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Detection theory
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Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (called noise, consisting of background stimuli and random activity of the detection machine and of the nervous system of the operator). In the field of electronics, the separation of such patterns from a disguising background is referred to as signal recovery.[1]
According to the theory, there are a number of determiners of how a detecting system will detect a signal, and where its threshold levels will be. The theory can explain how changing the threshold will affect the ability to discern, often exposing how adapted the system is to the task, purpose or goal at which it is aimed.
Another field which is closely related to signal detection theory is called compressed sensing (or compressive sensing). The objective of compressed sensing is to recover high dimensional but with low complexity entities from only a few measurements. Thus, one of the most important applications of compressed sensing is in the recovery of high dimensional signals which are known to be sparse (or nearly sparse) with only a few linear measurements. The number of measurements needed in the recovery of signals is by far smaller than what Nyquist sampling theorem requires provided that the signal is sparse, meaning that it only contains a few non-zero elements. There are different methods of signal recovery in compressed sensing including basis pursuit , expander recovery algorithm[2], CoSaMP [3]and also fast non-iterative algorithm[4]. In all of the recovery methods mentioned above, choosing an appropriate measurement matrix using probabilistic constructions or deterministic constructions, is of great importance. In other words, measurement matrices must satisfy certain specific conditions such as RIP (Restricted Isometry Property) or Null-Space property in order to achieve robust sparse recovery.
Back to the detecting theory, when the detecting system is a human being, characteristics such as experience, expectations, physiological state (e.g., fatigue) and other factors can affect the threshold applied. For instance, a sentry in wartime might be likely to detect fainter stimuli than the same sentry in peacetime due to a lower criterion, however they might also be more likely to treat innocuous stimuli as a threat.
Much of the early work in detection theory was done by radar researchers.[5] By 1954, the theory was fully developed on the theoretical side as described by Peterson, Birdsall and Fox[6] and the foundation for the psychological theory was made by Wilson P. Tanner, David M. Green, and John A. Swets, also in 1954.[7] Detection theory was used in 1966 by John A. Swets and David M. Green for psychophysics.[8] Green and Swets criticized the traditional methods of psychophysics for their inability to discriminate between the real sensitivity of subjects and their (potential) response biases.[9]
Detection theory has applications in many fields such as diagnostics of any kind, quality control, telecommunications, and psychology. The concept is similar to the signal to noise ratio used in the sciences and confusion matrices used in artificial intelligence. It is also usable in alarm management, where it is important to separate important events from background noise.
Contents
[hide]
1 Psychology
2 Applications
2.1 Sensitivity or discriminability
2.2 Bias
3 Mathematics
3.1 P(H1|y) > P(H2|y) / MAP testing
3.2 Bayes criterion
4 See also
5 References
6 External links
Psychology[edit]
Signal detection theory (SDT) is used when psychologists want to measure the way we make decisions under conditions of uncertainty, such as how we would perceive distances in foggy conditions. SDT assumes that the decision maker is not a passive receiver of information, but an active decision-maker who makes difficult perceptual judgments under conditions of uncertainty. In foggy circumstances, we are forced to decide how far away from us an object is, based solely upon visual stimulus which is impaired by the fog. Since the brightness of the object, such as a traffic light, is used by the brain to discriminate the distance of an object, and the fog reduces the brightness of objects, we perceive the object to be much farther away than it actually is (see also decision theory).
To apply signal detection theory to a data set where stimuli were either present or absent, and the observer categorized each trial as having the stimulus present or absent, the trials are sorted into one of four categories:
Respond "Absent"
Respond "Present"
Stimulus Present
Miss Hit
Stimulus Absent
Correct Rejection False Alarm
Based on the proportions of these types of trials, numerical estimates of sensitivity can be obtained with statistics like the sensitivity index d' and A',[10] and response bias can be estimated with statistics like c and β.[10]
Signal detection theory can also be applied to memory experiments, where items are presented on a study list for later testing. A test list is created by combining these 'old' items with novel, 'new' items that did not appear on the study list. On each test trial the subject will respond 'yes, this was on the study list' or 'no, this was not on the study list'. Items presented on the study list are called Targets, and new items are called Distractors. Saying 'Yes' to a target constitutes a Hit, while saying 'Yes' to a distractor constitutes a False Alarm.
Respond "No"
Respond "Yes"
Target
Miss Hit
Distractor
Correct Rejection False Alarm
Applications[edit]
Signal Detection Theory has wide application, both in humans and animals. Topics include memory, stimulus characterists of schedules of reinforcement, etc.
