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# Statistical Pattern Recognition - Science topic

Explore the latest questions and answers in Statistical Pattern Recognition, and find Statistical Pattern Recognition experts.

Questions related to Statistical Pattern Recognition

Hi all!

I am wondering on what would you consider to be the 10 most essential formulas in statistics and 10 in signal processing necessary for statistical pattern recognition and structural health monitoring.

I have aquired the coordinates (X and Y) of the placement of objects (cubes) in a defined space (a tray) made by different individuals. I know when the first object has been disposed, the second one etc. and I can create a trajectory starting from the first object disposed to the last one (I attach a figure to be more specific). I am very new to this type of data and I was wondering how can I analyze coordinates and trajectories (I have 50 trajectories) comparing them to each other? Mainly I would like to find similarities between the spatio-temporal pattern of placement of the subjectcs, and check for common placement strategies. What kind of analysis shoud I run and what software I should use?

Thank you in advance!

Hi!

We are trying to estimate body mass (W) heritability and cross-sex genetic correlation using MCMCglmm. Our data matrix consists of three columns: ID, sex, and W. Body mass data is NOT normally distributed.

Following previous advice, we first separated weight data into two columns, WF and WM. WF listed weight data for female specimens and “NA” for males, and vice-versa in the WM column. We used the following prior and model combination:

prior1 <- list(R=list(V=diag(2)/2, nu=2), G=list(G1=list(V=diag(2)/2, nu=2)))

modelmulti <- MCMCglmm(cbind(WF,WM)~trait-1, random=~us(trait):animal, rcov=~us(trait):units, prior=prior1, pedigree=Ped, data=Data1, nitt=100000, burnin=10000, thin=10)

The resulting posterior means of posterior distribution were suspiciously low (e.g. 0.00002). We calculated heritability values anyway, using the following:

herit1 <- modelmulti$VCV[,'traitWF:trait WF.animal']/

(modelmulti$VCV[,'traitWF:trai tWF.animal']+modelmulti$VCV[,' traitWF:traitWF.units'])

herit2 <- modelmulti$VCV[,'traitWM:trait WM.animal']/

(modelmulti$VCV[,'traitWM:trai tWM.animal']+modelmulti$VCV[,' traitWM:traitWM.units'])

corr.gen <- modelmulti$VCV[,traitWF.traitW M.animal']/

sqrt(modelmulti$VCV[,'traitWF: traitWF.animal']*modelmulti$VC V[,'traitWM:traitWM.animal'])

We get heritability estimates of about 50%, which is reasonable, but correlation estimates were extremely low, about 0.04%.

Suspecting the model was wrong, we used the original dataset with all weight data in a single column and tried the following model:

prior2 <- list(R=list(V=1, nu=0.02), G=list(G1=list(V=1, nu=1, alpha.mu=0, alpha.V=1000)))

model <- MCMCglmm(W~sex, random=~us(sex):animal, rcov=~us(sex):units, prior=prior2, pedigree=Ped, data=Data1, nitt=100000, burnin=10000, thin=10)

The model runs, but it refuses to calculate “herit” values, with the error message “subscript out of bounds”. We’d also add that in this case, the posterior density graph for sex2:sex.animal is not shaped like a bell.

What are we doing wrong? Are we even using the correct models?

Eva and Simona

what is the differences between classifires and associative memories ?

A-B-C ABOUT IDENTIFICATION OF GRAPHS

John-Tagore Tevet

Let us try to open the essence of graphs, from that's so far tried to circumvent.

1. What is a graph

Graph is an association of elements with relationships between these that has a certain structure.

Graphs are represented for different purposes. On the early rock paintings have been found the constellations show schemes. Graphs was used also for explain the theological tenets.

Example 1. Graph (structural formula) of isobutane C4H10:

Graphs began to investigate after then when Leonhard Euler in 1736 has solved the problem of routing on the seven bridges between four banks of Königsberg [1].

