Hierarchical Cellular Tree: An Efficient

Indexing Scheme for Content-Based

Retrieval on Multimedia Databases

Serkan Kiranyaz and Moncef Gabbouj

Objective• To present the technique of using a

Hierarchical Cellular Tree (HCT) as an indexing scheme for content-based retrieval on multimedia databases.

Why is this technique important?• Technological hardware and network

improvements• Daily usage of Internet• Technique reduces costly I/O

operations

HCT Overview• Is a MAM(Metric Access Method)

technique.• Based off the M-tree• Is a dynamic, cell-based, hierarchical

structured indexing method• Items are partitioned based on

distances and stored within cells based on their similarity proximity• Self-organized tree implemented via

genetic programming principles

Indexing Technique Categories

SAM (spatial access method)

• (dis-)similarity distance only measured through Euclidean distance.o Not suited for

deep spanning trees

MAM (metric access method) • Support black

box approach to (dis-)similarity distance.o Allows for deep

trees• Do not support

dynamic changes*

*M-tree Similarities• Is a dynamic MAM• Has a hierarchical structure based on

the mitosis of a cello Tree grows one level upwards whenever a

split occurs at the top level• Each cell is represented by a nucleus

(except the top most cell)

M-tree Problems• Achieves a balanced tree with low I/O

cost in large datasetso Problem: Multimedia databases are seldom

balanced at all.o HCT: Cells are unbalanced and can vary in

size• Must know the size of the database

entries/Cells before building (capacity M)o Problem: All M-tree structures can hit upper

limits (size non dynamic)o HCT: Removes limit on cell size as long as

they keep a definite "compactness" measure

M-tree Problems• M-tree compactness is only measured

with respect to distance of nucleus to furthest object (covering radius)o Problem: Determining compactness this way

does not allow for dynamic sizing of cells.o HCT: Uses all cell items and their minimum

distances to the cell(instead of a single nucleus item alone), compactness is constantly being updated.

Related Work in Multimedia Databases (SAM trees)• KD-Trees

o Hierarchical tree structureo Use space-partitioning methods to divide the

feature space into predefined hyperplanes• R-Trees

o Feature space divided according to distribution of database items

o Region overlapping may occur

Related Work in Multimedia Databases (SAM trees)• R*-trees

o Improves the node splitting of R-tree by taking overlapping areas into consideration

• TV-treeo Uses telescope vectorso Authors call telescope vectors "so called

telescope vectors"o Google search does not come up with

anything meaningful for telescope vectors

Related Work in Multimedia Databases (SAM trees)• X-tree

o Avoids overlapping of region bounding boxes by using a new organization of the directory

o Boxes can still intersect at higher levels in the tree

o Paper does not go into detail on what a bounding box is (assumption bounding box = cell)

• SS-treeo Uses minimum bounding spheres instead of

boxeso Less intersects at higher levels

Related Work in Multimedia Databases (MAM trees)• vp-tree(vantage point)

o organizes feature vectors(data points) into two groups according to their similarity distances with respect to a single point(vantage point)

• mvp-tree(multiple vantage point)o assigns multiple vantage points instead of

one

HCT Structure - Cell Structure• Basic container in which similar

database items are stored.• Ground level cells contain the entire

database items• Cells carry an MST (Minimum Spanning

Tree)o Holds minimum (dis-)similarity distance of each item to other

items within the cell.o Used to determine when mitosis should occur.

Splits occur at longest branch.o This is actually very similar to MVP-tree except every cell is

treated as a vantage point. Better idea about the similarity proximity of an item.

HCT Structure - Cell Structure• Cells cannot undergo mitosis before

reaching a specific level of maturityo This works like real cellso Reason for this is not like real cells

• Nucleuso Represents the owner cell of a higher levelo Nucleus is found through MST

Item with maximum number of brancheso Nucleus is updated with every operation

performed M-tree does not do this

HCT Structure - Cell Structure• Cell Compactness

o How tight focused the clustering for items within the cell

o High variations are eliminated by using more than a single item(vantage point)

HCT Structure - Cell Structure• Cell Mitosis

o Two conditions for mitosis Maturity (Nc > Nm)

• c = number of items in cell• m = maturity minimum limit

Cell Compactness (CFc > CThrL)• CFc = Compactness feature• CThrL = current level compactness

thresholdo Cell Mitosis has no cost as the cell is simply

split by breaking longest branch

HCT Structure - Cell Structure

HCT Structure - Level Structure• Top level always single cell

o If mitosis occurs on top level, new top level is created to preserve single cell top level.

• Each level attempts to dynamically maximize compactness of cells

HCT Structure - HCT Operations• Three operations

o Cell mitosiso Item insertiono Item removal

• As stated before all three operations cause a recalculation of Compactness

HCT Structure - HCT Operations• Insert

o First performs the Pre-Emptive cell search recursively descends HCT from top to

target levelo Once target located, insert item into target

cello Perform post-processing check

Check for mitosis Recalculate compactness for single or

multiple cellso If mitosis was performed

Remove old nucleus item from higher level Consecutively call Insert for new nucleus

HCT Structure - HCT Indexing• HCT can index using any set of

available featureso Must have fusion mechanismo Must have similarity measure

• Consists of two operationso Incremental constructiono Optional periodic fitness check

HCT Structure - HCT Indexing• HCT Incremental Construction

o Takes a Database D and appends all new items contained in an Array

o If an HCT does not already exist for database D All current items of D are inserted into the

Array A new HCT body is constructed from D

o Else if an HCT does exist for database D HCT body is first loaded HCT body is updated with contents of Array

HCT Structure - HCT Indexing• HCT Fitness Check

o Aims to minimize corruption which can happen during construction of HCT body Corruption happens because the order of

items that are inserted is not handledo Outliers Check

Reduces the "crowd effect" by removing redundant minority cells• minority cells, cells with a few or one item in it

All minority cells are reintroduced into the system to see if they fit into another cell

HCT Structure - HCT Indexing

o Cell Merging If a cell merge occurs that is later deemed

as not meeting the requirements of cell compactness it can be merged.

HCT - Examples

HCT-Examples

QA