Sensitivity or discriminability[edit]
Conceptually, sensitivity refers to how hard or easy it is to detect that a target stimulus is present from background events. For example, in a recognition memory paradigm, having longer to study to-be-remembered words makes it easier to recognize previously seen or heard words. In contrast, having to remember 30 words rather than 5 makes the discrimination harder. One of the most commonly used statistics for computing sensitivity is the so-called sensitivity index or d'. There are also non-parametric measures, such as the area under the ROC-curve.[9]
Bias[edit]
Bias is the extent to which one response is more probable than another. That is, a receiver may be more likely to respond that a stimulus is present or more likely to respond that a stimulus is not present. Bias is independent of sensitivity. For example, if there is a penalty for either false alarms or misses, this may influence bias. If the stimulus is a bomber, then a miss (failing to detect the plane) may increase deaths, so a liberal bias is likely. In contrast, crying wolf (a false alarm) too often may make people less likely to respond, grounds for a conservative bias.
Mathematics[edit]
P(H1|y) > P(H2|y) / MAP testing[edit]
In the case of making a decision between two hypotheses, H1, absent, and H2, present, in the event of a particular observation, y, a classical approach is to choose H1 when p(H1|y) > p(H2|y) and H2 in the reverse case.[11] In the event that the two a posteriori probabilities are equal, one might choose to default to a single choice (either always choose H1 or always choose H2), or might randomly select either H1 or H2. The a priori probabilities of H1 and H2 can guide this choice, e.g. by always choosing the hypothesis with the higher a priori probability.
When taking this approach, usually what one knows are the conditional probabilities, p(y|H1) and p(y|H2), and the a priori probabilities p ( H 1 ) = π 1 {\displaystyle p(H1)=\pi _{1}} and p ( H 2 ) = π 2 {\displaystyle p(H2)=\pi _{2}} . In this case,
p ( H 1 | y ) = p ( y | H 1 ) ⋅ π 1 p ( y ) {\displaystyle p(H1|y)={\frac {p(y|H1)\cdot \pi _{1}}{p(y)}}} ,
p ( H 2 | y ) = p ( y | H 2 ) ⋅ π 2 p ( y ) {\displaystyle p(H2|y)={\frac {p(y|H2)\cdot \pi _{2}}{p(y)}}}
where p(y) is the total probability of event y,
p ( y | H 1 ) ⋅ π 1 + p ( y | H 2 ) ⋅ π 2 {\displaystyle p(y|H1)\cdot \pi _{1}+p(y|H2)\cdot \pi _{2}} .
H2 is chosen in case
p ( y | H 2 ) ⋅ π 2 p ( y | H 1 ) ⋅ π 1 + p ( y | H 2 ) ⋅ π 2 ≥ p ( y | H 1 ) ⋅ π 1 p ( y | H 1 ) ⋅ π 1 + p ( y | H 2 ) ⋅ π 2 {\displaystyle {\frac {p(y|H2)\cdot \pi _{2}}{p(y|H1)\cdot \pi _{1}+p(y|H2)\cdot \pi _{2}}}\geq {\frac {p(y|H1)\cdot \pi _{1}}{p(y|H1)\cdot \pi _{1}+p(y|H2)\cdot \pi _{2}}}}
⇒ p ( y | H 2 ) p ( y | H 1 ) ≥ π 1 π 2 {\displaystyle \Rightarrow {\frac {p(y|H2)}{p(y|H1)}}\geq {\frac {\pi _{1}}{\pi _{2}}}}
and H1 otherwise.
Often, the ratio π 1 π 2 {\displaystyle {\frac {\pi _{1}}{\pi _{2}}}} is called τ M A P {\displaystyle \tau _{MAP}} and p ( y | H 2 ) p ( y | H 1 ) {\displaystyle {\frac {p(y|H2)}{p(y|H1)}}} is called L ( y ) {\displaystyle L(y)} , the likelihood ratio.
Using this terminology, H2 is chosen in case L ( y ) ≥ τ M A P {\displaystyle L(y)\geq \tau _{MAP}} . This is called MAP testing, where MAP stands for "maximum a posteriori").
Taking this approach minimizes the expected number of errors one will make.
Bayes criterion[edit]
In some cases, it is far more important to respond appropriately to H1 than it is to respond appropriately to H2. For example, if an alarm goes off, indicating H1 (an incoming bomber is carrying a nuclear weapon), it is much more important to shoot down the bomber if H1 = TRUE, than it is to avoid sending a fighter squadron to inspect a false alarm (i.e., H1 = FALSE, H2 = TRUE) (assuming a large supply of fighter squadrons). The Bayes criterion is an approach suitable for such cases.[11]
Here a utility is associated with each of four situations:
U 11 {\displaystyle U_{11}} : One responds with behavior appropriate to H1 and H1 is true: fighters destroy bomber, incurring fuel, maintenance, and weapons costs, take risk of some being shot down;
U 12 {\displaystyle U_{12}} : One responds with behavior appropriate to H1 and H2 is true: fighters sent out, incurring fuel and maintenance costs, bomber location remains unknown;
U 21 {\displaystyle U_{21}} : One responds with behavior appropriate to H2 and H1 is true: city destroyed;
U 22 {\displaystyle U_{22}} : One responds with behavior appropriate to H2 and H2 is true: fighters stay home, bomber location remains unknown;
As is shown below, what is important are the differences, U 11 − U 21 {\displaystyle U_{11}-U_{21}} and U 22 − U 12 {\displaystyle U_{22}-U_{12}} .