Example 2. Königsberg’s bridges and corresponding graph:

Also in present time used the graphs mainly for solving the problems of routing and flowing. Already in 1976 considered that such one-sided approach is a hindering factor for studying of graphs [2]. To the essence of graph, to its structure and symmetry properties has the interest practically non-existent. The last explorer was evidently Boris Weisfeiler in 1976 [9].

Definition a graph as an object consisting in node set V and edge set E, G=(V, E), is a half-truth that beget confusions. Essential is to explain the properties of inner organizing (inner building) or structure, i.e. identification of graphs.

Graph is presentable: 1) as a list L of adjacencies; 2) in the form of adjacency matrix E; 3) graphically G, where the elements to “nodes” and relations to “edges” called.

Example 3. List of adjacencies L, corresponding adjacency matrix E and for both corresponded graphs GA and GB:

Explanations:

The outward look and location of the enumerated elements in graph not have something meaning. But on the emotional level it rather engenders some confusion.

One graph can be differs from the other on its looking or its inner organizing (inner-building) or structure S what in ordinarily visually not be opened. Maybe just due to this is to the present days the existence of structure ignored.

We can here make sure that graphs GA and GB have the same structure and these are isomorphic GA @ GB. Ordinarily differentiate in the objects just the “outward” differences and refuse to see some common structure.

Propositions 1. Structure axioms:

P1.1. Structure S is presentable as a graph G and each graph G has its certain structure S.

P1.2. Isomorphic graphs have the same structure – structure is the complete invariant of isomorphic graphs.

Identification of graph is based on identification the binary relations between elements [3 - 8]. Binary relation can a “distance relation”, “circle relation”, “clique relation” etc. and is measurable. Binary relation characterized by corresponding binary sign.

2. Identification of the graph

For identification of the graphs uses two each others complementary ways:

Multiplicative identification (products of adjacency matrixes);

Heuristic identification.

Propositions 2. Multiplicative identification: multiplication the adjacency matrixes:

P2.1. To multiplying the adjacency matrix with itself E´E´E´…=En and fixing in case of each degree n the number p of different multiplicative binary signs enij that as rule enlarges. Forming the sequence vectors ui of different multiplicative binary signs.

P2.2. In each case if p enlarges (change) must transpose the rows and columns of En correspondingly to the obtained frequency vectors ui.

P2.3. Stop the multiply if p more no enlarges and to present the current En and the following En+1.

Explanation: Multiplicative signs differentiate the binary signs but no characterize these.

Example 4. Adjacency matrix E and its transposed products E2, E3 of graphs on example 3:

1 2 3 4 5 6| i

0 1 0 1 0 1| 1

1 0 1 0 1 1| 2

E 0 1 0 1 0 1| 3

1 0 1 0 1 0| 4

0 1 0 1 0 1| 5

1 1 1 0 1 0| 6

ui

2 6| 1 3 5| 4 | i 0 1 3 4 k

4 3| 1 1 1| 3 | 2 0 3 2 1 1

3 4| 1 1 1| 3 | 6 0 3 2 1 1

E2 1 1| 3 3 3| 0 | 1 1 2 3 0 2

1 1| 3 3 3| 0 | 3 1 2 3 0 2

1 1| 3 3 3| 0 | 5 1 2 3 0 2

3 3| 0 0 0| 3 | 4 3 0 3 0 3

ui

2 6| 1 3 5| 4| i 0 2 3 6 7 9 10 k

6 7|10 10 10| 3| 2 0 0 1 1 1 0 3 1

7 6|10 10 10| 3| 6 0 0 1 1 1 0 3 1

E3 10 10| 2 2 2| 9| 1 0 3 0 0 0 1 2 2

10 10| 2 2 2| 9| 3 0 3 0 0 0 1 2 2

10 10| 2 2 2| 9| 5 0 3 0 0 0 1 2 2

3 3| 9 9 9| 0| 4 1 0 2 0 0 3 0 3

Explanations:

a) The set of similar relations (and elements) recognize their position W in the structure. Position W is in group theory known as transitivity domain of automorphisnsms, equivalence class or orbit.

