individual that is selected for local improvements. A learning mechanism, which gives the more effective LS operator greater chance for the later individual refinement, is introduced in order to execute a robust local search. To maintain a sufficient population diversity for the algorithms to adapt well to the environmental changes, two diversity maintaining methods, adaptive dual mapping (ADM) and triggered random immigrants (TRI), are introduced into our proposed MA.. From the experimental results, we can draw the following conclusions on the dynamic test problems.. First, MAs enhanced by suitable diversity methods can exhibit a better performance in dynamic environments. For most dynamic test problems, our MA always outperforms other peer EAs.. Second, the ADM and TRI approaches are both efficient for improving the performance of MAs in dynamic environments. However, the two diversity methods have different effect in different dynamic environments. The ADM method does better when the environment involves significant changes (i.e., ρ = 0.9) and the TRI method performs better when the environmental severity ρ = 0.5. It is a good choice that the two diversity methods are both introduced into MAs in dynamic environments.. Third, the LS operator is problem dependent. The AHC strategy can help MAs execute a robust individual refinement since it employs multiple LS operators under the mechanism of cooperation and competition.. Fourth, the difficulty of DOPs depends on the environmental dynamics, including severity and speed of changes and the difficulty of the base stationary problems. In our experiments, MAs perform better with the increasing of the frequency of changes and the effect of the severity of changes is problem dependent.. Generally speaking, the experimental results indicate that the proposed MA, where the adaptive hill climbing operator is used as a local search technique for individual refinement, with adaptive dual mapping and triggered random immigrants schemes seems a good EA optimizer for dynamic optimization problems.. For the future work, it is straightforward to introduce other mechanisms, such as memory-based methods [38] and multi-population approaches [27] , into MAs for dynamic optimization problems. Another interesting research work is to extend the triggered immigrants and dual mapping scheme to other EAs and examine their performance in dynamic environments. In addition, it is also valuable to carry out the sensitivity analysis on the effect of parameters, e.g., θ 0 , α, β, and δ, on the performance of MAs in the future.

O B I O O O O O O B I I O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O B I O O O O O O O O O O O B I O B I I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O B I O B I O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Mining frequent itemsets in time-varying data streams Mining frequent itemsets in data streams is beneficial to many real-world applications but is also a challenging task since data streams are unbounded and have high arrival rates. Moreover, the distribution of data streams can change over time, which makes the task of maintaining frequent itemsets even harder. In this paper, we propose a falsenegative oriented algorithm, called TWIM, that can find most of the frequent itemsets, detect distribution changes, and update the mining results accordingly. Experimental results show that our algorithm performs as good as other false-negative algorithms on data streams without distribution change, and has the ability to detect changes over time-varying data streams in real-time with a high accuracy rate. Mining frequent itemsets in data stream applications is beneficial for a number of purposes such as knowledge discovery, trend learning, fraud detection, transaction prediction and estimation. However, the characteristics of stream data -unbounded, continuous, fast arriving, and time-changing -make this a challenging task. Existing mining techniques that focus on relational data cannot handle streaming data well [4] .. Mining frequent itemsets is a continuous process that runs throughout a data stream's life-span. Since the total number of itemsets is exponential, it is impractical to keep statistics for each itemset due to bounded memory. Therefore, usually Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. only the itemsets that are already known to be frequent are recorded and monitored, and statistics of other infrequent itemsets are discarded. However, data streams can change over time. Hence, an itemset that was once infrequent can become frequent if a stream changes its distribution. It is hard to detect such itemsets that change from infrequent to frequent, since they are not maintained due to limited memory. Furthermore, even if we could detect these itemsets, we would not be able to obtain their statistics (supports), since mining a data stream is a one-pass procedure and history information is not retrievable. Distribution changes over data streams might have considerable impact on the mining results, but few of the previous works have addressed this issue.. In this paper, we develop a new algorithm, called TWIM, that can find most of the frequent itemsets in real time. It can also predict the distribution change and update the mining results accordingly. Our approach maintains two tumbling windows over a data stream: a maintenance window and a prediction window. All current frequent itemsets are recorded and maintained in the maintenance window, and we use the prediction window to keep track of candidates that have the potential of becoming frequent if the distribution of stream values changes. Every time the windows tumble, we check if new frequent itemsets and candidates should be added, and if some existing ones need to be removed from the lists. Since we do not keep statistics for every itemset within the windows, memory usage is limited. Experimental results show that TWIM is as effective as previous approaches for non-time-varying data streams, but is superior to them since it can also capture the distribution change for time-varying streams in real-time. In this paper, we propose a novel algorithm called TWIM for mining frequent itemsets. Our approach has the ability to detect changes in a data stream and update mining results in real-time. We use two tumbling windows to maintain current frequent itemsets and predict distribution changes. A list of candidate itemsets that have the potential to become frequent if distribution changes is generated and updated during mining. Every time the two tumbling windows move, we apply a set of heuristics to update the candidate list and maintain frequent itemsets. Our approach produces only true frequent itemsets, and requires less memory. Experimental results demonstrate that TWIM has promising performance on mining data streams with or without distribution changes.. We are currently investigating a number of issues, including proving the complexity for finding the kth frequent itemset in a data stream, developing more heuristics for maintaining candidate itemsets, designing a more sophisticated and more efficient counting system, and analyzing the relationship among thresholds, window sizes, and memory space for different applications. Mining frequent items and itemsets is a challenging task and has attracted attention in recent years. Jiang and Gruenwald [5] provide a good review of research issues in frequent itemsets and association rule mining over data streams. One of the classical frequent itemset mining techniques for relational DBMSs is Apriori [1] , which is based on the heuristic that if one itemset is frequent, then its supersets may also be frequent. However, Apriori-based approaches suffer from a long delay when discovering large sized frequent itemsets, and may miss some frequent itemsets that can be easily detected using TWIM. Most of the techniques proposed in literature are false-positive oriented. False-positive techniques may consume more memory, and are not suitable for many applications where accurate results, even if not complete, are preferred. We conduct a series of experiments to evaluate TWIM's performance in comparison with three others: SW method [2] , which is a sliding window based technique suitable for dynamic data streams, FDPM [7] , which is also a falsenegative algorithm, and Lossy Counting (LC) [6] , which is a widely-adopted false positive algorithm. We use synthetic data streams in our experiments to gain easy control over the data distributions. We adopt parameters similar to those used in previous studies [3, 7] . The total number of different items in I is 1000, and the average size of transactions in Tt is 8. The number of transactions in each data stream is 100,000.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O