Similarly, there are four probabilities, P 11 {\displaystyle P_{11}} , P 12 {\displaystyle P_{12}} , etc., for each of the cases (which are dependent on one's decision strategy).
The Bayes criterion approach is to maximize the expected utility:
U = P 11 ⋅ U 11 + P 21 ⋅ U 21 + P 12 ⋅ U 12 + P 22 ⋅ U 22 {\displaystyle U=P_{11}\cdot U_{11}+P_{21}\cdot U_{21}+P_{12}\cdot U_{12}+P_{22}\cdot U_{22}}
U = P 11 ⋅ U 11 + ( 1 − P 11 ) ⋅ U 21 + P 12 ⋅ U 12 + ( 1 − P 12 ) ⋅ U 22 {\displaystyle U=P_{11}\cdot U_{11}+(1-P_{11})\cdot U_{21}+P_{12}\cdot U_{12}+(1-P_{12})\cdot U_{22}}
U = U 21 + U 22 + P 11 ⋅ ( U 11 − U 21 ) − P 12 ⋅ ( U 22 − U 12 ) {\displaystyle U=U_{21}+U_{22}+P_{11}\cdot (U_{11}-U_{21})-P_{12}\cdot (U_{22}-U_{12})}
Effectively, one may maximize the sum,
U ′ = P 11 ⋅ ( U 11 − U 21 ) − P 12 ⋅ ( U 22 − U 12 ) {\displaystyle U'=P_{11}\cdot (U_{11}-U_{21})-P_{12}\cdot (U_{22}-U_{12})} ,
and make the following substitutions:
P 11 = π 1 ⋅ ∫ R 1 p ( y | H 1 ) d y {\displaystyle P_{11}=\pi _{1}\cdot \int _{R_{1}}p(y|H1)\,dy}
P 12 = π 2 ⋅ ∫ R 1 p ( y | H 2 ) d y {\displaystyle P_{12}=\pi _{2}\cdot \int _{R_{1}}p(y|H2)\,dy}
where π 1 {\displaystyle \pi _{1}} and π 2 {\displaystyle \pi _{2}} are the a priori probabilities, P ( H 1 ) {\displaystyle P(H1)} and P ( H 2 ) {\displaystyle P(H2)} , and R 1 {\displaystyle R_{1}} is the region of observation events, y, that are responded to as though H1 is true.
⇒ U ′ = ∫ R 1 { π 1 ⋅ ( U 11 − U 21 ) ⋅ p ( y | H 1 ) − π 2 ⋅ ( U 22 − U 12 ) ⋅ p ( y | H 2 ) } d y {\displaystyle \Rightarrow U'=\int _{R_{1}}\left\{\pi _{1}\cdot (U_{11}-U_{21})\cdot p(y|H1)-\pi _{2}\cdot (U_{22}-U_{12})\cdot p(y|H2)\right\}\,dy}
U ′ {\displaystyle U'} and thus U {\displaystyle U} are maximized by extending R 1 {\displaystyle R_{1}} over the region where
π 1 ⋅ ( U 11 − U 21 ) ⋅ p ( y | H 1 ) − π 2 ⋅ ( U 22 − U 12 ) ⋅ p ( y | H 2 ) > 0 {\displaystyle \pi _{1}\cdot (U_{11}-U_{21})\cdot p(y|H1)-\pi _{2}\cdot (U_{22}-U_{12})\cdot p(y|H2)>0}
This is accomplished by deciding H2 in case
π 2 ⋅ ( U 22 − U 12 ) ⋅ p ( y | H 2 ) ≥ π 1 ⋅ ( U 11 − U 21 ) ⋅ p ( y | H 1 ) {\displaystyle \pi _{2}\cdot (U_{22}-U_{12})\cdot p(y|H2)\geq \pi _{1}\cdot (U_{11}-U_{21})\cdot p(y|H1)}
⇒ L ( y ) ≡ p ( y | H 2 ) p ( y | H 1 ) ≥ π 1 ⋅ ( U 11 − U 21 ) π 2 ⋅ ( U 22 − U 12 ) ≡ τ B {\displaystyle \Rightarrow L(y)\equiv {\frac {p(y|H2)}{p(y|H1)}}\geq {\frac {\pi _{1}\cdot (U_{11}-U_{21})}{\pi _{2}\cdot (U_{22}-U_{12})}}\equiv \tau _{B}}
and H1 otherwise, where L(y) is the so-defined likelihood ratio.