Multiplicative binary signs enij recognize here five positions of binary relations WR and on they base three positions of elements WV.

Propositions 3. Position axioms:

P3.1. If structural elements (graph nodes) vi , vj , … have in graph G the same position WVk then corresponding sub-graphs (Gi=G\vi) @ (Gj=G\vj) @.... are isomorphic.

P3.2. If relations (edges) eij, ei*j*, … have in graph G the same binary(+)position WR+n then corresponding greatest subgraphs (Gij=G\eij) @ (Gi*j*=G\ei*j*) @.... are isomorphic.

P3.3. If relations (“non-edges”) eij, ei*j*, … have in graph G the same binary(–)position WRn– then corresponding smallest supergraphs (Gij=GÈeij) @ (Gi*j*=GÈei*j*) @.... are isomorphic.

Before elaboration of the multiplicative identification way was elaborated a heuristic way.

Propositions 4. Heuristic identification:

P4.1. Fix an element i and form its neighborhood Ni, where the elements, connected with i divide according to distance d to entries Cd.

P4.2. Fix an element j and fix its neighborhood Nj by condition P4.1.

P4.3. Fix the intersection Ni ÇNj as a binary graph gij, and fix the distance –d between i and j (in case of adjacency collateral distance +d), the number n of elements (nodes) in gij, number q of adjacencies (edges). Fixing the heuristic binary sign ±d.n.q.ij of obtained graph gij.

P4.4. Realize P4.1 to P4.3 for each pair i,jÎ[1, |V|]. Obtained preliminary heuristic structure model SMH.

P4.5. Fixing for each row i its frequency vector ui. Transpose the preliminary model SM by frequency vectors ui lexicographically to partial models SMk.

P4.6. In the framework of SMk transpose the rows and columns lexicographically by position vectors si to complementary partial models. Repeat P4.6 up to complementary transposing no arises.

Explanation: Heuristic binary signs differentiate the binary signs and characterize these.

Example 5. On the Example 3 presented differently enumerated graphs GA and GB, their heuristic binary signs and structure models SMA and SMB with their common product E3:

ui

3 4| 1 4 5| 2| iA

1 2| 1 2 5| 6| iB 0 2 3 6 7 9 10 k

6 7|10 10 10| 3| 3 3 0 0 1 1 1 0 3 1

6|10 10 10| 3| 4 6 0 0 1 1 1 0 3 1

E3 | 2 2 2| 9| 1 1 0 3 0 0 0 1 2 2

….. | 2 2| 9| 2 4 0 3 0 0 0 1 2 2

| 2| 9| 5 5 0 3 0 0 0 1 2 2

| | 0| 6 2 1 0 2 0 0 3 0 3

Explanations:

”Diverse” graphs GA and GB have equivalent heuristic structure models SMA » SMB and the same multiplicative model E3. This means that structures are equivalent and all on the examples 2 and 4 presented graphs GA and GB are isomorphic GA @ GB.

The binaries are divided to five binary positions WRn, where the “adjacent pairs” or “edges” divided to three binary(+)positions (full line, a dotted, dashed-line) that coincide with heuristic binary signs C, D, E and corresponding multiplicy binary signs 10, 7, 2, and with two binary(–)positions with signs –A and –B and multiplicative signs 9 and 3. In base of these divide the structural elements to three positions WVk.

The column ui constitutes frequency vectors, where each element i characterize its relationships with other elements. On the base of frequency vectors ui obtained the positions of elements WVk.

The column si constitutes position vectors that represent the connecting of i with elements on the position k.

A principal theoretical algorithm of isomorphism recognition exists really – it consists in rearranging (transposing) the rows and columns of adjacency matrices EA of graph GA as yet these coincides with the EB of GB. But this has an essential lacking – it is too complicated, the number of steps can be up to factorial n!

Propositions 5. On the relationships between isomorphism and structural equivalence:

P5.1. Isomorphism GA@GB is a such one-to-one correspondence, a bijection j: VA®VB, between elements what retains the structure GS of graphs GA and GB.

P5.2. Isomorphism recognition does not recognize the structure GS and its properties (positions etc.), but the structure models SM and En recognize the structure and its properties with exactness up to isomorphism.

P5.3. Structural equivalence SMA»SMB and EnA»EnB is a coincidence or bijection j: WA®WB on the level of binary positions WRn and positions of nodes (elements) WVk.

P5.4. In the case of large symmetric graphs recognizes the products En the binary positions more exact than heuristic models SM, where need to use the binary signs of higher degree. That why it is necessary to treat both in together, bearing in mind also that the heuristic binary signs characterize the essence of relationship itself.

P5.5. Recognition of the positions by the structure model is more effective than detecting the orbits on the base of the group AutG.

Example 6. To the recognition on the Example 1 represented structure of isobutane suffice use the heuristic model SM:

Explanation: Decomposing the elements C and H to four positions corresponds to actuality. The positions are visually appreciable also on the Example 1.

3. List of tasks that solving based on the identified graphs (structure)

To conclusion it should be emphasized that the recognition of graph’s structure (organizing) is based on the identification (distinction) of binary relations between elements. Binary relation can be measured as a “relation of the distance”, “circle relation”, “clique relation”, etc. Binary relation is recognizable by the corresponding binary sign.

The complex of tasks that are based to recognizing structures is broad, various and novel (differ from up to now set up) [3 - 8]. We list here some.

1. The relations between structural positions, automorphismsm and group-theoretical orbits.

2. Structural classification the symmetry properties of graphs.

3. Measurement the symmetry of graphs.

4. Analyzing different situations of structural equivalency and graphs isomorphism.

5. Positional structures that open the “hidden sides” of graphs.

6. Unknown sides of well-known graphs.

7. Adjacent structures and reconstruction problem. It is connected with general solving the notorious Ulam’s Conjecture.

8. Sequences of adjacent structures and their associations – the systems of graph structures.

9. Probabilistic characteristics of graph’s systems.

10. The relations of graph systems with classical attributes.

References

1. Euler. L. Solutio problematis ad geometriam situs pertinentis. – Comment. Academiae Sci. I. Petropolitanae 8 (1736), 128-140.

2. Mayer, J. Developments recents de la theorie des graphes. – Historia Mathematica 3 (1976) 55-62.

3. Tevet, J.-T. Semiotic testing of the graphs: a constructive approach and development. S.E.R.R., Tallinn, 2001.

4. Hidden sides of the graphs. S.E.R.R. Talinn, 2010.

5. Semiotic modeling of the structure. ISBN 9781503367456, Amazon Books. 2014.

6. Süsteem. ISBN 9789949388844. S.E.R.R., Tallinn, 2016.

7. Systematizing of graphs with n nodes. ISBN 9789949812592. S.E.R.R., Tallinn, 2016.

8. What is a graph and how it to study. ISBN 9789949817559. S.E.R.R., Tallinn, 2017.

9. Weisfeiler, B. On Construction and Identification of Graphs. Springer Lect. Notes Math., 558, 1976 (last issue 2006).

I have a data frame called p.1 with several column of information for each of the points recorded by the Argos system of a penguin.

In the beggining I calculated that the distance travelled by the penguin in each trip is the sum of the distances from the coast, but that´s wrong, the distance travelled per trip is the distance between the first points plus the distance between the second and third point and successively and re-start for every trip. With the next code I could calculate the distance between points:

distancebetwenpoints=spDists(locs1_utm, longlat=FALSE)

p.1$dist=distancebetwenpoints

locs1_utm$dist=distancebetwenpoints

where locs1_utm is the same as p.1 but converted into a SpatialPointsDataFrame.

**The problem of this code is**that I obtain a huge matrix of the distances between all the points, I tried several alternatives to just select the column that i need but don´t work.

Does someone know how i can calculate the distances of every trip made by the penguin?

In the attached file there are some columns called todelete those i just created to clean better the data.

what is the difference between random binary sensing matrix and random Gaussian sensing matrix??

What the advantages and disadvantages of each matrix??