See also[edit]
Binary classification
Constant false alarm rate
Decision theory
Demodulation
Detector (radio)
Estimation theory
Just-noticeable difference
Likelihood-ratio test
Modulation
Neyman–Pearson lemma
Psychometric function
Receiver operating characteristic
Statistical hypothesis testing
Statistical signal processing
Two-alternative forced choice
Type I and type II errors
References[edit]
Jump up ^ T. H. Wilmshurst (1990). Signal Recovery from Noise in Electronic Instrumentation (2nd ed.). CRC Press. pp. 11 ff. ISBN 0-7503-0058-2.
Jump up ^ Jafarpour, S.; Xu, W.; Hassibi, B.; Calderbank, R. (September 2009). "Efficient and Robust Compressed Sensing Using Optimized Expander Graphs". IEEE Transactions on Information Theory. 55 (9): 4299–4308. doi:10.1109/tit.2009.2025528. ISSN 0018-9448.
Jump up ^ Needell, D.; Tropp, J.A. "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples". Applied and Computational Harmonic Analysis. 26 (3): 301–321. doi:10.1016/j.acha.2008.07.002.
Jump up ^ Lotfi, M.; Vidyasagar, M."A Fast Noniterative Algorithm for Compressive Sensing Using Binary Measurement Matrices".
Jump up ^ Marcum, J. I. (1947). "A Statistical Theory of Target Detection by Pulsed Radar". The Research Memorandum: 90. Retrieved 2009-06-28.
Jump up ^ Peterson, W.W., Birdsall, T. G. & Fox, W. C. (1954) The theory of signal detectability. Proceedings of the IRE Professional Group on Information Theory 4, 171-212.
Jump up ^ Tanner Jr., Wilson P.; John A. Swets (November 1954). "A decision-making theory of visual detection". Psychological Review. 61 (6): 401–409. doi:10.1037/h0058700. PMID 13215690. Retrieved 2009-06-24.
Jump up ^ Swets, J.A. (ed.) (1964) Signal detection and recognition by human observers. New York: Wiley
^ Jump up to: a b Green, D.M., Swets J.A. (1966) Signal Detection Theory and Psychophysics. New York: Wiley. (ISBN 0-471-32420-5)
^ Jump up to: a b Stanislaw, H; Todorov, N (February 1999). "Calculation of signal detection theory measures". Behavior Research Methods, Instruments, and Computers. 31 (1): 137–49. PMID 10495845.
^ Jump up to: a b Schonhoff, T.A. and Giordano, A.A. (2006) Detection and Estimation Theory and Its Applications. New Jersey: Pearson Education (ISBN 0-13-089499-0)
This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (April 2009) (Learn how and when to remove this template message)
Coren, S., Ward, L.M., Enns, J. T. (1994) Sensation and Perception. (4th Ed.) Toronto: Harcourt Brace.
Kay, SM. Fundamentals of Statistical Signal Processing: Detection Theory (ISBN 0-13-504135-X)
McNichol, D. (1972) A Primer of Signal Detection Theory. London: George Allen & Unwin.
Van Trees HL. Detection, Estimation, and Modulation Theory, Part 1 (ISBN 0-471-09517-6; website)
Wickens, Thomas D., (2002) Elementary Signal Detection Theory. New York: Oxford University Press. (ISBN 0-19-509250-3)
External links[edit]
A Description of Signal Detection Theory
An application of SDT to safety
Signal Detection Theory by Garrett Neske, The Wolfram Demonstrations Project
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Mongol invasions of India
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Invasions of India
Part of the Mongol conquests, Mongol invasion of Central Asia
Date
1222–1225, 1235–1241, 1254–1255, 1257–1258, 1293–1298, 1299–1306, 1320, 1327
Location
North-Western South Asia and parts of Central Asia
Result
Mongol Empire conquers Indian borderlands but repelled from interior. Mongols continue raids throughout the 14th century.
Territorial
changes
Mongol Empire gains control of Central Asia, Kashmir, and exterior portions of Pakistan. Punjab and Sindh retain independence. Delhi Sultanate retains hold of Indian interior.
Belligerents
Mongol Empire
Mongol Empire
Khokhar
Mongol Empire
Ilkhanate
Qara'unas
Sindh
Chagatai Khanate
Qara'unas
Chagatai Khanate
Qara'unas
Qara'unas Punjab
Sindh
Kerman
Kashmir
Delhi Sultanate
Delhi Sultanate
Delhi Sultanate
Delhi Sultanate
Delhi Sultanate Khwarazmian dynasty
Ghor
Peshawar
Salt Range
Ghori
Turkmen
Commanders and leaders
Genghis Khan
Dorbei the Fierce
Bala
Turtai
Ögedei Khan
Dayir
Möngke Khan
Sali
Sham al-Din Muhammad Kart
Hulagu Khan
Sali Bahadur
Sali Noyan
Abdullah
Ulugh
Saldi
Qutlugh Khwaja
Kopek
Ali Beg
Tartaq
Abachi
Tarmashirin
Zulju Unknown
Unknown
Unknown
Zafar Khan
Alauddin Khalji
Zafar Khan
Ghazi Malik
Malik Kafur
Ulugh Khan
Muhammad bin Tughluq
Suhadeva
Ramacandra Jalal ad-Din Mingburnu
Kalich Khan
Uzbek Pai
Hassan Qarlugh
Genghis Khan
The Mongol Empire launched several invasions into the Indian subcontinent from 1221 to 1327, with many of the later raids made by the unruly Qaraunas of Mongol origin. The Mongols occupied parts of modern Pakistan and other parts of Punjab for decades. As the Mongols progressed into the Indian hinterland and reached the outskirts of Delhi, the Delhi Sultanate led a campaign against them in which the Mongol army suffered serious defeats.