How can i choose the suitable matrix for a certain signal ?

For image processing, unlike the methods which split the image into pitches, total variation is on the whole image. In this case, for an image with size n by n, what is the complexity of total variation minimization? Is total variation too slow compared to the pitch based method? Thanks.

I am working in applying sparse representation to classification tasks. In Sparse Representation Classifier (SRC), the test signal is assigned to the dictionary(class) that gives the minimum residual error. Another class assignment measure is the minimum sparsity. My question is: Does the sign of the sparse coefficients plays a role in class assignment or no?.

Is it important correlation between labels in multi-label classification?why?

I am trying to compare the dominant colors in approx. 40.000 images. The papers I find offer the mathematics for comparing two colors. I need to create clusters, or palettes to represent the colors of such clusters.

I need human gait data for ascending stairs, is there any database for this type of data? I need RAW dataset.

I want matlab code I can use to extract features from this cattle image using Fourier descriptor. And also code to applied them as input to ANN for classification. I don't know how to go about it. Can any one help me?

Hi all,

I want to ask that I have total 11 classes [A,B,C,D,E,F,G,H,I,J,K] in which 7 classes are used in training i.e [A,B,C,D,E,F,G]. Remaining 4 are not used in training. So, those 4 classes are considered as reject classes i.e. [H,I,J,K], when they are used in testing.

My current system is actually finding the similarity measure between the tested instance with the set of all available classes used in training. So, in that case, my system is currently reporting that the tested sample belongs to one of the class which is used in training, which has high similarity measure.

Now, I want to improve it by implementing reject class threshold. So, system should report that as similarity measure value lies under threshold value, that tested sample belongs to the rejected class.

So, can you please guide me about how can I identify threshold values for those reject classes [H,I,J,K]?

How can I do it by using Matlab code? Please let me know about it.

i am using this formula of gabor kernel

it return zero value for x,y>10 due to which when it is multiplied with pixel value it returns 0 and filter effect applied to pixel becomes 0. Can anybody help me with this?

The defenitions for FPIR, SEL, FNIR for an identification problem are as follows, but they look complicated for me. (specially using Rank and L candidates concept in computation).

Specially the concept of selectivity is complicated for me!

can any one explain them by a simple identification example?

FPIR (N,T,L)=(Num. nonmate searches where one or more enrolled candidates are returned at or above threshold, T)/(Num. nonmate searches attempted)

SEL(N,T,L)=(Num. nonmate enrolled candidates returned at or above threshold, T)/(Num. nonmate searches attempted)

FNIR(N,R,T,L)=(Num. mate searches with enrolled mate found outside top R ranks or score below threshold, T)/(Num. mate searches attempted)

Has any R package to exhausting search a sub sequencing like a pattern with 5 minutes walking then 5 minutes sitting with Actigraph accelerometer data? I would like to fives a behavior with with 5 minutes walking then 5 minutes sitting, is there any existing pattern?

It's easy to understand what bias and variance mean in general in machine learning. The link below makes this very clear. But, its always hard to figure out which classifiers are of high/low bias and variance. Each classifier would have its own set of tuning parameters to alter this characteristic.

So, how will one determine whether a given classifier is of high bias or high variance?

Dear all,

I have a long list of ordered factor level combinations A = {a1...an}, .... E = {e1...ek} which is non-exhaustive (e.g. not full-factorial) e.g.:

A B C D E

...

a1 b1 c1 d1 e1

a1 b1 c1 d1 e2

a2 b1 c1 d1 e1

...

Now I want to merge all entries which differ only by 1 factor at a time (e.g. E) into a pattern. In the example this should lead to

A B C D E

...

a1 b1 c1 d1 {e1,e2}

a2 b1 c1 d1 e1

...

Now my problem is to do that for all factors. In the example keeping A fixed, one can not simple merge the two entries to:

{a1,a2} b1 c1 d1 {e1,e2}

since this implies that also the combination

a2 b1 c1 d1 e2

was part of the original factor combinations - which it wasn't.