Contents
1 Background
2 Mongol conquest of Kashmir and conflicts with the Delhi Sultanate
3 Chagatai Khanate vs. the Khaljis
4 Late Mongol invasions
5 Timur and Babur
6 See also
7 References
7.1 Bibliography
Background[edit]
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Mongol invasions of India
Indus
Lahore
Beas river
Punjab (1292)
Punjab (1297–98)
Sindh (1298–99)
Kili (1299)
Delhi (1303)
Amroha (1305)
Ravi (1306)
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India
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After pursuing Jalal ad-Din into India from Samarkand and defeating him at the battle of Indus in 1221, Genghis Khan sent two tumens (20,000 soldiers) under commanders Dorbei the Fierce and Bala to continue the chase. The Mongol commander Bala chased Jalal ad-Din throughout the Punjab region and attacked outlying towns like Bhera and Multan, and even sacked the outskirts of Lahore. Jalal ad-Din regrouped, forming a small army from survivors of the battle and sought an alliance, or even an asylum, with the Turkic rulers of Delhi Sultanate, but was turned down.
Jalal ad-Din fought against the local rulers in Punjab, after being defeated by many of them in the open, he retreated to the outskirts of Punjab seeking refuge in Multan.[citation needed]
While fighting against the local governor of Sindh, Jalal ad-Din heard of an uprising in the Kirman province of southern Iran and he immediately set out for that place, passing through southern Baluchistan on the way. Jalal ad-Din was also joined by forces from Ghor and Peshawar, including members of the Khalji, Turkoman, and Ghori tribes. With his new allies he marched on Ghazni and defeated a Mongol division under Turtai, which had been assigned the task of hunting him down. The victorious allies quarreled over the division of the captured booty; subsequently the Khalji, Turkoman, and Ghori tribesmen deserted Jalal ad-Din and returned to Peshawar. By this time Ögedei Khan, third son of Genghis Khan, had become Great Khan of the Mongol Empire. A Mongol general named Chormaqan sent by the Khan attacked and defeated Jalal ad-Din, thus ending the Khwārazm-Shāh dynasty.[1]
Mongol conquest of Kashmir and conflicts with the Delhi Sultanate[edit]
Some of this article's listed sources may not be reliable. Please help this article by looking for better, more reliable sources. Unreliable citations may be challenged or deleted. (August 2018) (Learn how and when to remove this template message)
Some time after 1235 another Mongol force invaded Kashmir, stationing a darughachi (administrative governor) there for several years, and Kashmir became a Mongolian dependency.[2] Around the same time, a Kashmiri Buddhist master, Otochi, and his brother Namo arrived at the court of Ögedei. Another Mongol general named Pakchak attacked Peshawar and defeated the army of tribes who had deserted Jalal ad-Din but were still a threat to the Mongols. These men, mostly Khaljis, escaped to Multan and were recruited into the army of the Delhi Sultanate. In winter 1241 the Mongol force invaded the Indus valley and besieged Lahore. However, on December 30, 1241, the Mongols under Munggetu butchered the town before withdrawing from the Delhi Sultanate. At the same time the Great Khan Ögedei died (1241).
The Kashmiris revolted in 1254–1255, and Möngke Khan, who became Great Khan in 1251, appointed his generals, Sali and Takudar, to replace the court and appointed the Buddhist master, Otochi, as darugachi of Kashmir. However, the Kashmiri king killed Otochi at Srinagar. Sali invaded Kashmir, killing the king, and put down the rebellion, after which the country remained subject to the Mongol Empire for many years.[3]
The Delhi prince, Jalal al-Din Masud, traveled to the Mongol capital at Karakorum to seek the assistance of Möngke Khan in seizing the throne from his elder brother in 1248. When Möngke was crowned as Great Khan, Jalal al-Din Masud attended the ceremony and asked for help from Möngke. Möngke ordered Sali to assist him to recover his ancestral realm. Sali made successive attacks on Multan and Lahore. Sham al-Din Muhammad Kart, the client malik (ruling prince) of Herat, accompanied the Mongols. Jalal al-Din was installed as client ruler of Lahore, Kujah and Sodra. In 1257 the governor of Sindh offered his entire province to Hulagu Khan, Mongke's brother, and sought Mongol protection from his overlord in Delhi. Hulagu led a strong force under Sali Bahadur into Sindh. In the winter of 1257 - beginning of 1258, Sali Noyan entered Sind in strength and dismantled the fortifications of Multan; his forces may also have invested the island fortress of Bakhkar on the Indus.
The Mongol Empire during the reign of Mongke Khan (r.1251-59)
But Hulagu refused to sanction a grand invasion of the Delhi Sultanate and a few years later diplomatic correspondence between the two rulers confirmed the growing desire for peace. Hulagu had many other areas of conquests to take care of in Syria and southwestern Asia. Large-scale Mongol invasions of India ceased and the Delhi Sultans used the respite to recover the frontier towns like Multan, Uch, and Lahore, and to punish the local Ranas and Rais who had joined hands with either the Khwarazim or the Mongol invaders.
Large numbers of tribes that took shelter in the Delhi Sultanate as a result of the Mongol invasions changed the balance of power in North India. The Khalji tribe usurped power from the older Delhi Sultans and began to rapidly project their power into other parts of India. At about this time the Mongol raids into India were also renewed (1300).
Chagatai Khanate vs. the Khaljis[edit]
The medieval sources claim invasions by hundreds of thousands of Mongols, numbers approximating (and probably based on) the size of the entire cavalry armies of the Mongol realms of Central Asia or the Middle East: about 150,000 men. A count of the Mongol commanders named in the sources as participating in the various invasions might give a better indication of the numbers involved, as these commanders probably led tumens, units nominally of 10,000 men.[4] These invasions were led by either various descendants of Genghis Khan or by Mongol divisional commanders; the size of such armies was always between 10,000-30,000 cavalry although the chroniclers of Delhi exaggerated the number to 100,000-200,000 cavalry.[5]
After civil war broke out in the Mongol Empire in the 1260s, the Chagatai Khanate controlled Central Asia and its leader since the 1280s was Duwa Khan who was second in command of Kaidu Khan. Duwa was active in Afghanistan, and attempted to extend Mongol rule into India. The Muslim Negudari governor Abdullah, who was a son of Chagatai Khan's great grandson,[6] invaded Punjab with his force in 1292, but their advance guard under Ulghu was defeated and taken prisoner by the Khalji Sultan Jalaluddin. The 4000 Mongol captives of the advance guard converted to Islam and came to live in Delhi as "new Muslims". The suburb they lived in was appropriately named Mughalpura.[7][8] Chagatai tumens were beaten by the Delhi Sultanate several times in 1296–1297.[9]
A 20th century artist's imagination of Alauddin Khalji (d. 1316), the ruler of Delhi.
Subsequently, the Mongols repeatedly invaded northern India during the reign of Jalaluddin's successor Alauddin; on at least two occasions, they came in strength. In the winter of 1297, the Chagatai noyan Kadar led an army that ravaged the Punjab region, and advanced as far as Kasur.[10] Alauddin's army, led by Ulugh Khan (and probably Zafar Khan), defeated the invaders on 6 February 1298.[10]
Later in 1298–99, a Mongol army (possibly Neguderi fugitives) invaded Sindh, and occupied the fort of Sivistan.[11] These Mongols were defeated by Zafar Khan: a number of them were arrested and brought to Delhi as captives.[12] At this time, the main branch of Alauddin's army, led by Ulugh Khan and Nusrat Khan was busy raiding Gujarat. When this army was returning from Gujarat to Delhi, some of its Mongol soldiers staged a mutiny over payment of khums (one-fifth of the share of loot).[13] The mutiny was crushed, and the mutineers families in Delhi were severely punished.[14]
In late 1299, Duwa dispatched his son Qutlugh Khwaja to conquer Delhi.[15] Alauddin led his army to Kili near Delhi, and tried to delay the battle, hoping that the Mongols would retreat amid a scarcity of provisions and that he would receive reinforcements from his provinces. However, his general Zafar Khan attacked the Mongol army without his permission.[16] The Mongols feigned a retreat, and tricked Zafar Khan's contingent into following them. Zafar Khan and his men were killed after inflicting heavy casualties on the invaders.[17] The Mongols retreated a couple of days later: their leader Qutlugh Khwaja was seriously wounded, and died during the return journey.[18]
In the winter of 1302–1303, Alauddin dispatched an army to ransack the Kakatiya capital Warangal, and himself marched to Chittor. Finding Delhi unprotected, the Mongols launched another invasion around August 1303.[19] Alauddin managed to reach Delhi before the invaders, but did not have enough time to prepare for a strong defence. He took shelter in a heavily-guarded camp at the under-construction Siri Fort. The Mongols ransacked Delhi and its neighbourhoods, but ultimately retreated after being unable to breach Siri.[20] This close encounter with the Mongols prompted Alauddin to strengthen the forts and the military presence along their routes to India.[21] He also implemented a series of economic reforms to ensure sufficient revenue inflows for maintaining a strong army.[22]
Shortly afterward, Duwa Khan sought to end the ongoing conflict with the Yuan Khagan Temür Öljeytü, and around 1304 a general peace among the Mongol khanates was declared, bringing an end to the conflict between the Yuan Dynasty and western khanates that had lasted for the better part of a half century. Soon after, he proposed a joint attack on India, but the campaign did not materialize.