My first try was to only merge entries where all levels of the fixed factor were present and replace the according pattern with a wildcard,e.g. for E = {e1,e2,e3}

a3 b2 c4 e1

a3 b2 c4 e2

a3 b2 c4 e3

becomes

a3 b2 c4 *

Since in this case I know that E is not important for the combination of factors A to C. But this approach is unsatisfactory since it leaves a lot of entries unmerged (e.g. the example in the beginning will not be merged).

So, could someone point me to a direction where a solution to this problem might be found (e.g. graph/subset reduction, also thought of bioinformatic methods treating the factor combinations somehow as strings).

Any help would be very welcome!

Greetings, David

Is there any stopping criteria that i should use to make the algorithm converge rather number of iterations??

I am building predictive models in the fraud domain. Does anybody of you have experience with supervised learning to predict learning to predict multiple offenders?

And the advantages and disadvantages of different ways of labelling (for example multiple offenders versus once upon a time offenders, or multiple offenders against the rest of the population)?

What are the experiences? And what are the benefits of different ways of labelling?

Thanks beforehand for everybody who can advice me from his/her experience.

Gerard Meester

Netherlands

Hi. I am looking for tips or any sort of help on a topic "Power Transmission Alarms Pattern recognition". A database of alarms and events collected by the ESKOM control centre is available.I am to use this database to find rules of association that will enable the prevention of unwanted event in real-time. Sequences of alarms are used to generate the inference of a particular event. I have attached one of the database to see how it is structured.

Although several approaches were developed for handling missing data, majority of them are only suitable to restore incomplete patterns which have random variation. When random variation exists beside shift, trend, systematic and cyclic behavior in which the order of data also contains valuable information, what is the best approach to handle missing data?

Hello everyone!

I'm developing a pattern recognition algorithm on images. So far I have been using the MNIST database but due to some reason I need to switch to another database with higher resolution. It would be highly appreciated if someone could help me to find one or if anyone knows a trick for that that would be great!

thanks in advance.

Dear colleagues,

I am currently working on classifying certain objects which are (visually) represented as waves/curves. I am wondering whether there is a way to characterize the curves so as to be able to build classification rules which can then be used to classify the curves.

P.S. I have 3 pre-defined classes of curves.

I am studying seasonal changes in abundance of a fish species along a disturbance gradient. I sampled three locations at four seasons. My sampling sites at each location were very heterogeneous and the overall data was overdispersed . I am planning to analyze data using a GLMM with zero inflated model, considering LOCATION as a fixed factor and sampling site as a random factor. Should I also consider SEASON as a random factor (due to probable autocorrelation) or just nest it within LOCATION?

Let us I have a student data like city,hobby , age, mother tongue, gender, UG Specialization .

Now i want to make group of those students , having some similarity/ common among them(for exp they have common hobby, same mother tongue, belonging from same city etc.).

Can I used k-means clustering for it?

Note:I stored these fields data in numeric value only.

Repeated polygonal shapes or repeated colours are sources of visual patterns. Another important source of patterns are the presence of convex sets and convex hulls in digital images, especially in naturally camouflaged or in artificially camouflaged objects . A set A is convex provided the line segment connecting any points A is contained in A. A convex hull is the smallest convex set containing a set of points (see the attached image). Also, see the many convex sets in the natural camouflage of the dragon in the attached image and in

Convex sets have many applications in the study of digital images. For example, convex sets are used in solving image recovery problems:

and in image restoration:

Convexity recognition is useful in object shape analysis in digital images:

Another important application of convexity is rooftop and building detection in aerial images:

During my research work I came across a constructive demonstration that two symmetric matrices can always be simultaneously diagonalised, provided one is positive definite. I am talking about pages 31--33 of "Introduction to Statistical

Pattern Recognition" by Keinosuke Fukunaga.

Now, it is well known that two matrices are simultaneously diagonalisable of and only if they commute [e.g. Horn & Johnson 1985, pp. 51–53].

This should imply that any positive-definite symmetric matrix commutes with any given symmetric matrices. This seems to me an unreasonably strong conclusion.