In December 1305, Duwa sent another army that bypassed the heavily guarded city of Delhi, and proceeded south-east to the Gangetic plains along the Himalayan foothills. Alauddin's 30,000-strong cavalry, led by Malik Nayak, defeated the Mongols at the Battle of Amroha.[23][24] A large number of Mongols were taken captive and killed.[25]
In 1306, another Mongol army sent by Duwa advanced up to the Ravi River, ransacking the territories along the way. This army included three contingents, led by Kopek, Iqbalmand, and Tai-Bu. Alauddin's forces, led by Malik Kafur, decisively defeated the invaders.[26]
In that same year the Mongol Khan, Duwa, died and in the dispute over his succession this spate of Mongol raids into India ended. Taking advantage of this situation, Alauddin's general Malik Tughluq regularly raided the Mongol territories located in present-day Afghanistan.[27][28]
Late Mongol invasions[edit]
In 1320 the Qaraunas under Zulju (Dulucha) entered Kashmir by the Jehlam Valley without meeting any serious resistance. The Kashmiri king, Suhadeva, tried to persuade Zulju to withdraw by paying a large ransom.[29] After he failed to organize resistance, Suhadeva fled to Kishtwar, leaving the people of Kashmir to the mercy of Zulju. The Mongols burned the dwellings, massacred the men and made women and children slaves. Only refugees under Ramacandra, commander in chief of the king, in the fort of Lar remained safe. The invaders continued to pillage for eight months until the commencement of winter. When Zulju was departing via Brinal, he lost most of his men and prisoners due to a severe snowfall in Divasar district.
The next major Mongol invasion took place after the Khaljis had been replaced by the Tughlaq dynasty in the Sultanate. In 1327 the Chagatai Mongols under Tarmashirin, who had sent envoys to Delhi to negotiate peace the previous year, sacked the frontier towns of Lamghan and Multan and besieged Delhi. The Tughlaq ruler paid a large ransom to spare his Sultanate from further ravages. Muhammad bin Tughluq asked the Ilkhan Abu Sa'id to form an alliance against Tarmashirin, who had invaded Khorasan, but an attack didn't materialize.[30] Tarmashirin was a Buddhist who later converted to Islam. Religious tensions in the Chagatai Khanate were a divisive factor among the Mongols.
No more large-scale invasions or raids into India were launched after Tamashirin's siege of Delhi. However, small groups of Mongol adventurers hired out their swords to the many local powers in the northwest. Amir Qazaghan raided northern India with his Qara'unas. He also sent several thousand troops to aid the Delhi Sultan Muhammad bin Tughluq in suppressing the rebellion in his country in 1350.
Timur and Babur[edit]
See also: Timur and Mughal Empire
Timur
Timur defeats the Sultan of Delhi, Nasir Al-Din Mahmum Tughluq, in the winter of 1397–1398
Babur, the Turco-Mongol descendant of Timur, who later invaded India in the 16th century.
The Delhi sultans had developed cordial relations with the Yuan dynasty in Mongolia and China and the Ilkhanate in Persia and the Middle East. Around 1338, Sultan Muhammad bin Tughluq of the Delhi Sultanate appointed Moroccan traveler Ibn Battuta an ambassador to the Yuan court under Toghon Temür (Emperor Huizong). The gifts he was to take included 200 slaves.
The Chagatai Khanate had split up by this time and an ambitious Mongol Turk chieftain named Timur had brought Central Asia and the regions beyond under his control. He followed the twin policies of Imperialism and Islamization, shifting various Mongol tribes to different parts of his empire and giving primacy to the Turkic people in his own army. Timur also reinforced the Islamic faith over the Chagatai Khanate and gave primacy to the laws of the Shari'ah over Genghis Khan's shamanist laws. He invaded India in 1398 to make war and plunder the wealth of the country.
Timur's empire broke up and his descendants failed to hold on to Central Asia, which split up into numerous principalities. The descendants of the Mongol Chagtais and the descendants of Timur empire lived side by side, occasionally fighting and occasionally inter-marrying.
One of the products of such a marriage was Babur, founder of the Mughal Empire[31]. His mother belonged to the family of the Mongol Khans of Tashkent. Babur was a true descendant of Timur and shared his beliefs: he believed that rules and regulations of Genghis Khan were deficient as he remarked, "they had no divine authority."
Even though his own mother was a Mongol, Babur was not very fond of the Mongol race and wrote a stinging verse in his autobiography:
"Were the Mughals an angel race, it would be bad,
Even write in gold, the Mughal name would be bad."