Also, since Fukunaga's method can be used also with Hermitian matrices, the same conclusion should be true even in this more general matrix field.

I seem to be missing something, can someone help me elaborate?

I used PCA and GA but I got only ranking of features I was unable to find best features

Fallowing data available for mining and pattern recognition

X coordination of the cursor with system time

y coordination of the cursor with system time

( System time for every 100 ms )

Each and every user's mouse movements data available for 30 min.

How identify mouse movements patters if exits among these user ?

Neger, Rietveld and Janse (2014; attached) recently found that perceptual and statistical learning may rely on the same mental mechanism. Now, fearless of stretching, if we relate that to the issue of symbol grounding in language comprehension (cf. modal/embodied vs. amodal/symbolic accounts), would the previous findings support the

*mixed*proposals that language comprehension is both perceptual and statistical (e.g., Barsalou's*Language and Situated Simulation*; Louwerse's*Symbol Interdependency*)?Thank you very much

I download a part of connectome fmri data related to working memory. I visualize it with connectome workbench, but how can I get the fmri signal with SPM8, there are so many files with suffix .nii the SPM8 tool didn't recognize any of them.

I am working on pattern detection of dermatological images and I would like to know how to extract and match them.

What other features such as shape, texture and color can be suggested to classify (recognize) the three dimensional fragments in order to reassemble/reconstruct fragmented objects using their 3D digital images?

Image processing in matlab

Classification using svm on image dataset.

As bwlabel() works for labeling binary image how can we do the same for greyscale image in matlab?

How would I specify that group 1=apple,group 2 = orange and group3=banana?

I have three 30x20 grids, and I am wondering if the pixel's value are similar amongst those grid...

Suppose we have two classes separated linearly. Do we always get a correct line (100% correct classification) for every data separated linearly using Fisher. How about SVM and when we have two classes not separated linearly, is the Fisher answer optimal? How about svm? I mean one line can classify two classes and results (1 misclassification) and another line 2 misclassification.

I'm preparing for an exam and looking for some exercises with solutions about pattern recognition and machine learning specially in the field of : SVM, Bayes, Decision Tree, Overfitting and underfitting, VC dimension, PCA, KNN, Kmeans, Combination, Renforcement learning,MAP and ML.

Genetic information gathered from autistic patients is transformed to multidimentional data. this is huge and requires machine learning techniques to create an automated Autism detection system. I wonder if there are publications along this track.

Assume we fit a GMM on a train set which contains normal samples. I'm wondering if we can use probability density function (which is a linear combination of component densities) in order to decide about new samples (test samples). In other words, our final decision about being normal or abnormal should be should be based on which probabilities: probability density function, Likelihood or posterior?

I have thought that even the feature is increase, the performance increase isn't it?

For example if we have color skin, eye and hair, it gives more performance for face recognition than situation than if we just have eye color.

That's why I am so confused about GMM where even the size of feature decrease the probability is increased. Suppose that following Matlab code:

train=[1 2 1 2 1 2 100 101 102 99 100 101 1000 1001 999 1003];

No_of_Iterations=10;

No_of_Clusters=3;

[mm,vv,ww]=gaussmix(train,[],No_of_Iterations,No_of_Clusters);

test1=[1 1 1 2 2 2 100 100 100 101 1000 1000 1000];

test2=[1 1 2 2 100 99 1000 999];

test3=[1 100 1000];

[lp,rp,kh,kp]=gaussmixp(test1,mm,vv,ww);

sum(lp)

[lp,rp,kh,kp]=gaussmixp(test2,mm,vv,ww);

sum(lp)

[lp,rp,kh,kp]=gaussmixp(test3,mm,vv,ww);

sum(lp)

The results are as follow :

ans =

-8.0912e+05

ans =

-8.1782e+05

ans =

-5.0381e+05

Why does the feature size decrease as the probability increases? I expect that with more feature the performance increases isn't it?

Given two groups of data (blue & red line in the figure), what's the most efficient unsupervised classifier that can locate the blue line in the figure?