When Babur occupied Kabul and began invading the Indian subcontinent, he was called a Mughal like all the earlier invaders from the Chagatai Khanate. Even the invasion of Timur had been considered a Mongol invasion since the Mongols had ruled over Central Asia for so long and had given their name to its people.
See also[edit]
India-Mongolia relations
References[edit]
Jump up ^ Chormaqan Noyan: The First Mongol Military Governor in the Middle East by Timothy May
Jump up ^ Thomas T. Allsen-Culture and Conquest in Mongol Eurasia, p.84
Jump up ^ André Wink-Al-Hind, the Making of the Indo-Islamic World, p.208
Jump up ^ John Masson Smith, Jr. Mongol Armies and Indian Campaigns.
Jump up ^ John Masson Smith, Jr. Mongol Armies and Indian Campaigns and J.A. Boyle, The Mongol Commanders in Afghanistan and India.
Jump up ^ Rashid ad-Din - The history of World
Jump up ^ Dr. A. Zahoor (21 May 2002). "Muslims in the Indian Subcontinent" (PDF). pp. 58–59. Retrieved 2015-08-20.
Jump up ^ J.A. Boyle, "The Mongol Commanders in Afghanistan and India According to the Tabaqat-I-Nasiri of Juzjani," Islamic Studies, II (1963); reprinted in idem, The Mongol World Empire (London: Variorum, 1977), see ch. IX, p. 239
Jump up ^ Although Muslim historians claimed Mongols were outnumbered and their army ranged from 100,000 to 200,000, their force was not enough to cow down Delhi mamluks in reality. See John Masson Smith, Jr. Mongol Armies and Indian Campaigns.
^ Jump up to: a b Banarsi Prasad Saksena 1992, p. 332.
Jump up ^ Peter Jackson 2003, pp. 219-220.
Jump up ^ Banarsi Prasad Saksena 1992, p. 336.
Jump up ^ Kishori Saran Lal 1950, p. 87.
Jump up ^ Kishori Saran Lal 1950, p. 88.
Jump up ^ Banarsi Prasad Saksena 1992, p. 338.
Jump up ^ Banarsi Prasad Saksena 1992, p. 340.
Jump up ^ Banarsi Prasad Saksena 1992, p. 341.
Jump up ^ Peter Jackson 2003, pp. 221-222.
Jump up ^ Banarsi Prasad Saksena 1992, p. 368.
Jump up ^ Banarsi Prasad Saksena 1992, pp. 369-370.
Jump up ^ Banarsi Prasad Saksena 1992, p. 372.
Jump up ^ Banarsi Prasad Saksena 1992, p. 373.
Jump up ^ Banarsi Prasad Saksena 1992, pp. 392-393.
Jump up ^ Peter Jackson 2003, pp. 227-228.
Jump up ^ Banarsi Prasad Saksena 1992, p. 393.
Jump up ^ Kishori Saran Lal 1950, pp. 171-172.
Jump up ^ Kishori Saran Lal 1950, p. 175.
Jump up ^ Peter Jackson 2003, p. 229.
Jump up ^ Mohibbul Hasan-Kashmir Under the Sultans, p.36
Jump up ^ The Chaghadaids and Islam: the conversion of Tarmashirin Khan (1331-34). The Journal of the American Oriental Society, October 1, 2002. Biran
Jump up ^ "BĀBOR, ẒAHĪR-AL-DĪN MOḤAMMAD – Encyclopaedia Iranica". www.iranicaonline.org. Retrieved 2018-01-30.
Bibliography[edit]
Banarsi Prasad Saksena (1992). "The Khaljis: Alauddin Khalji". In Mohammad Habib and Khaliq Ahmad Nizami. A Comprehensive History of India: The Delhi Sultanat (A.D. 1206-1526). 5 (Second ed.). The Indian History Congress / People's Publishing House. OCLC 31870180.
Chormaqan Noyan: The First Mongol Military Governor in the Middle East by Timothy May [1]
Harold Lamb, Genghis Khan: Emperor of All Men. ISBN 0-88411-798-7
J.A. Boyle, "The Mongol Commanders in Afghanistan and India According to the Tabaqat-i-Nasiri of Juzjani." Central Asiatic Journal 9 (1964): 235-247. Reprinted in The Mongol World Empire, 1206–1370, edited by John A. Boyle, Variorum Reprints, 1977.
John Masson Smith, Jr. - MONGOL ARMIES AND INDIAN CAMPAIGNS, University of California, Berkeley [2]
Kishori Saran Lal (1950). History of the Khaljis (1290-1320). Allahabad: The Indian Press. OCLC 685167335.
Peter Jackson (2003). The Delhi Sultanate: A Political and Military History. Cambridge University Press. ISBN 978-0-521-54329-3.
René Grousset (1970). The Empire of the Steppes: A History of Central Asia. Rutgers University Press. ISBN 978-0-8135-1304-1.
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